Edexcel IAL Mathematics Study Plans
Comprehensive 3-month and 5-month study plans for all Edexcel IAL Mathematics subjects
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Math With Fahim
Edexcel IAL Pure Mathematics 1 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 1
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 11 chapters of Pure Mathematics 1. The plan is structured to build foundational knowledge in the first month, develop problem-solving skills in the second month, and focus on exam preparation in the final month. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Algebraic Expressions
1.1 Index Laws
1.2 Expanding Brackets
1.3 Factorising
1.4 Negative and Fractional Indices
1.5 Surds
1.6 Rationalising Denominators
Key Points
Laws of indices: am × an = a(m+n), (am)n = amn, a0 = 1
Expanding brackets: FOIL method, binomial expansion
Factorising: common factors, difference of squares, quadratics
Negative indices: a-n = 1an
Fractional indices: a1/n = n√a, am/n = (n√a)m
Surds: √(ab) = √a × √b, rationalising denominators
Practice
Complete 25-30 practice questions from textbook exercises
Focus on: Index law applications (8 questions), Expanding brackets (6 questions), Factorising (8 questions), Surds (8 questions)
Question types: Basic calculations, simplification, algebraic manipulation
Review Chapter Review 1 questions
Create formula sheet for index laws and surd rules
Week 2
|
of 12
Topics
Chapter 2: Quadratics
2.1 Solving Quadratic Equations
2.2 Completing the Square
2.3 Functions
2.4 Quadratic Graphs
2.5 The Discriminant
Key Points
Quadratic formula: x = -b ± √(b2 - 4ac)2a
Completing the square: ax2 + bx + c = a(x + b2a)2 + (c - b24a)
Discriminant: Δ = b2 - 4ac (Δ > 0: two roots, Δ = 0: one root, Δ < 0: no real roots)
Quadratic graphs: vertex, axis of symmetry, y-intercept
Function notation: f(x), domain, range
Practice
Complete 30-35 practice questions
Focus on: Solving quadratics (10 questions), Completing square (8 questions), Discriminant (7 questions), Graphs (10 questions)
Question types: Factorisation, formula method, completing square, graph sketching, word problems
Review Chapter Review 2 questions
Practice sketching quadratic graphs with transformations
Week 3
|
of 12
Topics
Chapter 3: Equations and Inequalities
3.1 Linear Simultaneous Equations
3.2 Quadratic Simultaneous Equations
3.3 Simultaneous Equations on Graphs
3.4 Linear Inequalities
3.5 Quadratic Inequalities
3.6 Inequalities on Graphs
Key Points
Solving simultaneous equations: substitution, elimination
Linear inequalities: direction changes when multiplying/dividing by negative
Quadratic inequalities: use sign diagram or graph
Graphical interpretation of solutions
Practice
Complete 25-30 practice questions
Focus on: Simultaneous equations (12 questions), Linear inequalities (6 questions), Quadratic inequalities (7 questions), Graph interpretation (5 questions)
Question types: Algebraic solving, graphical methods, word problems
Review Chapter Review 3 questions
Week 4
|
of 12
Topics
Chapter 4: Graphs and Transformations
4.1 Cubic Graphs
4.2 Reciprocal Graphs
4.3 Points of Intersection
4.4 Translating Graphs
4.5 Stretching Graphs
Chapter 5: Straight Line Graphs
5.1 y = mx + c
5.2 Equations of Straight Lines
5.3 Parallel and Perpendicular Lines
5.4 Length and Area
Key Points
Graph transformations: f(x+a), f(x)+a, f(ax), af(x)
Straight line: y = mx + c, gradient = y2 - y1x2 - x1
Parallel lines: m1 = m2
Perpendicular lines: m1 × m2 = -1
Distance formula: √[(x2 - x1)2 + (y2 - y1)2]
Practice
Complete 30-35 practice questions
Focus on: Graph transformations (12 questions), Straight lines (10 questions), Parallel/perpendicular (8 questions), Length/area (5 questions)
Question types: Graph sketching, transformation descriptions, coordinate geometry
Review Chapter Reviews 4 & 5
Week 5
|
of 12
Topics
Chapter 6: Trigonometric Ratios
6.1 The Cosine Rule
6.2 The Sine Rule
6.3 Areas of Triangles
6.4 Solving Triangle Problems
6.5 Graphs of Sine, Cosine and Tangent
Key Points
Sine rule: a/sin A = b/sin B = c/sin C
Cosine rule: a² = b² + c² - 2bc cos A
Area: ½ab sin C
Trig graphs: period, amplitude, transformations
Practice
Complete 30-35 practice questions
Focus on: Sine/cosine rules (15 questions), Area calculations (8 questions), Graph sketching (7 questions)
Question types: Triangle solving, ambiguous case, graph transformations
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-6 topics)
Review Chapter Review 6
Week 6
|
of 12
Topics
Chapter 7: Radians
7.1 Radian Measure
7.2 Arc Length
7.3 Areas of Sectors and Segments
Chapter 8: Differentiation
8.1 Gradients of Curves
8.2 Finding the Derivative
8.3 Differentiating xn
8.4 Differentiating Quadratics
8.5 Differentiating Functions with Two or More Terms
8.6 Gradients, Tangents and Normals
8.7 Second Order Derivatives
Key Points
Radians: 180° = π radians, arc length = rθ, area = ½r²θ
Differentiation: d/dx(xn) = nxn-1
Gradient of tangent = derivative at point
Normal: perpendicular to tangent, mnormal = -1/mtangent
Second derivative: d2y/dx2
Practice
Complete 35-40 practice questions
Focus on: Radians (10 questions), Differentiation basics (15 questions), Tangents/normals (10 questions)
Question types: Differentiation, gradient finding, equation of tangents/normals
PAST PAPERS: Solve 15-18 individual questions from past papers (mixed topics)
Review Chapter Reviews 7 & 8
Week 7
|
of 12
Topics
Chapter 9: Integration
9.1 Integrating xn
9.2 Indefinite Integrals
9.3 Finding Functions
Key Points
Integration: ∫xn dx = xn+1n+1 + C (n ≠ -1)
Indefinite integrals: include constant of integration
Finding functions: use given conditions to find C
Practice
Complete 25-30 practice questions
Focus on: Basic integration (15 questions), Finding functions (10 questions), Mixed problems (5 questions)
Question types: Integration, reverse differentiation, application problems
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 9
Week 8
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-9
Identify weak areas
Strengthen problem-solving skills
Key Focus Areas
Review all formulas and key concepts
Practice mixed topic questions
Work on time management
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 9
|
of 12
Topics
Weak Areas Focus
Target specific weak topics identified
Additional practice on challenging areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Focus on time management and exam technique
Review solutions thoroughly
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 5, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 1 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 1
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 9 chapters of Pure Mathematics 1 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 8 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Algebraic Expressions
1.1 Index Laws
1.2 Expanding Brackets
1.3 Factorising
Key Points
Laws of indices: am × an = a(m+n), (am)n = amn, a0 = 1
Expanding brackets: FOIL method, binomial expansion
Factorising: common factors, difference of squares
Practice
Complete 20-25 practice questions from textbook exercises
Focus on: Index law applications (8 questions), Expanding brackets (6 questions), Factorising (8 questions)
Question types: Basic calculations, simplification, algebraic manipulation
Create formula sheet for index laws
Week 2
|
of 20
Topics
Chapter 1: Algebraic Expressions (Continued)
1.4 Negative and Fractional Indices
1.5 Surds
1.6 Rationalising Denominators
Key Points
Negative indices: a-n = 1an
Fractional indices: a1/n = n√a, am/n = (n√a)m
Surds: √(ab) = √a × √b, rationalising denominators
Practice
Complete 20-25 practice questions
Focus on: Negative/fractional indices (8 questions), Surds (10 questions), Rationalising (7 questions)
Question types: Simplification, rationalisation, mixed index problems
Review Chapter Review 1 questions
Week 3
|
of 20
Topics
Chapter 2: Quadratics
2.1 Solving Quadratic Equations
2.2 Completing the Square
2.3 Functions
Key Points
Quadratic formula: x = -b ± √(b2 - 4ac)2a
Completing the square: ax2 + bx + c = a(x + b2a)2 + (c - b24a)
Function notation: f(x), domain, range
Practice
Complete 25-30 practice questions
Focus on: Solving quadratics (12 questions), Completing square (10 questions), Functions (8 questions)
Question types: Factorisation, formula method, completing square, function evaluation
Week 4
|
of 20
Topics
Chapter 2: Quadratics (Continued)
2.4 Quadratic Graphs
2.5 The Discriminant
Key Points
Discriminant: Δ = b2 - 4ac (Δ > 0: two roots, Δ = 0: one root, Δ < 0: no real roots)
Quadratic graphs: vertex, axis of symmetry, y-intercept
Practice
Complete 20-25 practice questions
Focus on: Discriminant (10 questions), Graph sketching (10 questions), Mixed problems (5 questions)
Question types: Graph sketching, discriminant analysis, word problems
Review Chapter Review 2 questions
Week 5
|
of 20
Topics
Chapter 3: Equations and Inequalities
3.1 Linear Simultaneous Equations
3.2 Quadratic Simultaneous Equations
3.3 Simultaneous Equations on Graphs
Key Points
Solving simultaneous equations: substitution, elimination
Graphical interpretation of solutions
Practice
Complete 20-25 practice questions
Focus on: Linear simultaneous (8 questions), Quadratic simultaneous (10 questions), Graph interpretation (7 questions)
Question types: Algebraic solving, graphical methods
Week 6
|
of 20
Topics
Chapter 3: Equations and Inequalities (Continued)
3.4 Linear Inequalities
3.5 Quadratic Inequalities
3.6 Inequalities on Graphs
Key Points
Linear inequalities: direction changes when multiplying/dividing by negative
Quadratic inequalities: use sign diagram or graph
Practice
Complete 20-25 practice questions
Focus on: Linear inequalities (8 questions), Quadratic inequalities (12 questions), Graph interpretation (5 questions)
Question types: Solving inequalities, sign diagrams, graphical representation
Review Chapter Review 3 questions
Week 7
|
of 20
Topics
Chapter 4: Graphs and Transformations
4.1 Cubic Graphs
4.2 Reciprocal Graphs
4.3 Points of Intersection
4.4 Translating Graphs
4.5 Stretching Graphs
Key Points
Graph transformations: f(x+a), f(x)+a, f(ax), af(x)
Practice
Complete 25-30 practice questions
Focus on: Graph sketching (12 questions), Transformations (10 questions), Intersections (8 questions)
Question types: Graph sketching, transformation descriptions
Review Chapter Review 4
Week 8
of 20
Topics Covered
- Chapter 5: Straight Line Graphs 5.1 y = mx + c | 5.2 Equations of Straight Lines | 5.3 Parallel and Perpendicular Lines | 5.4 Length and Area
Key Points to Learn
- Straight line: y = mx + c, gradient = (y₂-y₁)/(x₂-x₁)
- Parallel lines: m₁ = m₂
- Perpendicular lines: m₁ × m₂ = -1
- Distance formula: √[(x₂-x₁)² + (y₂-y₁)²]
Actions & Practice
- Complete 25-30 practice questions
- Focus on: Straight lines (10 questions), Parallel/perpendicular (10 questions), Length/area (10 questions)
- Question types: Coordinate geometry, equation finding, distance/area calculations
- START PAST PAPER PRACTICE: Solve 8-10 individual questions from past papers (Chapters 1-5 topics)
- Review Chapter Review 5
Week 9
of 20
Topics Covered
- Chapter 6: Trigonometric Ratios 6.1 The Cosine Rule | 6.2 The Sine Rule | 6.3 Areas of Triangles
Key Points to Learn
- Sine rule: a/sin A = b/sin B = c/sin C
- Cosine rule: a² = b² + c² - 2bc cos A
- Area: ½ab sin C
Actions & Practice
- Complete 25-30 practice questions
- Focus on: Sine/cosine rules (15 questions), Area calculations (10 questions)
- Question types: Triangle solving, ambiguous case
- PAST PAPERS: Solve 12-15 individual questions from past papers
Week 10
of 20
Topics Covered
- Chapter 6: Trigonometric Ratios (Continued) 6.4 Solving Triangle Problems | 6.5 Graphs of Sine, Cosine and Tangent
Key Points to Learn
- Trig graphs: period, amplitude, transformations
Actions & Practice
- Complete 20-25 practice questions
- Focus on: Triangle problems (10 questions), Graph sketching (10 questions), Mixed (5 questions)
- Question types: Complex triangle problems, graph transformations
- PAST PAPERS: Solve 15-18 individual questions from past papers
- Review Chapter Review 6
Week 11
of 20
Topics Covered
- Chapter 7: Radians 7.1 Radian Measure | 7.2 Arc Length | 7.3 Areas of Sectors and Segments
Key Points to Learn
- Radians: 180° = π radians, arc length = rθ, area = ½r²θ
Actions & Practice
- Complete 20-25 practice questions
- Focus on: Radian conversion (8 questions), Arc length (8 questions), Sector/segment area (9 questions)
- Question types: Conversion, arc length, area calculations
- PAST PAPERS: Solve 18-20 individual questions from past papers
- Review Chapter Review 7
Week 12
of 20
Topics Covered
- Chapter 8: Differentiation 8.1 Gradients of Curves | 8.2 Finding the Derivative | 8.3 Differentiating x^n | 8.4 Differentiating Quadratics
Key Points to Learn
- Differentiation: d/dx(x^n) = nx^(n-1)
Actions & Practice
- Complete 25-30 practice questions
- Focus on: Basic differentiation (20 questions), Gradient finding (10 questions)
- Question types: Differentiation, gradient calculations
- PAST PAPERS: Solve 20-25 individual questions from past papers
Week 13
of 20
Topics Covered
- Chapter 8: Differentiation (Continued) 8.5 Differentiating Functions with Two or More Terms | 8.6 Gradients, Tangents and Normals | 8.7 Second Order Derivatives
Key Points to Learn
- Gradient of tangent = derivative at point
- Normal: perpendicular to tangent, m_normal = -1/m_tangent
- Second derivative: d²y/dx²
Actions & Practice
- Complete 25-30 practice questions
- Focus on: Multiple terms (10 questions), Tangents/normals (12 questions), Second derivatives (8 questions)
- Question types: Differentiation, equation of tangents/normals
- PAST PAPERS: Solve 25-30 individual questions from past papers
- Review Chapter Review 8
Week 14
of 20
Topics Covered
- Chapter 9: Integration 9.1 Integrating x^n | 9.2 Indefinite Integrals | 9.3 Finding Functions
Key Points to Learn
- Integration: ∫x^n dx = x^(n+1)/(n+1) + C (n ≠ -1)
- Indefinite integrals: include constant of integration
- Finding functions: use given conditions to find C
Actions & Practice
- Complete 25-30 practice questions
- Focus on: Basic integration (15 questions), Finding functions (10 questions), Mixed problems (5 questions)
- Question types: Integration, reverse differentiation, application problems
- PAST PAPERS: Solve 30-35 individual questions from past papers
- Review Chapter Review 9
Week 15
of 20
Revision & Consolidation
- Comprehensive Review
• Review all chapters 1-9• Identify weak areas• Strengthen problem-solving skills
Key Focus Areas
- Review all formulas and key concepts
- Practice mixed topic questions
- Work on time management
Actions & Practice
- Complete 35-45 mixed practice questions
- PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
- Mark your work using mark schemes
- Create error log of common mistakes
Week 16
of 20
Exam Preparation
- Full Past Paper Practice
• Complete full papers under exam conditions
Actions & Practice
- PAST PAPERS: Complete 1 full past paper (timed - 1.5 hours)
- Focus on time management and exam technique
- Mark strictly using mark schemes
- Review examiner reports
Week 17
of 20
Weak Areas Focus
- Targeted Practice
• Target specific weak topics identified• Additional practice on challenging areas
Actions & Practice
- Complete 30-40 targeted practice questions on weak areas
- PAST PAPERS: Complete 1 full past paper (timed)
- Review solutions thoroughly
Week 18
of 20
Intensive Exam Practice
Actions & Practice
- PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
- Mark strictly using mark schemes
- Analyze mistakes and patterns
- Review examiner reports
Week 19
of 20
Intensive Exam Practice
Actions & Practice
- PAST PAPERS: Complete 2 full past papers (timed)
- Focus on recent papers (last 3-5 years)
- Time yourself strictly
- Review all incorrect answers
Week 20
of 20
Final Preparation
Actions & Practice
- PAST PAPERS: Complete 1 full past paper (timed)
- Final review of all formulas
- Review error log
- Light practice on weak areas
- Mental preparation and exam strategy
- Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 8, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 2 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 2
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 8 chapters of Pure Mathematics 2. The plan builds on P1 knowledge, focusing on advanced algebraic methods, coordinate geometry, exponentials/logarithms, sequences, trigonometry, and calculus. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Algebraic Methods
1.1 Algebraic Fractions
1.2 Dividing Polynomials
1.3 The Factor Theorem
1.4 The Remainder Theorem
1.5 Mathematical Proof
1.6 Methods of Proof
Key Points
Algebraic fractions: addition, subtraction, multiplication, division
Polynomial division: long division, synthetic division
Factor theorem: if f(a) = 0, then (x-a) is a factor
Remainder theorem: remainder when dividing by (x-a) is f(a)
Proof methods: direct proof, proof by contradiction, proof by exhaustion
Practice
Complete 30-35 practice questions from textbook exercises
Focus on: Algebraic fractions (10 questions), Polynomial division (8 questions), Factor/Remainder theorems (10 questions), Proof (7 questions)
Question types: Simplification, division, factor finding, proof writing
Review Chapter Review 1 questions
Create formula sheet for factor and remainder theorems
Week 2
|
of 12
Topics
Chapter 2: Coordinate Geometry in the Plane
2.1 Midpoints and Perpendicular Bisectors
2.2 Equation of a Circle
2.3 Intersections of Straight Lines and Circles
2.4 Use Tangent and Chord Properties
2.5 Circles and Triangles
Key Points
Midpoint: x1 + x22, y1 + y22
Circle equation: (x-a)2 + (y-b)2 = r2, center (a,b), radius r
Perpendicular bisector: line through midpoint, perpendicular to chord
Tangent properties: perpendicular to radius at point of contact
Intersection: substitute line equation into circle equation
Practice
Complete 30-35 practice questions
Focus on: Circle equations (12 questions), Intersections (10 questions), Tangents (8 questions), Mixed problems (5 questions)
Question types: Finding equations, intersection points, tangent problems, geometric proofs
Review Chapter Review 2 questions
Week 3
|
of 12
Topics
Chapter 3: Exponentials and Logarithms
3.1 Exponential Functions
3.2 Logarithms
3.3 Laws of Logarithms
3.4 Solving Equations Using Logarithms
3.5 Changing the Base of a Logarithm
Key Points
Exponential: y = ax, graph properties
Logarithm: loga(x) = y means ay = x
Laws: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), log(an) = n log(a)
Change of base: loga(x) = logb(x)logb(a)
Solving: take logs of both sides, use laws to simplify
Practice
Complete 30-35 practice questions
Focus on: Exponential functions (8 questions), Logarithm laws (12 questions), Solving equations (10 questions), Change of base (5 questions)
Question types: Simplification, equation solving, graph sketching, applications
Review Chapter Review 3 questions
Week 4
|
of 12
Topics
Chapter 4: The Binomial Expansion
4.1 Pascal's Triangle
4.2 Factorial Notation
4.3 The Binomial Expansion
4.4 Solving Binomial Problems
4.5 Binomial Estimation
Key Points
Factorial: n! = n × (n-1) × ... × 2 × 1
Binomial coefficient: nCr = n!r!(n-r)!
Binomial expansion: (a+b)n = Σ(nCr) an-r br
For (1+x)n: valid when |x| < 1
Estimation: use first few terms for approximations
Practice
Complete 25-30 practice questions
Focus on: Binomial expansion (15 questions), Finding coefficients (8 questions), Estimation (7 questions)
Question types: Expansion, coefficient finding, approximation, validity
Review Chapter Review 4 questions
Week 5
|
of 12
Topics
Chapter 5: Sequences and Series
5.1 Arithmetic Sequences
5.2 Arithmetic Series
5.3 Geometric Sequences
5.4 Geometric Series
5.5 Sum to Infinity
5.6 Sigma Notation
5.7 Recurrence Relations
5.8 Modelling with Series
Key Points
Arithmetic: un = a + (n-1)d, Sn = n2[2a + (n-1)d]
Geometric: un = arn-1, Sn = a(1-rn)1-r
Sum to infinity: S∞ = a1-r when |r| < 1
Sigma notation: Σ notation for sums
Recurrence: un+1 = f(un)
Practice
Complete 30-35 practice questions
Focus on: Arithmetic (10 questions), Geometric (12 questions), Sum to infinity (8 questions), Sigma notation (5 questions)
Question types: Finding terms, sums, convergence, modelling
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-5 topics)
Review Chapter Review 5
Week 6
|
of 12
Topics
Chapter 6: Trigonometric Identities and Equations
6.1 Angles in All Four Quadrants
6.2 Exact Values of Trigonometrical Ratios
6.3 Trigonometric Identities
6.4 Solve Simple Trigonometric Equations
6.5 Harder Trigonometric Equations
6.6 Equations and Identities
Key Points
CAST diagram: signs in each quadrant
Exact values: sin/cos/tan of 0°, 30°, 45°, 60°, 90°
Identities: sin2θ + cos2θ = 1, tanθ = sinθcosθ
Solving equations: find all solutions in given range
Use identities to simplify before solving
Practice
Complete 30-35 practice questions
Focus on: Identities (12 questions), Simple equations (10 questions), Harder equations (13 questions)
Question types: Identity proofs, equation solving, exact values
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 6
Week 7
|
of 12
Topics
Chapter 7: Differentiation
7.1 Increasing and Decreasing Functions
7.2 Stationary Points
7.3 Sketching Gradient Functions
7.4 Modelling with Differentiation
Key Points
Increasing: f'(x) > 0, Decreasing: f'(x) < 0
Stationary points: f'(x) = 0
Max/min: use second derivative or sign of f'(x)
Gradient function: sketch derivative from original function
Practice
Complete 25-30 practice questions
Focus on: Increasing/decreasing (8 questions), Stationary points (12 questions), Gradient functions (10 questions)
Question types: Finding intervals, optimization, graph sketching
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 7
Week 8
|
of 12
Topics
Chapter 8: Integration
8.1 Definite Integrals
8.2 Areas Under Curves
8.3 Areas Under the x-axis
8.4 Areas Between Curves and Lines
8.5 Areas Between Two Curves
8.6 The Trapezium Rule
Key Points
Definite integral: ∫ab f(x) dx = F(b) - F(a)
Area under curve: ∫ab f(x) dx (positive area)
Below x-axis: take absolute value or subtract
Between curves: ∫ab (f(x) - g(x)) dx
Trapezium rule: approximate area using trapeziums
Practice
Complete 30-35 practice questions
Focus on: Definite integrals (10 questions), Areas under curves (12 questions), Between curves (8 questions), Trapezium rule (5 questions)
Question types: Integration, area calculations, numerical methods
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Review Chapter Review 8
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Key Focus Areas
Review all formulas and key concepts
Practice mixed topic questions
Work on time management
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 5, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 2 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 2
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 8 chapters of Pure Mathematics 2 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Algebraic Methods (Part 1)
1.1 Algebraic Fractions
1.2 Dividing Polynomials
1.3 The Factor Theorem
Key Points
Algebraic fractions: addition, subtraction, multiplication, division
Polynomial division: long division, synthetic division
Factor theorem: if f(a) = 0, then (x-a) is a factor
Practice
Complete 25-30 practice questions
Focus on: Algebraic fractions (10 questions), Polynomial division (8 questions), Factor theorem (7 questions)
Question types: Simplification, division, factor finding
Week 2
|
of 20
Topics
Chapter 1: Algebraic Methods (Part 2)
1.4 The Remainder Theorem
1.5 Mathematical Proof
1.6 Methods of Proof
Key Points
Remainder theorem: remainder when dividing by (x-a) is f(a)
Proof methods: direct proof, proof by contradiction, proof by exhaustion
Practice
Complete 25-30 practice questions
Focus on: Remainder theorem (8 questions), Proof writing (12 questions)
Question types: Finding remainders, proof writing
Review Chapter Review 1
Week 3
|
of 20
Topics
Chapter 2: Coordinate Geometry in the Plane (Part 1)
2.1 Midpoints and Perpendicular Bisectors
2.2 Equation of a Circle
2.3 Intersections of Straight Lines and Circles
Key Points
Midpoint: x1 + x22, y1 + y22
Circle equation: (x-a)2 + (y-b)2 = r2
Intersection: substitute line equation into circle equation
Practice
Complete 25-30 practice questions
Focus on: Circle equations (12 questions), Intersections (10 questions), Midpoints (8 questions)
Question types: Finding equations, intersection points
Week 4
|
of 20
Topics
Chapter 2: Coordinate Geometry in the Plane (Part 2)
2.4 Use Tangent and Chord Properties
2.5 Circles and Triangles
Key Points
Tangent properties: perpendicular to radius at point of contact
Chord properties: perpendicular bisector passes through center
Geometric problems involving circles and triangles
Practice
Complete 25-30 practice questions
Focus on: Tangents (12 questions), Geometric problems (13 questions)
Question types: Tangent problems, geometric proofs
Review Chapter Review 2
Week 5
|
of 20
Topics
Chapter 3: Exponentials and Logarithms (Part 1)
3.1 Exponential Functions
3.2 Logarithms
3.3 Laws of Logarithms
Key Points
Exponential: y = ax, graph properties
Logarithm: loga(x) = y means ay = x
Laws: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), log(an) = n log(a)
Practice
Complete 25-30 practice questions
Focus on: Exponential functions (8 questions), Logarithm laws (12 questions), Simplification (10 questions)
Question types: Simplification, graph sketching
Week 6
|
of 20
Topics
Chapter 3: Exponentials and Logarithms (Part 2)
3.4 Solving Equations Using Logarithms
3.5 Changing the Base of a Logarithm
Key Points
Solving: take logs of both sides, use laws to simplify
Change of base: loga(x) = logb(x)logb(a)
Practice
Complete 25-30 practice questions
Focus on: Solving equations (15 questions), Change of base (10 questions), Applications (5 questions)
Question types: Equation solving, applications
Review Chapter Review 3
Week 7
|
of 20
Topics
Chapter 4: The Binomial Expansion
4.1 Pascal's Triangle
4.2 Factorial Notation
4.3 The Binomial Expansion
4.4 Solving Binomial Problems
4.5 Binomial Estimation
Key Points
Factorial: n! = n × (n-1) × ... × 2 × 1
Binomial coefficient: nCr = n!r!(n-r)!
Binomial expansion: (a+b)n = Σ(nCr) an-r br
For (1+x)n: valid when |x| < 1
Practice
Complete 30-35 practice questions
Focus on: Binomial expansion (15 questions), Finding coefficients (8 questions), Estimation (7 questions)
Question types: Expansion, coefficient finding, approximation
Review Chapter Review 4
Week 8
|
of 20
Topics
Chapter 5: Sequences and Series (Part 1)
5.1 Arithmetic Sequences
5.2 Arithmetic Series
5.3 Geometric Sequences
5.4 Geometric Series
Key Points
Arithmetic: un = a + (n-1)d, Sn = n2[2a + (n-1)d]
Geometric: un = arn-1, Sn = a(1-rn)1-r
Practice
Complete 30-35 practice questions
Focus on: Arithmetic (10 questions), Geometric (12 questions), Mixed problems (8 questions)
Question types: Finding terms, sums
Week 9
|
of 20
Topics
Chapter 5: Sequences and Series (Part 2)
5.5 Sum to Infinity
5.6 Sigma Notation
5.7 Recurrence Relations
5.8 Modelling with Series
Key Points
Sum to infinity: S∞ = a1-r when |r| < 1
Sigma notation: Σ notation for sums
Recurrence: un+1 = f(un)
Practice
Complete 30-35 practice questions
Focus on: Sum to infinity (10 questions), Sigma notation (8 questions), Recurrence (7 questions), Modelling (10 questions)
Question types: Convergence, sigma notation, modelling
Review Chapter Review 5
Week 10
|
of 20
Topics
Chapter 6: Trigonometric Identities and Equations
6.1 Angles in All Four Quadrants
6.2 Exact Values of Trigonometrical Ratios
6.3 Trigonometric Identities
6.4 Solve Simple Trigonometric Equations
6.5 Harder Trigonometric Equations
6.6 Equations and Identities
Key Points
CAST diagram: signs in each quadrant
Exact values: sin/cos/tan of 0°, 30°, 45°, 60°, 90°
Identities: sin2θ + cos2θ = 1, tanθ = sinθcosθ
Solving equations: find all solutions in given range
Practice
Complete 30-35 practice questions
Focus on: Identities (12 questions), Simple equations (10 questions), Harder equations (13 questions)
Question types: Identity proofs, equation solving, exact values
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Review Chapter Review 6
Week 11
|
of 20
Topics
Chapter 7: Differentiation (Part 1)
7.1 Increasing and Decreasing Functions
7.2 Stationary Points
7.3 Sketching Gradient Functions
Key Points
Increasing: f'(x) > 0, Decreasing: f'(x) < 0
Stationary points: f'(x) = 0
Max/min: use second derivative or sign of f'(x)
Gradient function: sketch derivative from original function
Practice
Complete 25-30 practice questions
Focus on: Increasing/decreasing (8 questions), Stationary points (12 questions), Gradient functions (10 questions)
Question types: Finding intervals, optimization, graph sketching
Week 12
|
of 20
Topics
Chapter 7: Differentiation (Part 2)
7.4 Modelling with Differentiation
Key Points
Optimization problems: set up function, find stationary points
Real-world applications: maximize/minimize quantities
Practice
Complete 25-30 practice questions
Focus on: Optimization problems (20 questions), Modelling (10 questions)
Question types: Optimization, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 7
Week 13
|
of 20
Topics
Chapter 8: Integration (Part 1)
8.1 Definite Integrals
8.2 Areas Under Curves
8.3 Areas Under the x-axis
8.4 Areas Between Curves and Lines
Key Points
Definite integral: ∫ab f(x) dx = F(b) - F(a)
Area under curve: ∫ab f(x) dx (positive area)
Below x-axis: take absolute value or subtract
Between curves: ∫ab (f(x) - g(x)) dx
Practice
Complete 30-35 practice questions
Focus on: Definite integrals (10 questions), Areas under curves (12 questions), Between curves (8 questions)
Question types: Integration, area calculations
Week 14
|
of 20
Topics
Chapter 8: Integration (Part 2)
8.5 Areas Between Two Curves
8.6 The Trapezium Rule
Key Points
Between two curves: ∫ab (f(x) - g(x)) dx
Trapezium rule: approximate area using trapeziums
Practice
Complete 30-35 practice questions
Focus on: Between curves (15 questions), Trapezium rule (10 questions), Mixed problems (10 questions)
Question types: Area calculations, numerical methods
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 8
Week 15
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 16
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 1 full past paper (timed - 1.5 hours)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Week 17
|
of 20
Exam Preparation
Full Past Paper Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 1 full past paper (timed - 1.5 hours)
Mark strictly, analyze mistakes
Practice presentation and working clearly
Week 18
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Week 19
|
of 20
Intensive Exam Practice
Continue intensive practice
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Focus on difficult question types
Practice time management
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 1 full past paper (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 3 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 3
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 8 chapters of Pure Mathematics 3. The plan builds on P1 and P2 knowledge, focusing on advanced functions, trigonometric identities, exponentials/logarithms, advanced calculus, and numerical methods. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Algebraic Methods
1.1 Arithmetic Operations with Algebraic Fractions
1.2 Improper Fractions
Chapter 2: Functions and Graphs
2.1 The Modulus Function
2.2 Functions and Mappings
2.3 Composite Functions
Key Points
Modulus: |x| = x if x ≥ 0, |x| = -x if x < 0
Composite functions: fg(x) = f(g(x))
Domain and range of composite functions
Practice
Complete 30-35 practice questions
Focus on: Algebraic fractions (10 questions), Modulus (12 questions), Composite functions (13 questions)
Question types: Simplification, solving modulus equations, function composition
Review Chapter Reviews 1 & 2
Week 2
|
of 12
Topics
Chapter 2: Functions and Graphs (Continued)
2.4 Inverse Functions
2.5 y = |f(x)| and y = f(|x|)
2.6 Combining Transformations
2.7 Solving Modulus Problems
Key Points
Inverse functions: f-1(f(x)) = x, domain/range swap
Modulus transformations: |f(x)| reflects negative parts, f(|x|) reflects left side
Combined transformations: order matters
Practice
Complete 30-35 practice questions
Focus on: Inverse functions (10 questions), Modulus transformations (12 questions), Combined transformations (13 questions)
Question types: Finding inverses, graph sketching, transformation descriptions
Week 3
|
of 12
Topics
Chapter 3: Trigonometric Functions
3.1 Secant, Cosecant and Cotangent
3.2 Graphs of sec x, cosec x and cot x
3.3 Using sec x, cosec x and cot x
3.4 Trigonometric Identities
3.5 Inverse Trigonometric Functions
Key Points
sec x = 1cos x, cosec x = 1sin x, cot x = 1tan x
Graphs: asymptotes, period, domain restrictions
Inverse trig functions: domain restrictions, principal values
Practice
Complete 30-35 practice questions
Focus on: Reciprocal functions (12 questions), Graphs (10 questions), Identities (8 questions), Inverse functions (5 questions)
Question types: Simplification, graph sketching, equation solving
Review Chapter Review 3
Week 4
|
of 12
Topics
Chapter 4: Trigonometric Addition Formulae
4.1 Addition Formulae
4.2 Using the Angle Addition Formulae
4.3 Double-Angle Formulae
4.4 Solving Trigonometric Equations
4.5 Simplifying a cos x ± b sin x
4.6 Proving Trigonometric Identities
Key Points
sin(A±B) = sin A cos B ± cos A sin B
cos(A±B) = cos A cos B ∓ sin A sin B
Double angle: sin 2A = 2 sin A cos A, cos 2A = cos2A - sin2A
R-formula: a cos x + b sin x = R cos(x - α)
Practice
Complete 35-40 practice questions
Focus on: Addition formulae (12 questions), Double angle (10 questions), R-formula (10 questions), Identity proofs (8 questions)
Question types: Simplification, equation solving, identity proofs
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Review Chapter Review 4
Week 5
|
of 12
Topics
Chapter 5: Exponentials and Logarithms
5.1 Exponential Functions
5.2 y = eax+b + c
5.3 Natural Logarithms
5.4 Logarithms and Non-Linear Data
5.5 Exponential Modelling
Key Points
Natural logarithm: ln x = loge x
Exponential transformations: eax+b + c
Linearizing data: log transformations
Practice
Complete 30-35 practice questions
Focus on: Exponential functions (10 questions), Natural logs (12 questions), Transformations (8 questions), Modelling (5 questions)
Question types: Function evaluation, equation solving, graph transformations, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 5
Week 6
|
of 12
Topics
Chapter 6: Differentiation
6.1 Differentiating sin x and cos x
6.2 Differentiating Exponentials and Logarithms
6.3 The Chain Rule
6.4 The Product Rule
6.5 The Quotient Rule
6.6 Differentiating Trigonometric Functions
Key Points
d/dx(sin x) = cos x, d/dx(cos x) = -sin x
d/dx(ex) = ex, d/dx(ln x) = 1x
Chain rule: d/dx(f(g(x))) = f'(g(x)) × g'(x)
Product rule: d/dx(uv) = u'v + uv'
Quotient rule: d/dx(u/v) = u'v - uv'v2
Practice
Complete 35-40 practice questions
Focus on: Chain rule (12 questions), Product rule (10 questions), Quotient rule (10 questions), Trig differentiation (8 questions)
Question types: Differentiation, composite functions, optimization
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 7
|
of 12
Topics
Chapter 7: Integration
7.1 Integrating Standard Functions
7.2 Integrating f(ax + b)
7.3 Using Trigonometric Identities
7.4 Reverse Chain Rule
Key Points
∫sin x dx = -cos x + C, ∫cos x dx = sin x + C
∫ex dx = ex + C, ∫1x dx = ln|x| + C
Reverse chain rule: recognize derivative patterns
Use identities to simplify before integrating
Practice
Complete 30-35 practice questions
Focus on: Standard integrals (10 questions), f(ax+b) (10 questions), Trig identities (8 questions), Reverse chain rule (7 questions)
Question types: Integration, area calculations, applications
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7
Week 8
|
of 12
Topics
Chapter 8: Numerical Methods
8.1 Locating Roots
8.2 Fixed Point Iteration
Key Points
Change of sign: if f(a) and f(b) have opposite signs, root exists between a and b
Fixed point iteration: xn+1 = g(xn)
Convergence: |g'(x)| < 1 near root
Practice
Complete 20-25 practice questions
Focus on: Root location (12 questions), Iteration (13 questions)
Question types: Interval finding, iteration calculations, convergence analysis
PAST PAPERS: Attempt 1 full past paper (untimed)
Review Chapter Review 8
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 3 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 3
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 8 chapters of Pure Mathematics 3 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Algebraic Methods
1.1 Arithmetic Operations with Algebraic Fractions
1.2 Improper Fractions
Chapter 2: Functions and Graphs (Part 1)
2.1 The Modulus Function
2.2 Functions and Mappings
2.3 Composite Functions
Key Points
Modulus: |x| = x if x ≥ 0, |x| = -x if x < 0
Composite functions: fg(x) = f(g(x))
Domain and range of composite functions
Practice
Complete 25-30 practice questions
Focus on: Algebraic fractions (8 questions), Modulus (10 questions), Composite functions (7 questions)
Question types: Simplification, solving modulus equations, function composition
Week 2
|
of 20
Topics
Chapter 2: Functions and Graphs (Part 2)
2.4 Inverse Functions
2.5 y = |f(x)| and y = f(|x|)
2.6 Combining Transformations
2.7 Solving Modulus Problems
Key Points
Inverse functions: f-1(f(x)) = x, domain/range swap
Modulus transformations: |f(x)| reflects negative parts, f(|x|) reflects left side
Combined transformations: order matters
Practice
Complete 25-30 practice questions
Focus on: Inverse functions (10 questions), Modulus transformations (10 questions), Combined transformations (10 questions)
Question types: Finding inverses, graph sketching, transformation descriptions
Review Chapter Reviews 1 & 2
Week 3
|
of 20
Topics
Chapter 3: Trigonometric Functions (Part 1)
3.1 Secant, Cosecant and Cotangent
3.2 Graphs of sec x, cosec x and cot x
3.3 Using sec x, cosec x and cot x
Key Points
sec x = 1cos x, cosec x = 1sin x, cot x = 1tan x
Graphs: asymptotes, period, domain restrictions
Practice
Complete 25-30 practice questions
Focus on: Reciprocal functions (12 questions), Graphs (10 questions), Using functions (8 questions)
Question types: Simplification, graph sketching
Week 4
|
of 20
Topics
Chapter 3: Trigonometric Functions (Part 2)
3.4 Trigonometric Identities
3.5 Inverse Trigonometric Functions
Key Points
Trigonometric identities involving sec, cosec, cot
Inverse trig functions: domain restrictions, principal values
Practice
Complete 25-30 practice questions
Focus on: Identities (12 questions), Inverse functions (10 questions), Mixed problems (8 questions)
Question types: Identity proofs, inverse function evaluation
Review Chapter Review 3
Week 5
|
of 20
Topics
Chapter 4: Trigonometric Addition Formulae (Part 1)
4.1 Addition Formulae
4.2 Using the Angle Addition Formulae
4.3 Double-Angle Formulae
Key Points
sin(A±B) = sin A cos B ± cos A sin B
cos(A±B) = cos A cos B ∓ sin A sin B
Double angle: sin 2A = 2 sin A cos A, cos 2A = cos2A - sin2A
Practice
Complete 30-35 practice questions
Focus on: Addition formulae (12 questions), Double angle (10 questions), Applications (8 questions)
Question types: Simplification, equation solving
Week 6
|
of 20
Topics
Chapter 4: Trigonometric Addition Formulae (Part 2)
4.4 Solving Trigonometric Equations
4.5 Simplifying a cos x ± b sin x
4.6 Proving Trigonometric Identities
Key Points
R-formula: a cos x + b sin x = R cos(x - α)
Use identities to simplify before solving
Identity proofs: start with one side, manipulate to get other side
Practice
Complete 30-35 practice questions
Focus on: R-formula (10 questions), Equation solving (12 questions), Identity proofs (8 questions)
Question types: Equation solving, identity proofs
Review Chapter Review 4
Week 7
|
of 20
Topics
Chapter 4: Review and Consolidation
Review all addition formulae topics
Mixed practice on all Chapter 4 concepts
Key Points
Review all formulae and identities
Practice applying formulae in different contexts
Practice
Complete 30-35 mixed practice questions
Focus on: Mixed problems covering all Chapter 4 topics
Question types: All types from Chapter 4
Week 8
|
of 20
Topics
Chapter 5: Exponentials and Logarithms (Part 1)
5.1 Exponential Functions
5.2 y = eax+b + c
5.3 Natural Logarithms
Key Points
Natural logarithm: ln x = loge x
Exponential transformations: eax+b + c
Properties of ex and ln x
Practice
Complete 25-30 practice questions
Focus on: Exponential functions (10 questions), Natural logs (12 questions), Transformations (8 questions)
Question types: Function evaluation, graph transformations
Week 9
|
of 20
Topics
Chapter 5: Exponentials and Logarithms (Part 2)
5.4 Logarithms and Non-Linear Data
5.5 Exponential Modelling
Key Points
Linearizing data: log transformations
Exponential modelling: y = aebx or y = abx
Applications in real-world problems
Practice
Complete 25-30 practice questions
Focus on: Linearizing data (10 questions), Modelling (15 questions)
Question types: Data analysis, modelling, applications
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Review Chapter Review 5
Week 10
|
of 20
Topics
Chapter 6: Differentiation (Part 1)
6.1 Differentiating sin x and cos x
6.2 Differentiating Exponentials and Logarithms
6.3 The Chain Rule
Key Points
d/dx(sin x) = cos x, d/dx(cos x) = -sin x
d/dx(ex) = ex, d/dx(ln x) = 1x
Chain rule: d/dx(f(g(x))) = f'(g(x)) × g'(x)
Practice
Complete 30-35 practice questions
Focus on: Trig differentiation (10 questions), Exponential/log differentiation (10 questions), Chain rule (12 questions)
Question types: Differentiation, composite functions
PAST PAPERS: Solve 15-18 individual questions from past papers
Week 11
|
of 20
Topics
Chapter 6: Differentiation (Part 2)
6.4 The Product Rule
6.5 The Quotient Rule
Key Points
Product rule: d/dx(uv) = u'v + uv'
Quotient rule: d/dx(u/v) = u'v - uv'v2
Practice
Complete 30-35 practice questions
Focus on: Product rule (15 questions), Quotient rule (15 questions)
Question types: Differentiation using product and quotient rules
PAST PAPERS: Solve 18-20 individual questions from past papers
Week 12
|
of 20
Topics
Chapter 6: Differentiation (Part 3)
6.6 Differentiating Trigonometric Functions
Key Points
Differentiating all trigonometric functions using chain/product/quotient rules
Combining rules for complex functions
Practice
Complete 30-35 practice questions
Focus on: Trig differentiation (20 questions), Mixed problems (15 questions)
Question types: All differentiation types, optimization
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 13
|
of 20
Topics
Chapter 7: Integration (Part 1)
7.1 Integrating Standard Functions
7.2 Integrating f(ax + b)
7.3 Using Trigonometric Identities
Key Points
∫sin x dx = -cos x + C, ∫cos x dx = sin x + C
∫ex dx = ex + C, ∫1x dx = ln|x| + C
Use identities to simplify before integrating
Practice
Complete 30-35 practice questions
Focus on: Standard integrals (10 questions), f(ax+b) (10 questions), Trig identities (8 questions)
Question types: Integration, area calculations
PAST PAPERS: Solve 25-30 individual questions from past papers
Week 14
|
of 20
Topics
Chapter 7: Integration (Part 2)
7.4 Reverse Chain Rule
Chapter 8: Numerical Methods
8.1 Locating Roots
8.2 Fixed Point Iteration
Key Points
Reverse chain rule: recognize derivative patterns
Change of sign: if f(a) and f(b) have opposite signs, root exists between a and b
Fixed point iteration: xn+1 = g(xn)
Convergence: |g'(x)| < 1 near root
Practice
Complete 30-35 practice questions
Focus on: Reverse chain rule (12 questions), Root location (10 questions), Iteration (13 questions)
Question types: Integration, interval finding, iteration calculations
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Review Chapter Reviews 7 & 8
Week 15
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 16
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 1 full past paper (timed - 1.5 hours)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Week 17
|
of 20
Exam Preparation
Full Past Paper Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 1 full past paper (timed - 1.5 hours)
Mark strictly, analyze mistakes
Practice presentation and working clearly
Week 18
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Week 19
|
of 20
Intensive Exam Practice
Continue intensive practice
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Focus on difficult question types
Practice time management
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 1 full past paper (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 9, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 4 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 4
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 7 chapters of Pure Mathematics 4. The plan builds on P1, P2, and P3 knowledge, focusing on proof, partial fractions, parametric equations, advanced binomial expansion, parametric/implicit differentiation, advanced integration, and vectors. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Proof
1.1 Proof by Contradiction
Chapter 2: Partial Fractions
2.1 Partial Fractions
2.2 Repeated Factors
2.3 Improper Fractions
Key Points
Proof by contradiction: assume opposite, show contradiction
Partial fractions: decompose rational functions
Repeated factors: (ax+b)2 requires Aax+b + B(ax+b)2
Practice
Complete 30-35 practice questions
Focus on: Proof by contradiction (8 questions), Partial fractions (15 questions), Repeated factors (7 questions), Improper fractions (5 questions)
Question types: Proof writing, decomposition, integration preparation
Review Chapter Reviews 1 & 2
Week 2
|
of 12
Topics
Chapter 3: Coordinate Geometry in the (x,y) Plane
3.1 Parametric Equations
3.2 Using Trigonometric Identities
3.3 Curve Sketching
Key Points
Parametric: x = f(t), y = g(t)
Eliminate parameter to get Cartesian equation
Use trig identities for parametric curves
Practice
Complete 30-35 practice questions
Focus on: Parametric equations (15 questions), Eliminating parameters (10 questions), Curve sketching (10 questions)
Question types: Converting forms, sketching, finding intersections
Review Chapter Review 3
Week 3
|
of 12
Topics
Chapter 4: Binomial Expansion
4.1 Expanding (1+x)n
4.2 Expanding (a+bx)n
4.3 Using Partial Fractions
Key Points
Binomial expansion for any n (not just positive integers)
Validity: |x| < 1 for (1+x)n
Combine with partial fractions for complex expansions
Practice
Complete 25-30 practice questions
Focus on: General binomial (12 questions), Validity (8 questions), Partial fractions (10 questions)
Question types: Expansion, coefficient finding, approximation
Review Chapter Review 4
Week 4
|
of 12
Topics
Chapter 5: Differentiation
5.1 Parametric Differentiation
5.2 Implicit Differentiation
5.3 Rates of Change
Key Points
Parametric: dydx = dy/dtdx/dt
Implicit: differentiate both sides, collect dy/dx terms
Rates of change: chain rule applications
Practice
Complete 30-35 practice questions
Focus on: Parametric differentiation (12 questions), Implicit (15 questions), Rates of change (8 questions)
Question types: Finding gradients, tangents, related rates
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Review Chapter Review 5
Week 5
|
of 12
Topics
Chapter 6: Integration (Part 1)
6.1 Finding the Area Under a Curve Defined Parametrically
6.2 Volumes of Revolution Around the x-axis
6.3 Integration by Substitution
6.4 Integration by Parts
Key Points
Parametric area: ∫ y (dx/dt) dt
Volume: V = π ∫ y2 dx
Substitution: u = g(x), du = g'(x) dx
Integration by parts: ∫ u dv = uv - ∫ v du
Practice
Complete 35-40 practice questions
Focus on: Parametric areas (8 questions), Volumes (10 questions), Substitution (12 questions), By parts (10 questions)
Question types: Area/volume calculations, integration techniques
PAST PAPERS: Solve 15-20 individual questions from past papers
Week 6
|
of 12
Topics
Chapter 6: Integration (Part 2)
6.5 Partial Fractions
6.6 Solving Differential Equations
6.7 Modelling with Differential Equations
Key Points
Use partial fractions for integration
Differential equations: separate variables, integrate
Modelling: set up DEs from real-world problems
Practice
Complete 30-35 practice questions
Focus on: Partial fractions (10 questions), Differential equations (15 questions), Modelling (10 questions)
Question types: Integration using partial fractions, solving DEs, applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 7
|
of 12
Topics
Chapter 7: Vectors (Part 1)
7.1 Vectors
7.2 Representing Vectors
7.3 Magnitude and Direction
7.4 Vectors in 3D
7.5 Solving Geometric Problems in 2D
7.6 Solving Geometric Problems in 3D
Key Points
Vector notation, magnitude, direction, unit vectors
3D vectors, position vectors
Geometric problems: parallel, perpendicular, intersections
Practice
Complete 35-40 practice questions
Focus on: Vector operations (15 questions), 3D geometry (15 questions), Geometric problems (10 questions)
Question types: Vector calculations, geometric applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Week 8
|
of 12
Topics
Chapter 7: Vectors (Part 2)
7.7 Position Vectors
7.8 3D Coordinates
7.9 Equation of a Line in 3D
7.10 Points of Intersection
7.11 Scalar Product
Key Points
Position vectors: r = xi + yj + zk
Line equations: r = a + λb
Scalar product: a·b = |a||b|cos θ, a·b = a1b1 + a2b2 + a3b3
Finding intersections and angles between lines
Practice
Complete 35-40 practice questions
Focus on: Line equations (15 questions), Scalar product (15 questions), Intersections (10 questions)
Question types: Line equations, intersections, angles
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Review Chapter Review 7
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Pure Mathematics 4 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Pure Mathematics 4
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 7 chapters of Pure Mathematics 4 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Proof
1.1 Proof by Contradiction
Key Points
Proof by contradiction: assume the opposite of what you want to prove
Show that this assumption leads to a logical contradiction
Conclude that the original statement must be true
Common applications: proving irrationality, uniqueness, non-existence
Practice
Complete 20-25 practice questions
Focus on: Proof by contradiction (20-25 questions)
Question types: Proving irrationality, uniqueness, non-existence, logical contradictions
Review Chapter Review 1 questions
Study worked examples carefully to understand proof structure
Week 2
|
of 20
Topics
Chapter 2: Partial Fractions (Part 1)
2.1 Partial Fractions
2.2 Repeated Factors
Key Points
Partial fractions: decompose rational functions into simpler fractions
For distinct linear factors: Ax-a + Bx-b
For repeated factors: Ax-a + B(x-a)2
For quadratic factors: Ax+Bx2+px+q
Practice
Complete 30-35 practice questions
Focus on: Basic partial fractions (12 questions), Repeated factors (10 questions), Mixed problems (8 questions)
Question types: Decomposition, finding constants
Week 3
|
of 20
Topics
Chapter 2: Partial Fractions (Part 2)
2.3 Improper Fractions
Key Points
Improper fractions: degree of numerator ≥ degree of denominator
Use polynomial division first for improper fractions
Practice
Complete 30-35 practice questions
Focus on: Improper fractions (15 questions), Mixed problems (15 questions)
Question types: Polynomial division, decomposition, integration preparation
Review Chapter Review 2 questions
Practice setting up equations and solving for constants
Week 4
|
of 20
Topics
Chapter 3: Coordinate Geometry in the (x,y) Plane (Part 1)
3.1 Parametric Equations
3.2 Using Trigonometric Identities
Key Points
Parametric equations: x = f(t), y = g(t)
Eliminate parameter: solve for t in one equation, substitute into other
Use trigonometric identities: sin2t + cos2t = 1, tan t = sin tcos t
Practice
Complete 30-35 practice questions
Focus on: Converting parametric to Cartesian (12 questions), Using trig identities (10 questions), Mixed problems (8 questions)
Question types: Parameter elimination, curve analysis
Week 5
|
of 20
Topics
Chapter 3: Coordinate Geometry in the (x,y) Plane (Part 2)
3.3 Curve Sketching
Key Points
Curve sketching: find key points, asymptotes, domain restrictions
Domain of parameter: restrictions on t values
Practice
Complete 30-35 practice questions
Focus on: Curve sketching (15 questions), Finding intersections (10 questions), Mixed problems (10 questions)
Question types: Curve analysis, coordinate geometry
Review Chapter Review 3 questions
Practice sketching curves from parametric equations
Week 6
|
of 20
Topics
Chapter 4: Binomial Expansion (Part 1)
4.1 Expanding (1+x)n
4.2 Expanding (a+bx)n
Key Points
Binomial expansion for any real n: (1+x)n = 1 + nx + n(n-1)2!x2 + ...
Validity: |x| < 1 for (1+x)n
For (a+bx)n: factor out an first: an(1 + bxa)n
Practice
Complete 30-35 practice questions
Focus on: General binomial expansion (15 questions), Validity conditions (8 questions), Coefficient finding (7 questions)
Question types: Expansion, approximation, coefficient calculations
Week 7
|
of 20
Topics
Chapter 4: Binomial Expansion (Part 2)
4.3 Using Partial Fractions
Key Points
Combine with partial fractions: decompose first, then expand each term
Finding coefficients: use general term formula
Practice
Complete 30-35 practice questions
Focus on: Partial fractions combination (15 questions), Mixed problems (15 questions)
Question types: Expansion with partial fractions, approximation
Review Chapter Review 4 questions
Practice checking validity conditions carefully
Week 8
|
of 20
Topics
Chapter 5: Differentiation (Part 1)
5.1 Parametric Differentiation
5.2 Implicit Differentiation
Key Points
Parametric differentiation: dydx = dy/dtdx/dt
Second derivative: d2ydx2 = ddx(dydx) = d/dt(dy/dx)dx/dt
Implicit differentiation: differentiate both sides with respect to x
Chain rule: d/dx(f(y)) = f'(y) × dydx
Practice
Complete 30-35 practice questions
Focus on: Parametric differentiation (12 questions), Implicit differentiation (15 questions), Mixed problems (8 questions)
Question types: Finding gradients, tangents, normals
Week 9
|
of 20
Topics
Chapter 5: Differentiation (Part 2)
5.3 Rates of Change
Key Points
Rates of change: related rates problems using chain rule
Practice
Complete 30-35 practice questions
Focus on: Rates of change (20 questions), Mixed problems (15 questions)
Question types: Related rates, applications
Review Chapter Review 5 questions
Practice setting up related rates problems
Week 10
|
of 20
Topics
Chapter 6: Integration (Part 1)
6.1 Finding the Area Under a Curve Defined Parametrically
6.2 Volumes of Revolution Around the x-axis
6.3 Integration by Substitution
Key Points
Parametric area: A = ∫ y (dx/dt) dt (with appropriate limits)
Volume of revolution: V = π ∫ y2 dx
Integration by substitution: u = g(x), du = g'(x) dx
Practice
Complete 35-40 practice questions
Focus on: Parametric areas (8 questions), Volumes (10 questions), Substitution (12 questions), Mixed problems (10 questions)
Question types: Area/volume calculations, integration techniques
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Week 11
|
of 20
Topics
Chapter 6: Integration (Part 2)
6.4 Integration by Parts
6.5 Partial Fractions
Key Points
Integration by parts: ∫ u dv = uv - ∫ v du (LIATE rule for choosing u)
Partial fractions: decompose then integrate each term
Practice
Complete 35-40 practice questions
Focus on: By parts (10 questions), Partial fractions (8 questions), Mixed problems (12 questions)
Question types: Integration techniques, mixed problems
PAST PAPERS: Solve 12-15 individual questions from past papers
Week 12
|
of 20
Topics
Chapter 6: Integration (Part 3)
6.6 Solving Differential Equations
6.7 Modelling with Differential Equations
Key Points
Differential equations: separate variables, integrate both sides
Initial conditions: use to find constant of integration
Modelling: set up DEs from real-world problems
Practice
Complete 35-40 practice questions
Focus on: Differential equations (15 questions), Modelling (15 questions), Mixed problems (10 questions)
Question types: Solving DEs, modeling, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 6 questions
Week 13
|
of 20
Topics
Chapter 7: Vectors (Part 1)
7.1 Vectors
7.2 Representing Vectors
7.3 Magnitude and Direction
7.4 Vectors in 3D
7.5 Solving Geometric Problems in 2D
7.6 Solving Geometric Problems in 3D
Key Points
Vector notation: column vectors, i, j, k notation
Magnitude: |a| = √(a12 + a22 + a32)
Unit vector: â = a|a|
Position vectors: vector from origin to point
Practice
Complete 35-40 practice questions
Focus on: Vector operations (12 questions), 3D geometry (15 questions), Geometric problems (13 questions)
Question types: Vector calculations, geometric applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Week 14
|
of 20
Topics
Chapter 7: Vectors (Part 2)
7.7 Position Vectors
7.8 3D Coordinates
7.9 Equation of a Line in 3D
Key Points
Line in 3D: r = a + λb (vector form)
Position vectors: r = xi + yj + zk
Practice
Complete 35-40 practice questions
Focus on: Line equations (15 questions), 3D coordinates (12 questions), Mixed problems (13 questions)
Question types: Line equations, coordinate geometry
PAST PAPERS: Solve 18-20 individual questions from past papers
Week 15
|
of 20
Topics
Chapter 7: Vectors (Part 3)
7.10 Points of Intersection
7.11 Scalar Product
Key Points
Scalar product: a·b = |a||b|cos θ = a1b1 + a2b2 + a3b3
Parallel vectors: b = ka for some scalar k
Perpendicular vectors: a·b = 0
Angle between vectors: cos θ = a·b|a||b|
Practice
Complete 35-40 practice questions
Focus on: Scalar product (15 questions), Intersections (12 questions), Mixed problems (13 questions)
Question types: Intersections, angles, distances
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Review Chapter Review 7 questions
Week 16
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 17
|
of 20
Weak Areas Focus
Targeted Practice
Target specific weak topics identified
Additional practice on challenging areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Focus on time management and exam technique
Review solutions thoroughly
Week 18
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Statistics 1 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Statistics 1
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 7 chapters of Statistics 1. The plan builds statistical thinking, data analysis skills, and probability concepts. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Mathematical Modelling
1.1 Mathematical Models
1.2 Designing a Model
Chapter 2: Measures of Location and Spread
2.1 Types of Data
2.2 Measures of Central Tendency
2.3 Other Measures of Location
Key Points
Mathematical models: simplifying real-world situations
Types of data: qualitative, quantitative, discrete, continuous
Mean: x̄ = Σxn
Median: middle value when data is ordered
Mode: most frequent value
Quartiles: Q1, Q2 (median), Q3
Practice
Complete 25-30 practice questions
Focus on: Data types (5 questions), Mean/median/mode (12 questions), Quartiles (8 questions), Modelling (5 questions)
Question types: Calculations, data classification, interpretation
Review Chapter Reviews 1 & 2
Create formula sheet for measures of location
Week 2
|
of 12
Topics
Chapter 2: Measures of Location and Spread (continued)
2.4 Measures of Spread
2.5 Variance and Standard Deviation
2.6 Coding
Key Points
Range: max - min
Interquartile range: IQR = Q3 - Q1
Variance: σ2 = Σ(x - x̄)2n or s2 = Σ(x - x̄)2n-1
Standard deviation: σ = √variance
Coding: y = ax + b, affects mean and standard deviation
Practice
Complete 30-35 practice questions
Focus on: Variance/standard deviation (15 questions), IQR (8 questions), Coding (12 questions)
Question types: Calculations, transformations, interpretation
Review Chapter Review 2
Practice using calculator functions for statistics
Week 3
|
of 12
Topics
Chapter 3: Representations of Data
3.1 Histograms
3.2 Outliers
3.3 Box Plots
3.4 Stem and Leaf Diagrams
3.5 Skewness
3.6 Comparing Data
Key Points
Histograms: frequency density = frequencyclass width
Outliers: values beyond Q1 - 1.5×IQR or Q3 + 1.5×IQR
Box plots: show quartiles, median, outliers
Skewness: positive (right), negative (left), symmetric
Comparing distributions: shape, location, spread
Practice
Complete 30-35 practice questions
Focus on: Histograms (10 questions), Box plots (10 questions), Skewness (8 questions), Comparing data (7 questions)
Question types: Drawing diagrams, interpretation, calculations
Review Chapter Review 3
Practice drawing accurate diagrams
Week 4
|
of 12
Topics
Chapter 4: Probability
4.1 Understanding the Vocabulary Used in Probability
4.2 Venn Diagrams
4.3 Mutually Exclusive and Independent Events
4.4 Set Notation
4.5 Conditional Probability
Key Points
Probability: P(A) = number of favorable outcomestotal outcomes
Mutually exclusive: P(A ∩ B) = 0
Independent: P(A ∩ B) = P(A) × P(B)
Conditional: P(A|B) = P(A ∩ B)P(B)
Set notation: ∪ (union), ∩ (intersection), A' (complement)
Practice
Complete 30-35 practice questions
Focus on: Basic probability (10 questions), Venn diagrams (10 questions), Conditional probability (10 questions), Set notation (5 questions)
Question types: Calculations, diagram drawing, word problems
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 4
Week 5
|
of 12
Topics
Chapter 4: Probability (continued)
4.6 Conditional Probabilities in Venn Diagrams
4.7 Probability Formulae
4.8 Tree Diagrams
Chapter 5: Correlation and Regression
5.1 Scatter Diagrams
5.2 Linear Regression
Key Points
Addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Tree diagrams: multiply along branches, add for different paths
Scatter diagrams: show relationship between two variables
Regression line: y = a + bx (least squares)
Practice
Complete 30-35 practice questions
Focus on: Tree diagrams (12 questions), Probability formulae (10 questions), Scatter diagrams (8 questions), Regression (5 questions)
Question types: Diagram drawing, calculations, interpretation
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Reviews 4 & 5
Week 6
|
of 12
Topics
Chapter 5: Correlation and Regression (continued)
5.3 Calculating Least Squares Linear Regression
5.4 The Product Moment Correlation Coefficient
Chapter 6: Discrete Random Variables
6.1 Discrete Random Variables
6.2 Finding the Cumulative Distribution Function
Key Points
PMCC: r = Sxy√(Sxx × Syy), where -1 ≤ r ≤ 1
Regression: b = SxySxx, a = ȳ - bx̄
Discrete random variable: takes countable values
Probability distribution: P(X = x) for all x
CDF: F(x) = P(X ≤ x)
Practice
Complete 30-35 practice questions
Focus on: PMCC calculations (12 questions), Regression (10 questions), Discrete RVs (8 questions), CDF (5 questions)
Question types: Calculations, interpretations, probability distributions
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Reviews 5 & 6
Week 7
|
of 12
Topics
Chapter 6: Discrete Random Variables (continued)
6.3 Expected Value of a Discrete Random Variable
6.4 Variance of a Discrete Random Variable
6.5 Expected Value and Variance of a Function of X
6.6 Solving Problems Involving Random Variables
6.7 Using Discrete Uniform Distribution
Key Points
E(X) = ΣxP(X=x)
Var(X) = E(X2) - [E(X)]2 = Σx2P(X=x) - [E(X)]2
E(aX + b) = aE(X) + b
Var(aX + b) = a2Var(X)
Discrete uniform: P(X=x) = 1n for x = 1,2,...,n
Practice
Complete 30-35 practice questions
Focus on: Expected value (10 questions), Variance (10 questions), Functions of X (8 questions), Uniform distribution (7 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 8
|
of 12
Topics
Chapter 7: The Normal Distribution
7.1 The Normal Distribution
7.2 Using Tables to Find Probabilities
7.3 Using Tables to Find the Value of z Given a Probability
7.4 The Standard Normal Distribution
7.5 Finding µ and σ
Key Points
Normal distribution: X ~ N(μ, σ2)
Standardization: Z = X - μσ, where Z ~ N(0,1)
Using tables: P(Z < z) from standard normal table
Symmetry: P(Z < -z) = 1 - P(Z < z)
Finding parameters: use inverse normal function
Practice
Complete 35-40 practice questions
Focus on: Standardization (12 questions), Using tables (15 questions), Finding parameters (8 questions), Applications (5 questions)
Question types: Calculations, table reading, problem-solving
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7 and Review Exercises 1 & 2
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Statistics 1 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Statistics 1
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 7 chapters of Statistics 1 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Mathematical Modelling
1.1 Mathematical Models
1.2 Designing a Model
Chapter 2: Measures of Location and Spread (Part 1)
2.1 Types of Data
2.2 Measures of Central Tendency
Key Points
Mathematical models: simplifying real-world situations
Types of data: qualitative, quantitative, discrete, continuous
Mean: x̄ = Σxn
Median: middle value when data is ordered
Mode: most frequent value
Practice
Complete 20-25 practice questions
Focus on: Data types (5 questions), Mean/median/mode (12 questions), Modelling (5 questions)
Question types: Calculations, data classification, interpretation
Week 2
|
of 20
Topics
Chapter 2: Measures of Location and Spread (Part 1 continued)
2.3 Other Measures of Location
Key Points
Quartiles: Q1, Q2 (median), Q3
Practice
Complete 20-25 practice questions
Focus on: Quartiles (15 questions), Mixed problems (10 questions)
Question types: Calculations, interpretation
Review Chapter Reviews 1 & 2
Create formula sheet for measures of location
Week 3
|
of 20
Topics
Chapter 2: Measures of Location and Spread (Part 2)
2.4 Measures of Spread
2.5 Variance and Standard Deviation
2.6 Coding
Key Points
Range: max - min
IQR: Q3 - Q1
Variance: σ2 = Σ(x - x̄)2n
Standard deviation: σ = √variance
Coding: y = ax + b
Practice
Complete 25-30 practice questions
Focus on: Variance/standard deviation (12 questions), IQR (8 questions), Coding (8 questions)
Question types: Calculations, transformations
Review Chapter Review 2
Week 4
|
of 20
Topics
Chapter 3: Representations of Data (Part 1)
3.1 Histograms
3.2 Outliers
3.3 Box Plots
Key Points
Histograms: frequency density = frequencyclass width
Outliers: values beyond Q1 - 1.5×IQR or Q3 + 1.5×IQR
Box plots: show quartiles, median, outliers
Practice
Complete 25-30 practice questions
Focus on: Histograms (10 questions), Box plots (10 questions), Outliers (8 questions)
Question types: Diagram drawing, calculations
Review Chapter Review 3
Week 5
|
of 20
Topics
Chapter 3: Representations of Data (Part 2)
3.4 Stem and Leaf Diagrams
3.5 Skewness
3.6 Comparing Data
Key Points
Skewness: positive (right), negative (left), symmetric
Comparing distributions: shape, location, spread
Practice
Complete 25-30 practice questions
Focus on: Skewness (8 questions), Comparing data (7 questions), Stem and leaf (8 questions), Mixed problems (7 questions)
Question types: Diagram drawing, interpretation, calculations
Review Chapter Review 3
Week 6
|
of 20
Topics
Chapter 4: Probability (Part 1)
4.1 Understanding the Vocabulary Used in Probability
4.2 Venn Diagrams
4.3 Mutually Exclusive and Independent Events
Key Points
Probability: P(A) = favorabletotal
Mutually exclusive: P(A ∩ B) = 0
Independent: P(A ∩ B) = P(A) × P(B)
Practice
Complete 25-30 practice questions
Focus on: Basic probability (10 questions), Venn diagrams (10 questions), Mutually exclusive/independent (10 questions)
Question types: Calculations, diagram drawing, word problems
Week 7
|
of 20
Topics
Chapter 4: Probability (Part 2)
4.4 Set Notation
4.5 Conditional Probability
4.6 Conditional Probabilities in Venn Diagrams
Key Points
Conditional: P(A|B) = P(A ∩ B)P(B)
Set notation: ∪ (union), ∩ (intersection), A' (complement)
Practice
Complete 30-35 practice questions
Focus on: Conditional probability (15 questions), Set notation (10 questions), Mixed problems (10 questions)
Question types: Calculations, diagram drawing
Week 8
|
of 20
Topics
Chapter 4: Probability (Part 3)
4.7 Probability Formulae
4.8 Tree Diagrams
Key Points
Addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Tree diagrams: multiply along branches, add for different paths
Practice
Complete 30-35 practice questions
Focus on: Tree diagrams (15 questions), Probability formulae (12 questions), Mixed problems (8 questions)
Question types: Diagram drawing, calculations
Review Chapter Review 4
Week 9
|
of 20
Topics
Chapter 5: Correlation and Regression
5.1 Scatter Diagrams
5.2 Linear Regression
5.3 Calculating Least Squares Linear Regression
5.4 The Product Moment Correlation Coefficient
Key Points
Scatter diagrams: show relationship between two variables
PMCC: r = Sxy√(Sxx × Syy), where -1 ≤ r ≤ 1
Regression: b = SxySxx, a = ȳ - bx̄
Practice
Complete 30-35 practice questions
Focus on: PMCC calculations (12 questions), Regression (12 questions), Scatter diagrams (8 questions), Mixed problems (8 questions)
Question types: Calculations, interpretations, diagram drawing
Review Chapter Review 5
Week 10
|
of 20
Topics
Chapter 6: Discrete Random Variables (Part 1)
6.1 Discrete Random Variables
6.2 Finding the Cumulative Distribution Function
6.3 Expected Value of a Discrete Random Variable
Key Points
Discrete random variable: takes countable values
Probability distribution: P(X = x) for all x
CDF: F(x) = P(X ≤ x)
E(X) = ΣxP(X=x)
Practice
Complete 30-35 practice questions
Focus on: Discrete RVs (12 questions), CDF (10 questions), Expected value (10 questions)
Question types: Calculations, probability distributions
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers
Week 11
|
of 20
Topics
Chapter 6: Discrete Random Variables (Part 2)
6.4 Variance of a Discrete Random Variable
6.5 Expected Value and Variance of a Function of X
Key Points
Var(X) = E(X2) - [E(X)]2 = Σx2P(X=x) - [E(X)]2
E(aX + b) = aE(X) + b
Var(aX + b) = a2Var(X)
Practice
Complete 30-35 practice questions
Focus on: Variance (15 questions), Functions of X (12 questions), Mixed problems (8 questions)
Question types: Calculations, problem-solving
PAST PAPERS: Solve 12-15 individual questions from past papers
Week 12
|
of 20
Topics
Chapter 6: Discrete Random Variables (Part 3)
6.6 Solving Problems Involving Random Variables
6.7 Using Discrete Uniform Distribution
Key Points
Discrete uniform: P(X=x) = 1n for x = 1,2,...,n
Applications: solving real-world problems with RVs
Practice
Complete 30-35 practice questions
Focus on: Uniform distribution (15 questions), Problem-solving (15 questions), Mixed problems (5 questions)
Question types: Applications, problem-solving
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 6
Week 13
|
of 20
Topics
Chapter 7: The Normal Distribution (Part 1)
7.1 The Normal Distribution
7.2 Using Tables to Find Probabilities
7.3 Using Tables to Find the Value of z Given a Probability
Key Points
Normal distribution: X ~ N(μ, σ2)
Standardization: Z = X - μσ, where Z ~ N(0,1)
Using tables: P(Z < z) from standard normal table
Symmetry: P(Z < -z) = 1 - P(Z < z)
Practice
Complete 35-40 practice questions
Focus on: Standardization (15 questions), Using tables (15 questions), Mixed problems (10 questions)
Question types: Calculations, table reading
PAST PAPERS: Solve 15-18 individual questions from past papers
Week 14
|
of 20
Topics
Chapter 7: The Normal Distribution (Part 2)
7.4 The Standard Normal Distribution
7.5 Finding µ and σ
Key Points
Finding parameters: use inverse normal function
Standard normal: Z ~ N(0,1)
Practice
Complete 35-40 practice questions
Focus on: Finding parameters (15 questions), Standard normal (15 questions), Applications (10 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 18-20 individual questions from past papers
Week 15
|
of 20
Topics
Chapter 7: The Normal Distribution (Part 3)
Review and consolidation of all normal distribution topics
Practice
Complete 35-40 practice questions
Focus on: Mixed normal distribution problems (25 questions), Applications (15 questions)
Question types: Mixed problems, applications
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Review Chapter Review 7 and Review Exercises 1 & 2
Week 16
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 17
|
of 20
Weak Areas Focus
Targeted Practice
Target specific weak topics identified
Additional practice on challenging areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Focus on time management and exam technique
Review solutions thoroughly
Week 18
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Statistics 2 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Statistics 2
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 7 chapters of Statistics 2. The plan builds on S1 knowledge, focusing on binomial and Poisson distributions, approximations, continuous random variables, sampling, and hypothesis testing. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Binomial Distributions
1.1 The Binomial Distribution
1.2 Cumulative Probabilities
1.3 Mean and Variance of the Binomial Distribution
Key Points
Binomial distribution: X ~ B(n, p)
Conditions: fixed n, independent trials, constant p, two outcomes
P(X = r) = nCr × pr × (1-p)n-r
E(X) = np, Var(X) = np(1-p)
Cumulative probabilities: P(X ≤ r) using tables
Practice
Complete 30-35 practice questions
Focus on: Binomial probability (15 questions), Cumulative probabilities (12 questions), Mean/variance (8 questions)
Question types: Calculations, table reading, applications
Review Chapter Review 1
Practice using binomial tables and calculator functions
Week 2
|
of 12
Topics
Chapter 2: Poisson Distributions
2.1 The Poisson Distribution
2.2 Modelling with the Poisson Distribution
2.3 Adding Poisson Distributions
2.4 Mean and Variance of a Poisson Distribution
Key Points
Poisson distribution: X ~ Po(λ)
P(X = r) = λr × e-λr!
Conditions: events occur randomly, independently, at constant rate
E(X) = λ, Var(X) = λ
Adding Poissons: X + Y ~ Po(λ1 + λ2) if independent
Practice
Complete 30-35 practice questions
Focus on: Poisson probability (15 questions), Modelling (10 questions), Adding Poissons (10 questions)
Question types: Calculations, table reading, applications
Review Chapter Review 2
Practice identifying when to use Poisson distribution
Week 3
|
of 12
Topics
Chapter 3: Approximations
3.1 Using the Poisson Distribution to Approximate the Binomial Distribution
3.2 Approximating a Binomial Distribution
3.3 Approximating a Poisson Distribution by a Normal Distribution
3.4 Choosing the Appropriate Approximation
Key Points
Binomial → Poisson: when n large, p small, np < 10, use λ = np
Binomial → Normal: when np > 5 and n(1-p) > 5, use N(np, np(1-p))
Poisson → Normal: when λ > 15, use N(λ, λ)
Continuity correction: add/subtract 0.5 when approximating discrete by continuous
Practice
Complete 30-35 practice questions
Focus on: Binomial→Poisson (10 questions), Binomial→Normal (12 questions), Poisson→Normal (8 questions), Choosing approximation (5 questions)
Question types: Calculations, approximations, continuity corrections
Review Chapter Review 3
Practice identifying when each approximation is appropriate
Week 4
|
of 12
Topics
Chapter 4: Continuous Random Variables
4.1 Continuous Random Variables
4.2 The Cumulative Distribution Function
4.3 Mean and Variance of a Continuous Distribution
4.4 Mode, Median, Quartiles and Percentiles
Key Points
PDF: f(x) such that ∫f(x)dx = 1 over range
CDF: F(x) = P(X ≤ x) = ∫f(t)dt from -∞ to x
E(X) = ∫xf(x)dx, E(X2) = ∫x2f(x)dx
Var(X) = E(X2) - [E(X)]2
Median: F(m) = 0.5, Quartiles: F(Q1) = 0.25, F(Q3) = 0.75
Practice
Complete 30-35 practice questions
Focus on: PDF/CDF (12 questions), Mean/variance (12 questions), Quartiles/percentiles (11 questions)
Question types: Integration, calculations, finding parameters
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 4
Week 5
|
of 12
Topics
Chapter 5: Continuous Uniform Distribution
5.1 The Continuous Uniform Distribution
5.2 Modelling with the Continuous Uniform Distribution
Chapter 6: Sampling and Sampling Distributions
6.1 Populations and Samples
6.2 The Concept of a Statistic
Key Points
Uniform distribution: X ~ U(a, b), f(x) = 1b-a for a ≤ x ≤ b
E(X) = a+b2, Var(X) = (b-a)212
Population vs sample: parameter vs statistic
Sampling distribution: distribution of a statistic
Practice
Complete 30-35 practice questions
Focus on: Uniform distribution (15 questions), Sampling concepts (10 questions), Sampling distributions (10 questions)
Question types: Calculations, probability, interpretations
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Reviews 5 & 6
Week 6
|
of 12
Topics
Chapter 6: Sampling and Sampling Distributions (continued)
6.3 The Sampling Distribution of a Statistic
Chapter 7: Hypothesis Testing (Part 1)
7.1 Hypothesis Testing
7.2 Finding Critical Values
Key Points
Sampling distribution of mean: X̄ ~ N(μ, σ2n) for large n
Hypothesis testing: H0 (null) vs H1 (alternative)
Significance level: α (usually 0.05 or 0.01)
Critical value: boundary of rejection region
Test statistic: calculated from sample data
Practice
Complete 30-35 practice questions
Focus on: Sampling distributions (12 questions), Hypothesis testing basics (12 questions), Critical values (11 questions)
Question types: Calculations, interpretations, test procedures
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Reviews 6 & 7
Week 7
|
of 12
Topics
Chapter 7: Hypothesis Testing (continued)
7.3 One-Tailed Tests
7.4 Two-Tailed Tests
7.5 Testing the Mean λ of a Poisson Distribution
7.6 Using Approximations
Key Points
One-tailed: H1 specifies direction (μ > μ0 or μ < μ0)
Two-tailed: H1 is μ ≠ μ0, split α equally
Testing Poisson: use Poisson distribution or normal approximation
p-value: probability of observing test statistic or more extreme
Reject H0 if p-value < α or test statistic in rejection region
Practice
Complete 35-40 practice questions
Focus on: One-tailed tests (12 questions), Two-tailed tests (12 questions), Poisson testing (10 questions), Approximations (6 questions)
Question types: Hypothesis testing procedures, calculations, conclusions
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 7 and Review Exercises 1 & 2
Week 8
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 9
|
of 12
Weak Areas Focus
Targeted Practice
Target specific weak topics identified
Additional practice on challenging areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Focus on time management and exam technique
Review solutions thoroughly
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Statistics 2 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Statistics 2
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 7 chapters of Statistics 2 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Binomial Distributions (Part 1)
1.1 The Binomial Distribution
1.2 Cumulative Probabilities
Key Points
Binomial distribution: X ~ B(n, p)
Conditions: fixed n, independent trials, constant p, two outcomes
P(X = r) = nCr × pr × (1-p)n-r
Cumulative probabilities: P(X ≤ r) using tables
Practice
Complete 20-25 practice questions
Focus on: Binomial probability (12 questions), Cumulative probabilities (13 questions)
Question types: Calculations, table reading, applications
Review Chapter Review 1
Practice using binomial tables and calculator functions
Week 2
|
of 20
Topics
Chapter 1: Binomial Distributions (Part 2)
1.3 Mean and Variance of the Binomial Distribution
Chapter 2: Poisson Distributions (Part 1)
2.1 The Poisson Distribution
2.2 Modelling with the Poisson Distribution
Key Points
E(X) = np, Var(X) = np(1-p) for binomial
Poisson distribution: X ~ Po(λ)
P(X = r) = λr × e-λr!
Conditions: events occur randomly, independently, at constant rate
Practice
Complete 25-30 practice questions
Focus on: Binomial mean/variance (8 questions), Poisson probability (12 questions), Modelling (10 questions)
Question types: Calculations, table reading, applications
Review Chapter Reviews 1 & 2
Week 3
|
of 20
Topics
Chapter 2: Poisson Distributions (Part 2)
2.3 Adding Poisson Distributions
2.4 Mean and Variance of a Poisson Distribution
Key Points
E(X) = λ, Var(X) = λ for Poisson
Adding Poissons: X + Y ~ Po(λ1 + λ2) if independent
Practice identifying when to use Poisson distribution
Practice
Complete 25-30 practice questions
Focus on: Adding Poissons (12 questions), Mean/variance (8 questions), Mixed problems (10 questions)
Question types: Calculations, applications, problem-solving
Review Chapter Review 2
Week 4
|
of 20
Topics
Chapter 3: Approximations (Part 1)
3.1 Using the Poisson Distribution to Approximate the Binomial Distribution
3.2 Approximating a Binomial Distribution
Key Points
Binomial → Poisson: when n large, p small, np < 10, use λ = np
Binomial → Normal: when np > 5 and n(1-p) > 5, use N(np, np(1-p))
Continuity correction: add/subtract 0.5 when approximating discrete by continuous
Practice
Complete 25-30 practice questions
Focus on: Binomial→Poisson (12 questions), Binomial→Normal (13 questions), Continuity corrections (5 questions)
Question types: Calculations, approximations, choosing appropriate method
Review Chapter Review 3
Week 5
|
of 20
Topics
Chapter 3: Approximations (Part 2)
3.3 Approximating a Poisson Distribution by a Normal Distribution
3.4 Choosing the Appropriate Approximation
Key Points
Poisson → Normal: when λ > 15, use N(λ, λ)
Choosing approximation: check conditions carefully
Always apply continuity correction when using normal approximation
Practice
Complete 25-30 practice questions
Focus on: Poisson→Normal (12 questions), Choosing approximation (13 questions), Mixed problems (5 questions)
Question types: Calculations, approximations, decision-making
Review Chapter Review 3
Week 6
|
of 20
Topics
Chapter 4: Continuous Random Variables (Part 1)
4.1 Continuous Random Variables
4.2 The Cumulative Distribution Function
Key Points
PDF: f(x) such that ∫f(x)dx = 1 over range
CDF: F(x) = P(X ≤ x) = ∫f(t)dt from -∞ to x
Relationship: f(x) = dF(x)dx
Practice
Complete 25-30 practice questions
Focus on: PDF/CDF (15 questions), Finding probabilities (10 questions), Mixed problems (5 questions)
Question types: Integration, calculations, finding parameters
Review Chapter Review 4
Week 7
|
of 20
Topics
Chapter 4: Continuous Random Variables (Part 2)
4.3 Mean and Variance of a Continuous Distribution
4.4 Mode, Median, Quartiles and Percentiles
Key Points
E(X) = ∫xf(x)dx, E(X2) = ∫x2f(x)dx
Var(X) = E(X2) - [E(X)]2
Median: F(m) = 0.5, Quartiles: F(Q1) = 0.25, F(Q3) = 0.75
Mode: value where f(x) is maximum
Practice
Complete 25-30 practice questions
Focus on: Mean/variance (12 questions), Quartiles/percentiles (13 questions), Mixed problems (5 questions)
Question types: Integration, calculations, finding parameters
Review Chapter Review 4
Week 8
|
of 20
Topics
Chapter 5: Continuous Uniform Distribution
5.1 The Continuous Uniform Distribution
5.2 Modelling with the Continuous Uniform Distribution
Key Points
Uniform distribution: X ~ U(a, b), f(x) = 1b-a for a ≤ x ≤ b
E(X) = a+b2, Var(X) = (b-a)212
F(x) = x-ab-a for a ≤ x ≤ b
Practice
Complete 25-30 practice questions
Focus on: Uniform distribution (15 questions), Modelling (10 questions), Applications (5 questions)
Question types: Calculations, probability, interpretations
Review Chapter Review 5
Week 9
|
of 20
Topics
Chapter 6: Sampling and Sampling Distributions
6.1 Populations and Samples
6.2 The Concept of a Statistic
6.3 The Sampling Distribution of a Statistic
Key Points
Population vs sample: parameter vs statistic
Sampling distribution: distribution of a statistic
Sampling distribution of mean: X̄ ~ N(μ, σ2n) for large n
Practice
Complete 25-30 practice questions
Focus on: Sampling concepts (12 questions), Sampling distributions (13 questions), Applications (5 questions)
Question types: Calculations, interpretations, problem-solving
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-6 topics)
Review Chapter Review 6
Week 10
|
of 20
Topics
Chapter 7: Hypothesis Testing (Part 1)
7.1 Hypothesis Testing
7.2 Finding Critical Values
Key Points
Hypothesis testing: H0 (null) vs H1 (alternative)
Significance level: α (usually 0.05 or 0.01)
Critical value: boundary of rejection region
Test statistic: calculated from sample data
Practice
Complete 25-30 practice questions
Focus on: Hypothesis testing basics (15 questions), Critical values (10 questions), Test procedures (5 questions)
Question types: Calculations, interpretations, test procedures
PAST PAPERS: Solve 12-15 individual questions from past papers
Review Chapter Review 7
Week 11
|
of 20
Topics
Chapter 7: Hypothesis Testing (Part 2)
7.3 One-Tailed Tests
7.4 Two-Tailed Tests
Key Points
One-tailed: H1 specifies direction (μ > μ0 or μ < μ0)
Two-tailed: H1 is μ ≠ μ0, split α equally
Reject H0 if test statistic in rejection region
Practice
Complete 25-30 practice questions
Focus on: One-tailed tests (12 questions), Two-tailed tests (13 questions), Mixed problems (5 questions)
Question types: Hypothesis testing procedures, calculations, conclusions
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 7
Week 12
|
of 20
Topics
Chapter 7: Hypothesis Testing (Part 3)
7.5 Testing the Mean λ of a Poisson Distribution
7.6 Using Approximations
Key Points
Testing Poisson: use Poisson distribution or normal approximation
p-value: probability of observing test statistic or more extreme
Reject H0 if p-value < α or test statistic in rejection region
Practice
Complete 30-35 practice questions
Focus on: Poisson testing (15 questions), Using approximations (12 questions), Mixed problems (8 questions)
Question types: Hypothesis testing procedures, calculations, conclusions
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 7 and Review Exercises 1 & 2
Week 13
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed) - focus on understanding question structure
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 14
|
of 20
Weak Areas Focus
Targeted Practice
Target specific weak topics identified
Additional practice on challenging areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Focus on time management and exam technique
Review solutions thoroughly
Week 15
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 16
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 17
|
of 20
Intensive Exam Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Review all incorrect answers thoroughly
Focus on time management
Practice difficult question types
Week 18
|
of 20
Exam Preparation
Continue full paper practice
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 9, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Mechanics 1 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Mechanics 1
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 8 chapters of Mechanics 1. The plan builds understanding of mathematical models in mechanics, constant acceleration, vectors, dynamics, forces, momentum, statics, and moments. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Mathematical Models in Mechanics
1.1 Constructing a Model
1.2 Modelling Assumptions
1.3 Quantities and Units
Chapter 2: Constant Acceleration (Part 1)
2.1 Displacement–Time Graphs
2.2 Velocity–Time Graphs
2.3 Acceleration–Time Graphs
Key Points
Mathematical models: simplifying assumptions (particle, smooth, light, inextensible)
Units: distance (m), time (s), mass (kg), force (N)
Displacement-time: gradient = velocity
Velocity-time: gradient = acceleration, area = displacement
Acceleration-time: area = change in velocity
Practice
Complete 25-30 practice questions
Focus on: Modelling assumptions (5 questions), Graph interpretation (15 questions), Units (5 questions), Graph drawing (5 questions)
Question types: Graph analysis, interpretations, calculations
Review Chapter Reviews 1 & 2
Practice drawing and interpreting motion graphs
Week 2
|
of 12
Topics
Chapter 2: Constant Acceleration (Part 2)
2.4 Constant Acceleration Formulae 1
2.5 Constant Acceleration Formulae 2
2.6 Vertical Motion Under Gravity
Key Points
SUVAT equations: v = u + at, s = ut + 12at2, v2 = u2 + 2as, s = 12(u+v)t, s = vt - 12at2
Vertical motion: a = -g (g = 9.8 m/s2)
Choose appropriate equation based on given information
Sign convention: up positive or down positive (be consistent)
Practice
Complete 30-35 practice questions
Focus on: SUVAT equations (20 questions), Vertical motion (10 questions), Mixed problems (5 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 2
Create formula sheet for SUVAT equations
Week 3
|
of 12
Topics
Chapter 3: Vectors in Mechanics
3.1 Working with Vectors
3.2 Solving Problems with Vectors Written Using I and J Notation
3.3 The Velocity of a Particle as a Vector
3.4 Solving Problems Involving Velocity and Time Using Vectors
Key Points
Vector notation: r = xi + yj, |r| = √(x2 + y2)
Position vector: r(t) = r0 + vt
Velocity vector: v = drdt
Constant velocity: r = r0 + vt
Constant acceleration: v = u + at, r = r0 + ut + 12at2
Practice
Complete 30-35 practice questions
Focus on: Vector operations (10 questions), Position/velocity vectors (15 questions), Vector SUVAT (10 questions)
Question types: Vector calculations, problem-solving, applications
Review Chapter Review 3
Practice working with i and j components
Week 4
|
of 12
Topics
Chapter 4: Dynamics of a Particle Moving in a Straight Line (Part 1)
4.1 Force Diagrams
4.2 Forces as Vectors
4.3 Forces and Acceleration
Key Points
Newton's second law: F = ma
Force diagrams: show all forces acting on particle
Resultant force: F = ΣF (vector sum)
Weight: W = mg (g = 9.8 m/s2)
Resolving forces: components in perpendicular directions
Practice
Complete 30-35 practice questions
Focus on: Force diagrams (10 questions), Newton's laws (15 questions), Resolving forces (10 questions)
Question types: Diagram drawing, calculations, problem-solving
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 4
Week 5
|
of 12
Topics
Chapter 4: Dynamics of a Particle Moving in a Straight Line (Part 2)
4.4 Motion in Two Dimensions
4.5 Connected Particles
4.6 Pulleys
Key Points
Two dimensions: resolve forces and accelerations
Connected particles: same acceleration magnitude, tension in string
Pulleys: smooth pulley changes direction of tension
Light inextensible string: tension same throughout
Practice
Complete 30-35 practice questions
Focus on: Two dimensions (10 questions), Connected particles (15 questions), Pulleys (10 questions)
Question types: Problem-solving, calculations, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 4
Week 6
|
of 12
Topics
Chapter 5: Forces and Friction
5.1 Resolving Forces
5.2 Inclined Planes
5.3 Friction
Key Points
Resolving forces: Fx = F cos θ, Fy = F sin θ
Inclined plane: resolve weight parallel and perpendicular to plane
Friction: F ≤ μR (limiting friction F = μR)
Coefficient of friction: μ = FR
Direction of friction: opposes motion or tendency to move
Practice
Complete 30-35 practice questions
Focus on: Resolving forces (12 questions), Inclined planes (12 questions), Friction (11 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 5
Week 7
|
of 12
Topics
Chapter 6: Momentum and Impulse
6.1 Momentum in One Dimension
6.2 Conservation of Momentum
Chapter 7: Statics of a Particle (Part 1)
7.1 Static Particles
7.2 Modelling with Statics
Key Points
Momentum: p = mv
Impulse: I = mv - mu = Ft
Conservation of momentum: total momentum before = total momentum after (in absence of external forces)
Static particle: resultant force = 0
Equilibrium: forces balance, no acceleration
Practice
Complete 30-35 practice questions
Focus on: Momentum (12 questions), Conservation (10 questions), Statics (13 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Reviews 6 & 7
Week 8
|
of 12
Topics
Chapter 7: Statics of a Particle (Part 2)
7.3 Friction and Static Particles
Chapter 8: Moments
8.1 Moments
8.2 Resultant Moments
8.3 Equilibrium
8.4 Centres of Mass
8.5 Tilting
Key Points
Friction in statics: F ≤ μR, direction opposes tendency to move
Moment: M = F × d (perpendicular distance)
Clockwise and anticlockwise moments
Equilibrium: sum of forces = 0, sum of moments = 0
Centre of mass: point where weight acts
Tilting: occurs when reaction force at one support becomes zero
Practice
Complete 35-40 practice questions
Focus on: Friction in statics (8 questions), Moments (15 questions), Equilibrium (10 questions), Centres of mass (7 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Reviews 7 & 8 and Review Exercises 1 & 2
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Mechanics 1 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Mechanics 1
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 8 chapters of Mechanics 1 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Mathematical Models in Mechanics
1.1 Constructing a Model
1.2 Modelling Assumptions
1.3 Quantities and Units
Key Points
Mathematical models: simplifying assumptions (particle, smooth, light, inextensible)
Units: distance (m), time (s), mass (kg), force (N)
Understanding when to use each assumption
Practice
Complete 20-25 practice questions
Focus on: Modelling assumptions (10 questions), Units (8 questions), Applications (7 questions)
Question types: Interpretations, problem identification
Review Chapter Review 1
Week 2
|
of 20
Topics
Chapter 2: Constant Acceleration (Part 1)
2.1 Displacement–Time Graphs
2.2 Velocity–Time Graphs
2.3 Acceleration–Time Graphs
Key Points
Displacement-time: gradient = velocity
Velocity-time: gradient = acceleration, area = displacement
Acceleration-time: area = change in velocity
Practice
Complete 25-30 practice questions
Focus on: Graph interpretation (15 questions), Graph drawing (10 questions), Calculations (5 questions)
Question types: Graph analysis, interpretations, calculations
Review Chapter Review 2
Practice drawing and interpreting motion graphs
Week 3
|
of 20
Topics
Chapter 2: Constant Acceleration (Part 2)
2.4 Constant Acceleration Formulae 1
2.5 Constant Acceleration Formulae 2
Key Points
SUVAT equations: v = u + at, s = ut + 12at2, v2 = u2 + 2as, s = 12(u+v)t, s = vt - 12at2
Choose appropriate equation based on given information
Sign convention: up positive or down positive (be consistent)
Practice
Complete 25-30 practice questions
Focus on: SUVAT equations (20 questions), Problem-solving (10 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 2
Create formula sheet for SUVAT equations
Week 4
|
of 20
Topics
Chapter 2: Constant Acceleration (Part 3)
2.6 Vertical Motion Under Gravity
Key Points
Vertical motion: a = -g (g = 9.8 m/s2)
Maximum height: v = 0 at top
Time of flight: solve for when displacement = 0
Practice
Complete 25-30 practice questions
Focus on: Vertical motion (20 questions), Maximum height (5 questions), Time of flight (5 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 2
Week 5
|
of 20
Topics
Chapter 3: Vectors in Mechanics (Part 1)
3.1 Working with Vectors
3.2 Solving Problems with Vectors Written Using I and J Notation
Key Points
Vector notation: r = xi + yj, |r| = √(x2 + y2)
Vector operations: addition, subtraction, scalar multiplication
Unit vectors: divide by magnitude
Practice
Complete 25-30 practice questions
Focus on: Vector operations (15 questions), i and j notation (10 questions), Magnitude/direction (5 questions)
Question types: Vector calculations, problem-solving
Review Chapter Review 3
Week 6
|
of 20
Topics
Chapter 3: Vectors in Mechanics (Part 2)
3.3 The Velocity of a Particle as a Vector
3.4 Solving Problems Involving Velocity and Time Using Vectors
Key Points
Position vector: r(t) = r0 + vt
Velocity vector: v = drdt
Constant velocity: r = r0 + vt
Constant acceleration: v = u + at, r = r0 + ut + 12at2
Practice
Complete 25-30 practice questions
Focus on: Position/velocity vectors (15 questions), Vector SUVAT (10 questions), Applications (5 questions)
Question types: Vector calculations, problem-solving, applications
Review Chapter Review 3
Practice working with i and j components
Week 7
|
of 20
Topics
Chapter 4: Dynamics of a Particle Moving in a Straight Line (Part 1)
4.1 Force Diagrams
4.2 Forces as Vectors
4.3 Forces and Acceleration
Key Points
Newton's second law: F = ma
Force diagrams: show all forces acting on particle
Resultant force: F = ΣF (vector sum)
Weight: W = mg (g = 9.8 m/s2)
Practice
Complete 25-30 practice questions
Focus on: Force diagrams (10 questions), Newton's laws (15 questions), Applications (5 questions)
Question types: Diagram drawing, calculations, problem-solving
Review Chapter Review 4
Week 8
|
of 20
Topics
Chapter 4: Dynamics of a Particle Moving in a Straight Line (Part 2)
4.4 Motion in Two Dimensions
4.5 Connected Particles
Key Points
Two dimensions: resolve forces and accelerations
Connected particles: same acceleration magnitude, tension in string
Light inextensible string: tension same throughout
Practice
Complete 25-30 practice questions
Focus on: Two dimensions (12 questions), Connected particles (13 questions), Applications (5 questions)
Question types: Problem-solving, calculations, applications
Review Chapter Review 4
Week 9
|
of 20
Topics
Chapter 4: Dynamics of a Particle Moving in a Straight Line (Part 3)
4.6 Pulleys
Chapter 5: Forces and Friction (Part 1)
5.1 Resolving Forces
Key Points
Pulleys: smooth pulley changes direction of tension
Resolving forces: Fx = F cos θ, Fy = F sin θ
Components in perpendicular directions
Practice
Complete 25-30 practice questions
Focus on: Pulleys (12 questions), Resolving forces (13 questions), Applications (5 questions)
Question types: Problem-solving, calculations, applications
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-5 topics)
Review Chapter Reviews 4 & 5
Week 10
|
of 20
Topics
Chapter 5: Forces and Friction (Part 2)
5.2 Inclined Planes
5.3 Friction
Key Points
Inclined plane: resolve weight parallel and perpendicular to plane
Friction: F ≤ μR (limiting friction F = μR)
Coefficient of friction: μ = FR
Direction of friction: opposes motion or tendency to move
Practice
Complete 25-30 practice questions
Focus on: Inclined planes (12 questions), Friction (13 questions), Mixed problems (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 12-15 individual questions from past papers
Review Chapter Review 5
Week 11
|
of 20
Topics
Chapter 6: Momentum and Impulse
6.1 Momentum in One Dimension
6.2 Conservation of Momentum
Key Points
Momentum: p = mv
Impulse: I = mv - mu = Ft
Conservation of momentum: total momentum before = total momentum after (in absence of external forces)
Practice
Complete 25-30 practice questions
Focus on: Momentum (12 questions), Conservation (13 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 6
Week 12
|
of 20
Topics
Chapter 7: Statics of a Particle
7.1 Static Particles
7.2 Modelling with Statics
7.3 Friction and Static Particles
Key Points
Static particle: resultant force = 0
Equilibrium: forces balance, no acceleration
Friction in statics: F ≤ μR, direction opposes tendency to move
Practice
Complete 25-30 practice questions
Focus on: Statics (15 questions), Friction in statics (10 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 7
Week 13
|
of 20
Topics
Chapter 8: Moments (Part 1)
8.1 Moments
8.2 Resultant Moments
8.3 Equilibrium
Key Points
Moment: M = F × d (perpendicular distance)
Clockwise and anticlockwise moments
Equilibrium: sum of forces = 0, sum of moments = 0
Practice
Complete 25-30 practice questions
Focus on: Moments (15 questions), Equilibrium (10 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 8
Week 14
|
of 20
Topics
Chapter 8: Moments (Part 2)
8.4 Centres of Mass
8.5 Tilting
Key Points
Centre of mass: point where weight acts
Tilting: occurs when reaction force at one support becomes zero
Finding centre of mass: use moments or symmetry
Practice
Complete 25-30 practice questions
Focus on: Centres of mass (15 questions), Tilting (10 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 8 and Review Exercises 1 & 2
Week 15
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 16
|
of 20
Weak Areas Focus
Targeted practice on identified weak areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark strictly using mark schemes
Analyze mistakes and patterns
Week 17
|
of 20
Exam Preparation
Full past paper practice under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly, analyze mistakes
Review examiner reports
Practice presentation and working clearly
Week 18
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 19
|
of 20
Intensive Exam Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Review all incorrect answers thoroughly
Focus on time management
Practice exam strategy
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 9, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Mechanics 2 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Mechanics 2
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 6 chapters of Mechanics 2. The plan builds on M1 knowledge, focusing on projectiles, variable acceleration, centres of mass, work and energy, impulses and collisions, and statics of rigid bodies. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Projectiles (Part 1)
1.1 Horizontal Projection
1.2 Horizontal and Vertical Components
Key Points
Horizontal projection: initial vertical velocity = 0
Resolve into horizontal (x) and vertical (y) components
Horizontal: constant velocity, x = ut
Vertical: constant acceleration, y = ut - 12gt2
Practice
Complete 25-30 practice questions
Focus on: Horizontal projection (15 questions), Component resolution (10 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 1
Practice resolving velocities and accelerations
Week 2
|
of 12
Topics
Chapter 1: Projectiles (Part 2)
1.3 Projection at Any Angle
1.4 Projectile Motion Formulae
Key Points
Projection at angle θ: ux = u cos θ, uy = u sin θ
Maximum height: vy = 0, h = (u sin θ)22g
Range: R = u2 sin 2θg
Time of flight: T = 2u sin θg
Trajectory equation: eliminate t to get y in terms of x
Practice
Complete 30-35 practice questions
Focus on: Projection at angle (15 questions), Maximum height/range (12 questions), Trajectory (8 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 1
Practice deriving and using projectile formulae
Week 3
|
of 12
Topics
Chapter 2: Variable Acceleration
2.1 Functions of Time
2.2 Using Differentiation
2.3 Using Integration
2.4 Differentiating Vectors
2.5 Integrating Vectors
2.6 Constant Acceleration Formulae
Key Points
v = drdt, a = dvdt = d2rdt2
r = ∫v dt, v = ∫a dt
Vector differentiation: differentiate each component
Vector integration: integrate each component, add constant vector
Use initial conditions to find constants
Practice
Complete 30-35 practice questions
Focus on: Differentiation (12 questions), Integration (12 questions), Vector calculus (11 questions)
Question types: Calculus, problem-solving, applications
Review Chapter Review 2
Practice calculus with vectors
Week 4
|
of 12
Topics
Chapter 3: Centres of Mass (Part 1)
3.1 Centre of Mass of a Set of Particles on a Straight Line
3.2 Centre of Mass of a Set of Particles Arranged in a Plane
3.3 Centres of Mass of Standard Uniform Plane Laminas
Key Points
Centre of mass: x̄ = Σ(mx)Σm, ȳ = Σ(my)Σm
For uniform lamina: use area instead of mass
Standard shapes: rectangle, triangle, semicircle, etc.
Use symmetry where possible
Practice
Complete 30-35 practice questions
Focus on: Particles on line (10 questions), Particles in plane (12 questions), Standard laminas (13 questions)
Question types: Calculations, problem-solving, applications
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-3 topics)
Review Chapter Review 3
Week 5
|
of 12
Topics
Chapter 3: Centres of Mass (Part 2)
3.4 Centre of Mass of a Composite Lamina
3.5 Centre of Mass of a Framework
3.6 Laminas in Equilibrium
3.7 Frameworks in Equilibrium
3.8 Non-Uniform Composite Laminas and Frameworks
Key Points
Composite lamina: treat as combination of standard shapes
Framework: treat as set of particles at vertices
Equilibrium: centre of mass directly above/below pivot
Non-uniform: use density or mass per unit area
Practice
Complete 30-35 practice questions
Focus on: Composite laminas (12 questions), Frameworks (10 questions), Equilibrium (8 questions), Non-uniform (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 3
Week 6
|
of 12
Topics
Chapter 4: Work and Energy
4.1 Work Done
4.2 Kinetic and Potential Energy
4.3 Conservation of Mechanical Energy and Work–Energy Principle
4.4 Power
Key Points
Work done: W = F × s (force × distance in direction of force)
Kinetic energy: KE = 12mv2
Potential energy: PE = mgh
Conservation: KE + PE = constant (no non-conservative forces)
Work-energy: W = ΔKE
Power: P = Fv = Wt
Practice
Complete 30-35 practice questions
Focus on: Work done (10 questions), Energy (12 questions), Conservation (8 questions), Power (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 4
Week 7
|
of 12
Topics
Chapter 5: Impulses and Collisions
5.1 Momentum as a Vector
5.2 Direct Impact and Newton's Law of Restitution
5.3 Direct Collision with a Smooth Plane
5.4 Loss of Kinetic Energy
5.5 Successive Direct Impacts
Key Points
Momentum as vector: p = mv
Newton's law of restitution: e = v2 - v1u1 - u2, 0 ≤ e ≤ 1
e = 1: perfectly elastic, e = 0: inelastic
Collision with plane: component perpendicular reverses, parallel unchanged
Loss of KE: ΔKE = 12m1m2(1-e2)(u1-u2)2/(m1+m2)
Practice
Complete 30-35 practice questions
Focus on: Vector momentum (8 questions), Restitution (12 questions), Collision with plane (8 questions), Energy loss (7 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 5
Week 8
|
of 12
Topics
Chapter 6: Statics of Rigid Bodies
6.1 Static Rigid Bodies
Key Points
Rigid body: sum of forces = 0, sum of moments = 0
Resolve forces in two perpendicular directions
Take moments about convenient point
Three equations for equilibrium (two force, one moment)
Practice
Complete 30-35 practice questions
Focus on: Static rigid bodies (30 questions), Equilibrium conditions (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 6 and Review Exercises 1 & 2
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-6
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Mechanics 2 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Mechanics 2
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 6 chapters of Mechanics 2 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Projectiles (Part 1)
1.1 Horizontal Projection
1.2 Horizontal and Vertical Components
Key Points
Horizontal projection: initial vertical velocity = 0
Resolve into horizontal (x) and vertical (y) components
Horizontal: constant velocity, x = ut
Vertical: constant acceleration, y = ut - 12gt2
Practice
Complete 20-25 practice questions
Focus on: Horizontal projection (12 questions), Component resolution (8 questions), Applications (5 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 1
Week 2
|
of 20
Topics
Chapter 1: Projectiles (Part 2)
1.3 Projection at Any Angle
1.4 Projectile Motion Formulae
Key Points
Projection at angle θ: ux = u cos θ, uy = u sin θ
Maximum height: h = (u sin θ)22g
Range: R = u2 sin 2θg
Time of flight: T = 2u sin θg
Practice
Complete 25-30 practice questions
Focus on: Projection at angle (15 questions), Maximum height/range (10 questions), Trajectory (5 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 1
Week 3
|
of 20
Topics
Chapter 2: Variable Acceleration (Part 1)
2.1 Functions of Time
2.2 Using Differentiation
2.3 Using Integration
Key Points
v = drdt, a = dvdt = d2rdt2
r = ∫v dt, v = ∫a dt
Use initial conditions to find constants
Practice
Complete 25-30 practice questions
Focus on: Differentiation (12 questions), Integration (13 questions), Applications (5 questions)
Question types: Calculus, problem-solving, applications
Review Chapter Review 2
Week 4
|
of 20
Topics
Chapter 2: Variable Acceleration (Part 2)
2.4 Differentiating Vectors
2.5 Integrating Vectors
2.6 Constant Acceleration Formulae
Key Points
Vector differentiation: differentiate each component
Vector integration: integrate each component, add constant vector
Practice with i and j notation
Practice
Complete 25-30 practice questions
Focus on: Vector differentiation (12 questions), Vector integration (13 questions), Applications (5 questions)
Question types: Calculus, problem-solving, applications
Review Chapter Review 2
Week 5
|
of 20
Topics
Chapter 3: Centres of Mass (Part 1)
3.1 Centre of Mass of a Set of Particles on a Straight Line
3.2 Centre of Mass of a Set of Particles Arranged in a Plane
Key Points
Centre of mass: x̄ = Σ(mx)Σm, ȳ = Σ(my)Σm
For uniform lamina: use area instead of mass
Practice
Complete 25-30 practice questions
Focus on: Particles on line (12 questions), Particles in plane (13 questions), Applications (5 questions)
Question types: Calculations, problem-solving
Review Chapter Review 3
Week 6
|
of 20
Topics
Chapter 3: Centres of Mass (Part 2)
3.3 Centres of Mass of Standard Uniform Plane Laminas
3.4 Centre of Mass of a Composite Lamina
Key Points
Standard shapes: rectangle, triangle, semicircle, etc.
Composite lamina: treat as combination of standard shapes
Use symmetry where possible
Practice
Complete 25-30 practice questions
Focus on: Standard laminas (12 questions), Composite laminas (13 questions), Applications (5 questions)
Question types: Calculations, problem-solving
Review Chapter Review 3
Week 7
|
of 20
Topics
Chapter 3: Centres of Mass (Part 3)
3.5 Centre of Mass of a Framework
3.6 Laminas in Equilibrium
3.7 Frameworks in Equilibrium
3.8 Non-Uniform Composite Laminas and Frameworks
Key Points
Framework: treat as set of particles at vertices
Equilibrium: centre of mass directly above/below pivot
Non-uniform: use density or mass per unit area
Practice
Complete 25-30 practice questions
Focus on: Frameworks (12 questions), Equilibrium (10 questions), Non-uniform (8 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 3
Week 8
|
of 20
Topics
Chapter 4: Work and Energy
4.1 Work Done
4.2 Kinetic and Potential Energy
4.3 Conservation of Mechanical Energy and Work–Energy Principle
4.4 Power
Key Points
Work done: W = F × s
Kinetic energy: KE = 12mv2
Potential energy: PE = mgh
Conservation: KE + PE = constant
Power: P = Fv = Wt
Practice
Complete 25-30 practice questions
Focus on: Work done (10 questions), Energy (12 questions), Conservation (8 questions)
Question types: Calculations, problem-solving, applications
Review Chapter Review 4
Week 9
|
of 20
Topics
Chapter 5: Impulses and Collisions
5.1 Momentum as a Vector
5.2 Direct Impact and Newton's Law of Restitution
5.3 Direct Collision with a Smooth Plane
5.4 Loss of Kinetic Energy
5.5 Successive Direct Impacts
Key Points
Momentum as vector: p = mv
Newton's law of restitution: e = v2 - v1u1 - u2
Collision with plane: component perpendicular reverses
Loss of KE: ΔKE = 12m1m2(1-e2)(u1-u2)2/(m1+m2)
Practice
Complete 30-35 practice questions
Focus on: Vector momentum (8 questions), Restitution (12 questions), Collision with plane (8 questions), Energy loss (7 questions)
Question types: Calculations, problem-solving, applications
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-5 topics)
Review Chapter Review 5
Week 10
|
of 20
Topics
Chapter 6: Statics of Rigid Bodies
6.1 Static Rigid Bodies
Key Points
Rigid body: sum of forces = 0, sum of moments = 0
Resolve forces in two perpendicular directions
Take moments about convenient point
Practice
Complete 30-35 practice questions
Focus on: Static rigid bodies (30 questions), Equilibrium conditions (5 questions)
Question types: Calculations, problem-solving, applications
PAST PAPERS: Solve 12-15 individual questions from past papers
Review Chapter Review 6 and Review Exercises 1 & 2
Week 11
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-6
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (untimed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 12
|
of 20
Weak Areas Focus
Targeted practice on identified weak areas
Practice
Complete 30-40 targeted practice questions on weak areas
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark strictly using mark schemes
Analyze mistakes and patterns
Week 13
|
of 20
Exam Preparation
Full past paper practice under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly, analyze mistakes
Review examiner reports
Practice presentation and working clearly
Week 14
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 15
|
of 20
Intensive Exam Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Review all incorrect answers thoroughly
Focus on time management
Practice exam strategy
Week 16
|
of 20
Exam Preparation
Full past paper practice under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly, analyze mistakes
Review examiner reports
Practice presentation and working clearly
Week 17
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 18
|
of 20
Intensive Exam Practice
Continue full paper practice
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Review all incorrect answers thoroughly
Focus on time management
Practice exam strategy
Week 19
|
of 20
Exam Preparation
Full past paper practice under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly, analyze mistakes
Review examiner reports
Practice presentation and working clearly
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 9, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Decision Mathematics 1 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Decision Mathematics 1
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 7 chapters of Decision Mathematics 1. The plan focuses on algorithms, graphs and networks, graph algorithms, route inspection, travelling salesman problem, critical path analysis, and linear programming. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Algorithms (Part 1)
1.1 Using and Understanding Algorithms
1.2 Flow Charts
1.3 Bubble Sort
Key Points
Algorithms: step-by-step procedures to solve problems
Flow charts: visual representation of algorithms
Bubble sort: compare adjacent elements, swap if needed, repeat
Time complexity: number of comparisons needed
Practice
Complete 25-30 practice questions
Focus on: Understanding algorithms (8 questions), Flow charts (10 questions), Bubble sort (12 questions)
Question types: Algorithm tracing, flow chart drawing, sorting
Review Chapter Review 1
Practice tracing algorithms step by step
Week 2
|
of 12
Topics
Chapter 1: Algorithms (Part 2)
1.4 Quick Sort
1.5 Bin-Packing Algorithms
1.6 Binary Search
Chapter 2: Graphs and Networks (Part 1)
2.1 Modelling with Graphs
2.2 Graph Theory
Key Points
Quick sort: choose pivot, partition, recursively sort
Bin-packing: first-fit, first-fit decreasing, full-bin
Binary search: divide and conquer, requires sorted list
Graph: vertices (nodes) and edges (arcs)
Degree: number of edges connected to vertex
Practice
Complete 30-35 practice questions
Focus on: Quick sort (10 questions), Bin-packing (10 questions), Binary search (8 questions), Graph basics (7 questions)
Question types: Algorithm tracing, sorting, searching, graph drawing
Review Chapter Reviews 1 & 2
Week 3
|
of 12
Topics
Chapter 2: Graphs and Networks (Part 2)
2.3 Special Types of Graph
2.4 Representing Graphs and Networks Using Matrices
Chapter 3: Algorithms on Graphs (Part 1)
3.1 Kruskal's Algorithm
3.2 Prim's Algorithm
Key Points
Special graphs: complete, bipartite, tree, planar
Adjacency matrix: A[i][j] = 1 if edge exists, 0 otherwise
Kruskal's: add edges in order of weight, avoid cycles
Prim's: start at vertex, add minimum weight edge from tree
Both find minimum spanning tree
Practice
Complete 30-35 practice questions
Focus on: Special graphs (8 questions), Matrices (10 questions), Kruskal's (9 questions), Prim's (8 questions)
Question types: Graph drawing, matrix operations, algorithm application
Review Chapter Reviews 2 & 3
Practice applying algorithms step by step
Week 4
|
of 12
Topics
Chapter 3: Algorithms on Graphs (Part 2)
3.3 Applying Prim's Algorithm to a Distance Matrix
3.4 The Nearest Neighbour Algorithm
3.5 Using Dijkstra's Algorithm to Find the Shortest Path
Key Points
Prim's on matrix: use table method
Nearest neighbour: greedy algorithm for TSP
Dijkstra's: finds shortest path from start to all vertices
Dijkstra's: label vertices with shortest distance found so far
Practice
Complete 30-35 practice questions
Focus on: Prim's on matrix (10 questions), Nearest neighbour (10 questions), Dijkstra's (15 questions)
Question types: Algorithm application, table filling, path finding
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-3 topics)
Review Chapter Review 3
Week 5
|
of 12
Topics
Chapter 4: Route Inspection
4.1 Eulerian Graphs
4.2 Using the Route Inspection Algorithm
Chapter 5: The Travelling Salesman Problem (Part 1)
5.1 The Classical and Practical Travelling Salesman Problems
5.2 Using a Minimum Spanning Tree Method to Find an Upper Bound
Key Points
Eulerian: all vertices have even degree (or exactly 2 odd)
Route inspection: find minimum route covering all edges
TSP: visit each vertex exactly once, return to start
Upper bound: use MST method (double edges, find tour)
Practice
Complete 30-35 practice questions
Focus on: Eulerian graphs (10 questions), Route inspection (12 questions), TSP basics (8 questions), Upper bounds (5 questions)
Question types: Algorithm application, route finding, problem-solving
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Reviews 4 & 5
Week 6
|
of 12
Topics
Chapter 5: The Travelling Salesman Problem (Part 2)
5.3 Using a Minimum Spanning Tree Method to Find a Lower Bound
5.4 Using the Nearest Neighbour Algorithm to Find an Upper Bound
Chapter 6: Critical Path Analysis (Part 1)
6.1 Modelling a Project
6.2 Dummy Activities
Key Points
Lower bound: MST weight + two smallest edges from start/end
Upper bound: use nearest neighbour or MST method
CPA: activities, events, dependencies
Dummy activities: maintain precedence, no duration
Practice
Complete 30-35 practice questions
Focus on: Lower bounds (10 questions), Upper bounds (10 questions), CPA basics (10 questions), Dummy activities (5 questions)
Question types: Algorithm application, network drawing, problem-solving
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Reviews 5 & 6
Week 7
|
of 12
Topics
Chapter 6: Critical Path Analysis (Part 2)
6.3 Early and Late Event Times
6.4 The Float of an Activity
6.5 Critical Activities
6.6 Gantt Charts
6.7 Scheduling Diagrams
Key Points
Early event time: earliest time event can occur
Late event time: latest time event can occur without delaying project
Float: late finish - early start - duration
Critical activities: float = 0, on critical path
Gantt chart: timeline showing activity durations
Practice
Complete 30-35 practice questions
Focus on: Early/late times (12 questions), Float (10 questions), Critical path (8 questions), Gantt charts (5 questions)
Question types: Network analysis, calculations, diagram drawing
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 8
|
of 12
Topics
Chapter 7: Linear Programming
7.1 Linear Programming Problems
7.2 Graphical Methods
7.3 Locating the Optimal Point
7.4 Solutions with Integer Values
Key Points
Linear programming: optimize objective function subject to constraints
Feasible region: area satisfying all constraints
Optimal point: at vertex of feasible region
Integer solutions: check integer points near optimal vertex
Objective line: move parallel to find optimum
Practice
Complete 30-35 practice questions
Focus on: Formulating problems (8 questions), Graphical method (15 questions), Finding optimum (7 questions), Integer solutions (5 questions)
Question types: Problem formulation, graph drawing, optimization
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7 and Review Exercise 2
Week 9
|
of 12
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 40-50 mixed practice questions
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Decision Mathematics 1 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Decision Mathematics 1
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 7 chapters of Decision Mathematics 1 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Algorithms (Part 1)
1.1 Using and Understanding Algorithms
1.2 Flow Charts
Key Points
Algorithms: step-by-step procedures to solve problems
Flow charts: visual representation of algorithms
Understanding algorithm structure and logic
Practice
Complete 20-25 practice questions
Focus on: Understanding algorithms (12 questions), Flow charts (13 questions)
Question types: Algorithm tracing, flow chart drawing
Review Chapter Review 1
Week 2
|
of 20
Topics
Chapter 1: Algorithms (Part 2)
1.3 Bubble Sort
Key Points
Bubble sort: compare adjacent elements, swap if needed, repeat
Time complexity: number of comparisons needed
Practice tracing bubble sort step by step
Practice
Complete 20-25 practice questions
Focus on: Bubble sort tracing (25 questions)
Question types: Sorting, algorithm tracing
Review Chapter Review 1
Week 3
|
of 20
Topics
Chapter 1: Algorithms (Part 3)
1.4 Quick Sort
1.5 Bin-Packing Algorithms
Key Points
Quick sort: choose pivot, partition, recursively sort
Bin-packing: first-fit, first-fit decreasing, full-bin
Compare efficiency of different algorithms
Practice
Complete 20-25 practice questions
Focus on: Quick sort (12 questions), Bin-packing (13 questions)
Question types: Algorithm tracing, sorting, bin-packing
Review Chapter Review 1
Week 4
|
of 20
Topics
Chapter 1: Algorithms (Part 4)
1.6 Binary Search
Chapter 2: Graphs and Networks (Part 1)
2.1 Modelling with Graphs
2.2 Graph Theory
Key Points
Binary search: divide and conquer, requires sorted list
Graph: vertices (nodes) and edges (arcs)
Degree: number of edges connected to vertex
Practice
Complete 20-25 practice questions
Focus on: Binary search (10 questions), Graph basics (15 questions)
Question types: Searching, graph drawing, terminology
Review Chapter Reviews 1 & 2
Week 5
|
of 20
Topics
Chapter 2: Graphs and Networks (Part 2)
2.3 Special Types of Graph
2.4 Representing Graphs and Networks Using Matrices
Key Points
Special graphs: complete, bipartite, tree, planar
Adjacency matrix: A[i][j] = 1 if edge exists, 0 otherwise
Distance matrix: weights of edges
Practice
Complete 20-25 practice questions
Focus on: Special graphs (10 questions), Matrices (15 questions)
Question types: Graph classification, matrix operations
Review Chapter Review 2
Week 6
|
of 20
Topics
Chapter 3: Algorithms on Graphs (Part 1)
3.1 Kruskal's Algorithm
3.2 Prim's Algorithm
Key Points
Kruskal's: add edges in order of weight, avoid cycles
Prim's: start at vertex, add minimum weight edge from tree
Both find minimum spanning tree
Practice
Complete 20-25 practice questions
Focus on: Kruskal's (12 questions), Prim's (13 questions)
Question types: Algorithm application, MST finding
Review Chapter Review 3
Week 7
|
of 20
Topics
Chapter 3: Algorithms on Graphs (Part 2)
3.3 Applying Prim's Algorithm to a Distance Matrix
3.4 The Nearest Neighbour Algorithm
Key Points
Prim's on matrix: use table method
Nearest neighbour: greedy algorithm for TSP
Practice table method for Prim's
Practice
Complete 20-25 practice questions
Focus on: Prim's on matrix (12 questions), Nearest neighbour (13 questions)
Question types: Table filling, algorithm application
Review Chapter Review 3
Week 8
|
of 20
Topics
Chapter 3: Algorithms on Graphs (Part 3)
3.5 Using Dijkstra's Algorithm to Find the Shortest Path
Key Points
Dijkstra's: finds shortest path from start to all vertices
Dijkstra's: label vertices with shortest distance found so far
Practice step-by-step application
Practice
Complete 20-25 practice questions
Focus on: Dijkstra's algorithm (25 questions)
Question types: Path finding, algorithm tracing
Review Chapter Review 3
Week 9
|
of 20
Topics
Chapter 4: Route Inspection
4.1 Eulerian Graphs
4.2 Using the Route Inspection Algorithm
Key Points
Eulerian: all vertices have even degree (or exactly 2 odd)
Route inspection: find minimum route covering all edges
Pair odd vertices, find shortest paths
Practice
Complete 20-25 practice questions
Focus on: Eulerian graphs (10 questions), Route inspection (15 questions)
Question types: Algorithm application, route finding
Review Chapter Review 4
Week 10
|
of 20
Topics
Chapter 5: The Travelling Salesman Problem (Part 1)
5.1 The Classical and Practical Travelling Salesman Problems
5.2 Using a Minimum Spanning Tree Method to Find an Upper Bound
Key Points
TSP: visit each vertex exactly once, return to start
Upper bound: use MST method (double edges, find tour)
Classical vs practical TSP
Practice
Complete 20-25 practice questions
Focus on: TSP basics (10 questions), Upper bounds (15 questions)
Question types: Problem-solving, algorithm application
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 5
Week 11
|
of 20
Topics
Chapter 5: The Travelling Salesman Problem (Part 2)
5.3 Using a Minimum Spanning Tree Method to Find a Lower Bound
5.4 Using the Nearest Neighbour Algorithm to Find an Upper Bound
Key Points
Lower bound: MST weight + two smallest edges from start/end
Upper bound: use nearest neighbour or MST method
Compare bounds to estimate optimal solution
Practice
Complete 20-25 practice questions
Focus on: Lower bounds (12 questions), Upper bounds (13 questions)
Question types: Algorithm application, bound calculation
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 5
Week 12
|
of 20
Topics
Chapter 6: Critical Path Analysis (Part 1)
6.1 Modelling a Project
6.2 Dummy Activities
Key Points
CPA: activities, events, dependencies
Dummy activities: maintain precedence, no duration
Draw activity networks
Practice
Complete 20-25 practice questions
Focus on: CPA basics (12 questions), Dummy activities (13 questions)
Question types: Network drawing, problem-solving
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 6
Week 13
|
of 20
Topics
Chapter 6: Critical Path Analysis (Part 2)
6.3 Early and Late Event Times
6.4 The Float of an Activity
6.5 Critical Activities
Key Points
Early event time: earliest time event can occur
Late event time: latest time event can occur without delaying project
Float: late finish - early start - duration
Critical activities: float = 0, on critical path
Practice
Complete 20-25 practice questions
Focus on: Early/late times (10 questions), Float (8 questions), Critical path (7 questions)
Question types: Network analysis, calculations
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 14
|
of 20
Topics
Chapter 6: Critical Path Analysis (Part 3)
6.6 Gantt Charts
6.7 Scheduling Diagrams
Key Points
Gantt chart: timeline showing activity durations
Scheduling diagrams: resource allocation
Practice drawing and interpreting charts
Practice
Complete 20-25 practice questions
Focus on: Gantt charts (12 questions), Scheduling (13 questions)
Question types: Diagram drawing, interpretation
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 6
Week 15
|
of 20
Topics
Chapter 7: Linear Programming (Part 1)
7.1 Linear Programming Problems
7.2 Graphical Methods
Key Points
Linear programming: optimize objective function subject to constraints
Feasible region: area satisfying all constraints
Draw constraint lines, shade feasible region
Practice
Complete 20-25 practice questions
Focus on: Formulating problems (10 questions), Graphical method (15 questions)
Question types: Problem formulation, graph drawing
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7
Week 16
|
of 20
Topics
Chapter 7: Linear Programming (Part 2)
7.3 Locating the Optimal Point
7.4 Solutions with Integer Values
Key Points
Optimal point: at vertex of feasible region
Integer solutions: check integer points near optimal vertex
Objective line: move parallel to find optimum
Practice
Complete 20-25 practice questions
Focus on: Finding optimum (12 questions), Integer solutions (13 questions)
Question types: Optimization, integer programming
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Review Chapter Review 7 and Review Exercise 2
Week 17
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-7
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 30-40 mixed practice questions
PAST PAPERS: Complete 2 full past papers (timed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 18
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 1 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 1
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 8 chapters of Further Pure Mathematics 1. The plan builds advanced mathematical concepts including complex numbers, matrices, series, and proof techniques. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Complex Numbers (Part 1)
1.1 Imaginary and Complex Numbers
1.2 Multiplying Complex Numbers
1.3 Complex Conjugation
Key Points
Complex number: z = a + bi, where i2 = -1
Adding/subtracting: (a+bi) ± (c+di) = (a±c) + (b±d)i
Multiplying: (a+bi)(c+di) = ac + adi + bci + bdi2 = (ac-bd) + (ad+bc)i
Conjugate: z̄ = a - bi, zz̄ = a2 + b2
Practice
Complete 25-30 practice questions
Focus on: Basic operations (15 questions), Conjugation (10 questions), Simplifying (5 questions)
Question types: Calculations, simplification, algebraic manipulation
Review Chapter Review 1
Week 2
|
of 12
Topics
Chapter 1: Complex Numbers (Part 2)
1.4 Argand Diagrams
1.5 Modulus and Argument
1.6 Modulus-Argument Form of Complex Numbers
Key Points
Argand diagram: complex plane with real (x) and imaginary (y) axes
Modulus: |z| = √(a2 + b2) = r
Argument: arg(z) = θ = tan-1(ba)
Modulus-argument form: z = r(cos θ + i sin θ) = r cis θ
Practice
Complete 25-30 practice questions
Focus on: Argand diagrams (10 questions), Modulus/argument (15 questions), Polar form (5 questions)
Question types: Graph plotting, calculations, conversions
Review Chapter Review 1
Week 3
|
of 12
Topics
Chapter 1: Complex Numbers (Part 3)
1.7 Roots of Quadratic Equations
1.8 Solving Cubic and Quartic Equations
Chapter 2: Roots of Quadratic Equations
2.1 Roots of a Quadratic Equation
2.2 Forming Quadratic Equations with New Roots
Key Points
Quadratic formula: x = -b ± √(b2-4ac)2a
Sum of roots: α + β = -ba
Product of roots: αβ = ca
Factor theorem for complex roots
Forming equations: x2 - (sum)x + (product) = 0
Practice
Complete 30-35 practice questions
Focus on: Complex roots (12 questions), Cubic/quartic (10 questions), Root relationships (13 questions)
Question types: Solving equations, forming equations, relationships
Review Chapter Reviews 1 & 2
Week 4
|
of 12
Topics
Chapter 3: Numerical Solutions of Equations
3.1 Locating Roots
3.2 Interval Bisection
3.3 Linear Interpolation
3.4 The Newton-Raphson Method
Key Points
Change of sign: if f(a) and f(b) have opposite signs, root exists in (a,b)
Interval bisection: repeatedly halve interval containing root
Linear interpolation: use similar triangles to estimate root
Newton-Raphson: xn+1 = xn - f(xn)f'(xn)
Practice
Complete 30-35 practice questions
Focus on: Locating roots (8 questions), Bisection (10 questions), Interpolation (8 questions), Newton-Raphson (9 questions)
Question types: Iterative methods, calculations, accuracy
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-3 topics)
Review Chapter Review 3
Week 5
|
of 12
Topics
Chapter 4: Coordinate Systems
4.1 Parametric Equations
4.2 The General Equation of a Parabola
4.3 The Equation for a Rectangular Hyperbola. The Equation of the Tangent and the Equation of the Normal
Key Points
Parametric equations: x = f(t), y = g(t)
Eliminating parameter: express t in terms of x or y
Parabola: y2 = 4ax (standard form)
Rectangular hyperbola: xy = c2
Tangent and normal: use differentiation
Practice
Complete 30-35 practice questions
Focus on: Parametric equations (12 questions), Parabola (10 questions), Hyperbola (13 questions)
Question types: Curve sketching, tangent/normal, elimination
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 4 and Review Exercise 1
Week 6
|
of 12
Topics
Chapter 5: Matrices (Part 1)
5.1 Introduction to Matrices
5.2 Matrix Multiplication
Key Points
Matrix: rectangular array of numbers
Order: m × n (m rows, n columns)
Matrix multiplication: (AB)ij = Σ AikBkj
Not commutative: AB ≠ BA in general
Practice
Complete 25-30 practice questions
Focus on: Matrix basics (10 questions), Multiplication (20 questions)
Question types: Calculations, operations, properties
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 5
Week 7
|
of 12
Topics
Chapter 5: Matrices (Part 2)
5.3 Determinants
5.4 Inverting a 2×2 Matrix
Chapter 6: Transformations Using Matrices (Part 1)
6.1 Linear Transformations in Two Dimensions
6.2 Reflections and Rotations
Key Points
Determinant: det(A) = ad - bc for 2×2 matrix
Inverse: A-1 = 1det(A) × [[d, -b], [-c, a]]
Linear transformation: maps points using matrix multiplication
Reflection matrices: in x-axis, y-axis, y=x, y=-x
Rotation matrices: R(θ) = [[cos θ, -sin θ], [sin θ, cos θ]]
Practice
Complete 30-35 practice questions
Focus on: Determinants (10 questions), Inverses (10 questions), Transformations (15 questions)
Question types: Calculations, transformations, geometry
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Reviews 5 & 6
Week 8
|
of 12
Topics
Chapter 6: Transformations Using Matrices (Part 2)
6.3 Enlargements and Stretches
6.4 Successive Transformations
6.5 The Inverse of a Linear Transformation
Chapter 7: Series (Part 1)
7.1 Sums of Natural Numbers
Key Points
Enlargement: scale factor k, matrix [[k, 0], [0, k]]
Stretch: in x-direction [[k, 0], [0, 1]], in y-direction [[1, 0], [0, k]]
Successive: apply transformations in order (right to left)
Sum of natural numbers: Σr = n(n+1)2
Practice
Complete 30-35 practice questions
Focus on: Enlargements/stretches (12 questions), Successive (10 questions), Series basics (13 questions)
Question types: Transformations, series calculations
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Reviews 6 & 7
Week 9
|
of 12
Topics
Chapter 7: Series (Part 2)
7.2 Sums of Squares and Cubes
Chapter 8: Proof (Part 1)
8.1 Proof by Mathematical Induction
8.2 Proving Divisibility Results
Key Points
Sum of squares: Σr2 = n(n+1)(2n+1)6
Sum of cubes: Σr3 = [n(n+1)2]2
Mathematical induction: base case, assume true for n=k, prove for n=k+1
Divisibility: show f(k+1) - f(k) is divisible
Practice
Complete 30-35 practice questions
Focus on: Series formulas (12 questions), Induction (15 questions), Divisibility (8 questions)
Question types: Series calculations, proof writing
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Review Chapter Reviews 7 & 8
Week 10
|
of 12
Topics
Chapter 8: Proof (Part 2)
8.3 Using Mathematical Induction to Produce a Proof for a General Term of a Recurrence Relation
8.4 Proving Statements Involving Matrices
Key Points
Recurrence relations: prove formula for un using induction
Matrix proofs: prove properties using matrix algebra
Practice structured proof writing
Practice
Complete 30-35 practice questions
Focus on: Recurrence relations (15 questions), Matrix proofs (20 questions)
Question types: Proof writing, mathematical reasoning
PAST PAPERS: Complete 2 full past papers (timed)
Review Chapter Review 8 and Review Exercise 2
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 1 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 1
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 8 chapters of Further Pure Mathematics 1 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Complex Numbers (Part 1)
1.1 Imaginary and Complex Numbers
1.2 Multiplying Complex Numbers
Key Points
Complex number: z = a + bi, where i2 = -1
Adding/subtracting: (a+bi) ± (c+di) = (a±c) + (b±d)i
Multiplying: (a+bi)(c+di) = (ac-bd) + (ad+bc)i
Practice
Complete 20-25 practice questions
Focus on: Basic operations (25 questions)
Question types: Calculations, simplification
Review Chapter Review 1
Week 2
|
of 20
Topics
Chapter 1: Complex Numbers (Part 2)
1.3 Complex Conjugation
1.4 Argand Diagrams
Key Points
Conjugate: z̄ = a - bi, zz̄ = a2 + b2
Argand diagram: complex plane with real (x) and imaginary (y) axes
Practice
Complete 20-25 practice questions
Focus on: Conjugation (12 questions), Argand diagrams (13 questions)
Question types: Calculations, graph plotting
Review Chapter Review 1
Week 3
|
of 20
Topics
Chapter 1: Complex Numbers (Part 3)
1.5 Modulus and Argument
1.6 Modulus-Argument Form of Complex Numbers
Key Points
Modulus: |z| = √(a2 + b2) = r
Argument: arg(z) = θ = tan-1(ba)
Modulus-argument form: z = r(cos θ + i sin θ) = r cis θ
Practice
Complete 20-25 practice questions
Focus on: Modulus/argument (20 questions), Polar form (5 questions)
Question types: Calculations, conversions
Review Chapter Review 1
Week 4
|
of 20
Topics
Chapter 1: Complex Numbers (Part 4)
1.7 Roots of Quadratic Equations
1.8 Solving Cubic and Quartic Equations
Key Points
Quadratic formula: x = -b ± √(b2-4ac)2a
Factor theorem for complex roots
Practice
Complete 20-25 practice questions
Focus on: Complex roots (12 questions), Cubic/quartic (13 questions)
Question types: Solving equations
Review Chapter Review 1
Week 5
|
of 20
Topics
Chapter 2: Roots of Quadratic Equations
2.1 Roots of a Quadratic Equation
2.2 Forming Quadratic Equations with New Roots
Key Points
Sum of roots: α + β = -ba
Product of roots: αβ = ca
Forming equations: x2 - (sum)x + (product) = 0
Practice
Complete 20-25 practice questions
Focus on: Root relationships (15 questions), Forming equations (10 questions)
Question types: Relationships, forming equations
Review Chapter Review 2
Week 6
|
of 20
Topics
Chapter 3: Numerical Solutions of Equations (Part 1)
3.1 Locating Roots
3.2 Interval Bisection
Key Points
Change of sign: if f(a) and f(b) have opposite signs, root exists in (a,b)
Interval bisection: repeatedly halve interval containing root
Practice
Complete 20-25 practice questions
Focus on: Locating roots (10 questions), Bisection (15 questions)
Question types: Iterative methods, calculations
Review Chapter Review 3
Week 7
|
of 20
Topics
Chapter 3: Numerical Solutions of Equations (Part 2)
3.3 Linear Interpolation
3.4 The Newton-Raphson Method
Key Points
Linear interpolation: use similar triangles to estimate root
Newton-Raphson: xn+1 = xn - f(xn)f'(xn)
Practice
Complete 20-25 practice questions
Focus on: Interpolation (10 questions), Newton-Raphson (15 questions)
Question types: Iterative methods, accuracy
Review Chapter Review 3
Week 8
|
of 20
Topics
Chapter 4: Coordinate Systems (Part 1)
4.1 Parametric Equations
4.2 The General Equation of a Parabola
Key Points
Parametric equations: x = f(t), y = g(t)
Eliminating parameter: express t in terms of x or y
Parabola: y2 = 4ax (standard form)
Practice
Complete 20-25 practice questions
Focus on: Parametric equations (15 questions), Parabola (10 questions)
Question types: Curve sketching, elimination
Review Chapter Review 4
Week 9
|
of 20
Topics
Chapter 4: Coordinate Systems (Part 2)
4.3 The Equation for a Rectangular Hyperbola. The Equation of the Tangent and the Equation of the Normal
Key Points
Rectangular hyperbola: xy = c2
Tangent and normal: use differentiation
Practice
Complete 20-25 practice questions
Focus on: Hyperbola (15 questions), Tangent/normal (10 questions)
Question types: Curve sketching, tangent/normal
Review Chapter Review 4 and Review Exercise 1
Week 10
|
of 20
Topics
Chapter 5: Matrices (Part 1)
5.1 Introduction to Matrices
5.2 Matrix Multiplication
Key Points
Matrix: rectangular array of numbers
Order: m × n (m rows, n columns)
Matrix multiplication: (AB)ij = Σ AikBkj
Practice
Complete 20-25 practice questions
Focus on: Matrix basics (10 questions), Multiplication (15 questions)
Question types: Calculations, operations
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 5
Week 11
|
of 20
Topics
Chapter 5: Matrices (Part 2)
5.3 Determinants
5.4 Inverting a 2×2 Matrix
Key Points
Determinant: det(A) = ad - bc for 2×2 matrix
Inverse: A-1 = 1det(A) × [[d, -b], [-c, a]]
Practice
Complete 20-25 practice questions
Focus on: Determinants (12 questions), Inverses (13 questions)
Question types: Calculations
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 5
Week 12
|
of 20
Topics
Chapter 6: Transformations Using Matrices (Part 1)
6.1 Linear Transformations in Two Dimensions
6.2 Reflections and Rotations
Key Points
Linear transformation: maps points using matrix multiplication
Reflection matrices: in x-axis, y-axis, y=x, y=-x
Rotation matrices: R(θ) = [[cos θ, -sin θ], [sin θ, cos θ]]
Practice
Complete 20-25 practice questions
Focus on: Transformations (15 questions), Reflections/rotations (10 questions)
Question types: Transformations, geometry
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 6
Week 13
|
of 20
Topics
Chapter 6: Transformations Using Matrices (Part 2)
6.3 Enlargements and Stretches
6.4 Successive Transformations
6.5 The Inverse of a Linear Transformation
Key Points
Enlargement: scale factor k, matrix [[k, 0], [0, k]]
Stretch: in x-direction [[k, 0], [0, 1]], in y-direction [[1, 0], [0, k]]
Successive: apply transformations in order (right to left)
Practice
Complete 20-25 practice questions
Focus on: Enlargements/stretches (12 questions), Successive (13 questions)
Question types: Transformations
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6
Week 14
|
of 20
Topics
Chapter 7: Series
7.1 Sums of Natural Numbers
7.2 Sums of Squares and Cubes
Key Points
Sum of natural numbers: Σr = n(n+1)2
Sum of squares: Σr2 = n(n+1)(2n+1)6
Sum of cubes: Σr3 = [n(n+1)2]2
Practice
Complete 20-25 practice questions
Focus on: Series formulas (25 questions)
Question types: Series calculations
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7
Week 15
|
of 20
Topics
Chapter 8: Proof (Part 1)
8.1 Proof by Mathematical Induction
8.2 Proving Divisibility Results
Key Points
Mathematical induction: base case, assume true for n=k, prove for n=k+1
Divisibility: show f(k+1) - f(k) is divisible
Practice
Complete 20-25 practice questions
Focus on: Induction (15 questions), Divisibility (10 questions)
Question types: Proof writing
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Review Chapter Review 8
Week 16
|
of 20
Topics
Chapter 8: Proof (Part 2)
8.3 Using Mathematical Induction to Produce a Proof for a General Term of a Recurrence Relation
8.4 Proving Statements Involving Matrices
Key Points
Recurrence relations: prove formula for un using induction
Matrix proofs: prove properties using matrix algebra
Practice
Complete 20-25 practice questions
Focus on: Recurrence relations (12 questions), Matrix proofs (13 questions)
Question types: Proof writing, mathematical reasoning
PAST PAPERS: Complete 2 full past papers (timed)
Review Chapter Review 8 and Review Exercise 2
Week 17
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 30-40 mixed practice questions
PAST PAPERS: Complete 2 full past papers (timed)
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 18
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 2 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 2
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 8 chapters of Further Pure Mathematics 2. The plan builds advanced mathematical concepts including inequalities, series, complex numbers, differential equations, and polar coordinates. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics
Chapter 1: Inequalities
1.1 Algebraic Methods
1.2 Using Graphs to Solve Inequalities
1.3 Modulus Inequalities
Key Points
Solving inequalities: reverse sign when multiplying/dividing by negative
Critical values: find where expression equals zero
Modulus: |x| = x if x ≥ 0, |x| = -x if x < 0
|x| < a means -a < x < a
|x| > a means x < -a or x > a
Practice
Complete 25-30 practice questions
Focus on: Algebraic methods (10 questions), Graphical methods (10 questions), Modulus (10 questions)
Question types: Solving inequalities, sketching regions
Review Chapter Review 1
Week 2
|
of 12
Topics
Chapter 2: Series
2.1 The Method of Differences
Chapter 3: Complex Numbers (Part 1)
3.1 Exponential Form of Complex Numbers
3.2 Multiplying and Dividing Complex Numbers
Key Points
Method of differences: telescoping series, canceling terms
Exponential form: z = reiθ = r(cos θ + i sin θ)
Multiplying: |z1z2| = |z1||z2|, arg(z1z2) = arg(z1) + arg(z2)
Dividing: |z1/z2| = |z1|/|z2|, arg(z1/z2) = arg(z1) - arg(z2)
Practice
Complete 30-35 practice questions
Focus on: Method of differences (12 questions), Exponential form (12 questions), Operations (11 questions)
Question types: Series summation, complex number operations
Review Chapter Reviews 2 & 3
Week 3
|
of 12
Topics
Chapter 3: Complex Numbers (Part 2)
3.3 De Moivre's Theorem
3.4 Trigonometric Identities
3.5 n-th Roots of a Complex Number
Key Points
De Moivre's: (cos θ + i sin θ)n = cos(nθ) + i sin(nθ)
Using De Moivre's to find cos(nθ) and sin(nθ)
n-th roots: z1/n = r1/n[cos((θ+2kπ)/n) + i sin((θ+2kπ)/n)], k = 0,1,...,n-1
Practice
Complete 30-35 practice questions
Focus on: De Moivre's (12 questions), Trigonometric identities (12 questions), n-th roots (11 questions)
Question types: Complex number calculations, identity proofs
Review Chapter Review 3
Week 4
|
of 12
Topics
Chapter 4: Further Argand Diagrams
4.1 Loci in an Argand Diagram
4.2 Further Loci in an Argand Diagram
4.3 Regions in an Argand Diagram
4.4 Further Regions in an Argand Diagram
4.5 Transformations of the Complex Plane
Key Points
Loci: |z - a| = r (circle), |z - a| = |z - b| (perpendicular bisector)
arg(z - a) = θ (half-line)
Regions: |z - a| < r (inside circle), |z - a| > r (outside circle)
Transformations: translation, rotation, enlargement
Practice
Complete 30-35 practice questions
Focus on: Loci (15 questions), Regions (12 questions), Transformations (8 questions)
Question types: Sketching, geometric interpretation
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-4 topics)
Review Chapter Review 4 and Review Exercise 1
Week 5
|
of 12
Topics
Chapter 5: First-Order Differential Equations
5.1 Solving First-Order Differential Equations with Separable Variables
5.2 First-Order Linear Differential Equations of the form (dydx + Py = Q), where P and Q are functions of x
5.3 Reducible First-Order Differential Equations
Key Points
Separable: dydx = f(x)g(y), separate and integrate
Linear: use integrating factor I = e∫P dx
Solution: yI = ∫QI dx + C
Reducible: use substitution to convert to standard form
Practice
Complete 30-35 practice questions
Focus on: Separable (12 questions), Linear (15 questions), Reducible (8 questions)
Question types: Solving differential equations, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 5
Week 6
|
of 12
Topics
Chapter 6: Second-Order Differential Equations (Part 1)
6.1 Second-Order Homogeneous Differential Equations
6.2 Second-Order Non-Homogeneous Differential Equations
Key Points
Homogeneous: ay'' + by' + cy = 0, solve auxiliary equation am2 + bm + c = 0
Real distinct roots: y = Aem1x + Bem2x
Real equal roots: y = (A + Bx)emx
Complex roots: y = eαx[A cos(βx) + B sin(βx)]
Non-homogeneous: find particular integral, add to complementary function
Practice
Complete 30-35 practice questions
Focus on: Homogeneous (15 questions), Non-homogeneous (20 questions)
Question types: Solving differential equations, finding particular integrals
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 6
Week 7
|
of 12
Topics
Chapter 6: Second-Order Differential Equations (Part 2)
6.3 Using Boundary Conditions
6.4 Reducible Second-Order Differential Equations
Chapter 7: Maclaurin and Taylor Series (Part 1)
7.1 Higher Derivatives
7.2 Maclaurin Series
Key Points
Boundary conditions: use to find constants A and B
Reducible: use substitution p = dydx to reduce order
Maclaurin: f(x) = f(0) + f'(0)x + f''(0)x22! + ...
Standard series: ex, sin x, cos x, ln(1+x), (1+x)n
Practice
Complete 30-35 practice questions
Focus on: Boundary conditions (10 questions), Reducible (10 questions), Maclaurin (15 questions)
Question types: Solving with conditions, series expansion
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Reviews 6 & 7
Week 8
|
of 12
Topics
Chapter 7: Maclaurin and Taylor Series (Part 2)
7.3 Series Expansions of Compound Functions
7.4 Taylor Series
7.5 Series Solutions of Differential Equations
Key Points
Compound functions: substitute into standard series
Taylor: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)22! + ...
Series solutions: assume y = Σanxn, find recurrence relation
Practice
Complete 30-35 practice questions
Focus on: Compound functions (12 questions), Taylor (12 questions), Series solutions (11 questions)
Question types: Series expansion, solving differential equations
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 7
Week 9
|
of 12
Topics
Chapter 8: Polar Coordinates
8.1 Polar Coordinates and Equations
8.2 Sketching Curves
8.3 Area Enclosed by a Polar Curve
8.4 Tangents to Polar Curves
Key Points
Polar coordinates: (r, θ) where r = distance from origin, θ = angle
Conversion: x = r cos θ, y = r sin θ, r2 = x2 + y2, tan θ = yx
Area: A = 12∫r2 dθ
Tangents: use dydx = dy/dθdx/dθ
Practice
Complete 30-35 practice questions
Focus on: Coordinates (10 questions), Sketching (10 questions), Area (10 questions), Tangents (5 questions)
Question types: Curve sketching, integration, differentiation
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Review Chapter Review 8 and Review Exercise 2
Week 10
|
of 12
Exam Preparation
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 2 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 2
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 8 chapters of Further Pure Mathematics 2 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics
Chapter 1: Inequalities (Part 1)
1.1 Algebraic Methods
1.2 Using Graphs to Solve Inequalities
Key Points
Solving inequalities: reverse sign when multiplying/dividing by negative
Critical values: find where expression equals zero
Graphical methods: sketch curves to visualize solutions
Practice
Complete 20-25 practice questions
Focus on: Algebraic methods (12 questions), Graphical methods (13 questions)
Question types: Solving inequalities, sketching regions
Review Chapter Review 1
Week 2
|
of 20
Topics
Chapter 1: Inequalities (Part 2)
1.3 Modulus Inequalities
Chapter 2: Series
2.1 The Method of Differences
Key Points
Modulus: |x| = x if x ≥ 0, |x| = -x if x < 0
|x| < a means -a < x < a
Method of differences: telescoping series, canceling terms
Practice
Complete 20-25 practice questions
Focus on: Modulus (12 questions), Method of differences (13 questions)
Question types: Solving inequalities, series summation
Review Chapter Reviews 1 & 2
Week 3
|
of 20
Topics
Chapter 3: Complex Numbers (Part 1)
3.1 Exponential Form of Complex Numbers
3.2 Multiplying and Dividing Complex Numbers
Key Points
Exponential form: z = reiθ = r(cos θ + i sin θ)
Multiplying: |z1z2| = |z1||z2|, arg(z1z2) = arg(z1) + arg(z2)
Dividing: |z1/z2| = |z1|/|z2|, arg(z1/z2) = arg(z1) - arg(z2)
Practice
Complete 20-25 practice questions
Focus on: Exponential form (12 questions), Operations (13 questions)
Question types: Complex number operations, conversions
Review Chapter Review 3
Week 4
|
of 20
Topics
Chapter 3: Complex Numbers (Part 2)
3.3 De Moivre's Theorem
3.4 Trigonometric Identities
Key Points
De Moivre's: (cos θ + i sin θ)n = cos(nθ) + i sin(nθ)
Using De Moivre's to find cos(nθ) and sin(nθ)
Practice
Complete 20-25 practice questions
Focus on: De Moivre's (12 questions), Trigonometric identities (13 questions)
Question types: Complex number calculations, identity proofs
Review Chapter Review 3
Week 5
|
of 20
Topics
Chapter 3: Complex Numbers (Part 3)
3.5 n-th Roots of a Complex Number
Chapter 4: Further Argand Diagrams (Part 1)
4.1 Loci in an Argand Diagram
4.2 Further Loci in an Argand Diagram
Key Points
n-th roots: z1/n = r1/n[cos((θ+2kπ)/n) + i sin((θ+2kπ)/n)], k = 0,1,...,n-1
Loci: |z - a| = r (circle), |z - a| = |z - b| (perpendicular bisector)
arg(z - a) = θ (half-line)
Practice
Complete 20-25 practice questions
Focus on: n-th roots (10 questions), Loci (15 questions)
Question types: Finding roots, sketching loci
Review Chapter Reviews 3 & 4
Week 6
|
of 20
Topics
Chapter 4: Further Argand Diagrams (Part 2)
4.3 Regions in an Argand Diagram
4.4 Further Regions in an Argand Diagram
4.5 Transformations of the Complex Plane
Key Points
Regions: |z - a| < r (inside circle), |z - a| > r (outside circle)
Transformations: translation, rotation, enlargement
Practice
Complete 20-25 practice questions
Focus on: Regions (15 questions), Transformations (10 questions)
Question types: Sketching, geometric interpretation
Review Chapter Review 4 and Review Exercise 1
Week 7
|
of 20
Topics
Chapter 5: First-Order Differential Equations (Part 1)
5.1 Solving First-Order Differential Equations with Separable Variables
5.2 First-Order Linear Differential Equations of the form (dydx + Py = Q), where P and Q are functions of x
Key Points
Separable: dydx = f(x)g(y), separate and integrate
Linear: use integrating factor I = e∫P dx
Solution: yI = ∫QI dx + C
Practice
Complete 20-25 practice questions
Focus on: Separable (12 questions), Linear (13 questions)
Question types: Solving differential equations
Review Chapter Review 5
Week 8
|
of 20
Topics
Chapter 5: First-Order Differential Equations (Part 2)
5.3 Reducible First-Order Differential Equations
Chapter 6: Second-Order Differential Equations (Part 1)
6.1 Second-Order Homogeneous Differential Equations
Key Points
Reducible: use substitution to convert to standard form
Homogeneous: ay'' + by' + cy = 0, solve auxiliary equation am2 + bm + c = 0
Real distinct roots: y = Aem1x + Bem2x
Practice
Complete 20-25 practice questions
Focus on: Reducible (10 questions), Homogeneous (15 questions)
Question types: Solving differential equations
Review Chapter Reviews 5 & 6
Week 9
|
of 20
Topics
Chapter 6: Second-Order Differential Equations (Part 2)
6.2 Second-Order Non-Homogeneous Differential Equations
6.3 Using Boundary Conditions
6.4 Reducible Second-Order Differential Equations
Key Points
Real equal roots: y = (A + Bx)emx
Complex roots: y = eαx[A cos(βx) + B sin(βx)]
Non-homogeneous: find particular integral, add to complementary function
Boundary conditions: use to find constants A and B
Practice
Complete 20-25 practice questions
Focus on: Non-homogeneous (12 questions), Boundary conditions (8 questions), Reducible (5 questions)
Question types: Solving differential equations, finding particular integrals
Review Chapter Review 6
Week 10
|
of 20
Topics
Chapter 7: Maclaurin and Taylor Series (Part 1)
7.1 Higher Derivatives
7.2 Maclaurin Series
Key Points
Maclaurin: f(x) = f(0) + f'(0)x + f''(0)x22! + ...
Standard series: ex, sin x, cos x, ln(1+x), (1+x)n
Practice
Complete 20-25 practice questions
Focus on: Higher derivatives (10 questions), Maclaurin (15 questions)
Question types: Series expansion
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-6 topics)
Review Chapter Review 7
Week 11
|
of 20
Topics
Chapter 7: Maclaurin and Taylor Series (Part 2)
7.3 Series Expansions of Compound Functions
7.4 Taylor Series
7.5 Series Solutions of Differential Equations
Key Points
Compound functions: substitute into standard series
Taylor: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)22! + ...
Series solutions: assume y = Σanxn, find recurrence relation
Practice
Complete 20-25 practice questions
Focus on: Compound functions (8 questions), Taylor (10 questions), Series solutions (7 questions)
Question types: Series expansion, solving differential equations
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 7
Week 12
|
of 20
Topics
Chapter 8: Polar Coordinates (Part 1)
8.1 Polar Coordinates and Equations
8.2 Sketching Curves
Key Points
Polar coordinates: (r, θ) where r = distance from origin, θ = angle
Conversion: x = r cos θ, y = r sin θ, r2 = x2 + y2, tan θ = yx
Practice
Complete 20-25 practice questions
Focus on: Coordinates (12 questions), Sketching (13 questions)
Question types: Curve sketching, conversions
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 8
Week 13
|
of 20
Topics
Chapter 8: Polar Coordinates (Part 2)
8.3 Area Enclosed by a Polar Curve
8.4 Tangents to Polar Curves
Key Points
Area: A = 12∫r2 dθ
Tangents: use dydx = dy/dθdx/dθ
Practice
Complete 20-25 practice questions
Focus on: Area (12 questions), Tangents (13 questions)
Question types: Integration, differentiation
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 8 and Review Exercise 2
Week 14
|
of 20
Revision & Consolidation
Comprehensive Review
Review all chapters 1-8
Identify weak areas
Strengthen problem-solving skills
Practice
Complete 30-40 mixed practice questions
PAST PAPERS: Solve 25-30 individual questions from past papers
Mark your work using mark schemes
Create error log of common mistakes
Review examiner reports for common pitfalls
Week 15
|
of 20
Revision & Consolidation
Continue comprehensive review
Practice
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 16
|
of 20
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 17
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 18
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 3 - 3 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 3
Duration:
12 Weeks (3 Months)
Recommended:
8-10 hours per week
Study Plan Overview
This 3-month intensive plan covers all 6 chapters of Further Pure Mathematics 3. The plan builds advanced mathematical concepts including hyperbolic functions, coordinate systems, advanced calculus, vectors, and matrix algebra. Past paper practice begins in Week 5 with individual questions, gradually increasing to full papers by Week 10.
Week 1
|
of 12
Topics Covered
Chapter 1: Hyperbolic Functions
1.1 Introduction to Hyperbolic Functions | 1.2 Sketching Graphs of Hyperbolic Functions | 1.3 Inverse Hyperbolic Functions | 1.4 Identities and Equations
Key Points to Learn
sinh x = ex - e-x2, cosh x = ex + e-x2, tanh x = sinh xcosh x
cosh²x - sinh²x = 1
1 - tanh²x = sech²x
Inverse functions: arsinh, arcosh, artanh
Actions & Practice
Complete 25-30 practice questions
Focus on: Definitions (8 questions), Graphs (8 questions), Inverses (7 questions), Identities (7 questions)
Question types: Calculations, graph sketching, solving equations
Review Chapter Review 1
Week 2
|
of 12
Topics Covered
Chapter 2: Further Coordinate Systems
2.1 Ellipses | 2.2 Hyperbolas | 2.3 Eccentricity | 2.4 Tangents and Normals to an Ellipse | 2.5 Tangents and Normals to a Hyperbola | 2.6 Loci
Key Points to Learn
Ellipse: x²a² + y²b² = 1, foci at (±c, 0) where c² = a² - b²
Hyperbola: x²a² - y²b² = 1, foci at (±c, 0) where c² = a² + b²
Eccentricity: e = ca (ellipse: 0 < e < 1, hyperbola: e > 1)
Tangents and normals: use differentiation
Actions & Practice
Complete 30-35 practice questions
Focus on: Ellipses (10 questions), Hyperbolas (10 questions), Eccentricity (5 questions), Tangents/normals (10 questions)
Question types: Curve sketching, differentiation, geometric properties
Review Chapter Review 2
Week 3
|
of 12
Topics Covered
Chapter 3: Differentiation
3.1 Differentiating Hyperbolic Functions | 3.2 Differentiating Inverse Hyperbolic Functions | 3.3 Differentiating Inverse Trigonometric Functions
Key Points to Learn
ddx(sinh x) = cosh x, ddx(cosh x) = sinh x, ddx(tanh x) = sech²x
ddx(arsinh x) = 1√(1+x²), ddx(arcosh x) = 1√(x²-1), ddx(artanh x) = 11-x²
ddx(arcsin x) = 1√(1-x²), ddx(arccos x) = -1√(1-x²), ddx(arctan x) = 11+x²
Actions & Practice
Complete 30-35 practice questions
Focus on: Hyperbolic (12 questions), Inverse hyperbolic (10 questions), Inverse trig (13 questions)
Question types: Differentiation, chain rule applications
Review Chapter Review 3
Week 4
|
of 12
Topics Covered
Chapter 4: Integration (Part 1)
4.1 Standard Integrals | 4.2 Integration | 4.3 Trigonometric and Hyperbolic Substitutions
Key Points to Learn
Standard integrals: ∫sinh x dx = cosh x + C, ∫cosh x dx = sinh x + C
Substitutions: x = a sin θ, x = a cosh u, x = a sinh u
Partial fractions, integration by parts
Actions & Practice
Complete 30-35 practice questions
Focus on: Standard integrals (10 questions), Integration techniques (15 questions), Substitutions (10 questions)
Question types: Integration, substitution methods
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-3 topics)
Review Chapter Review 4
Week 5
|
of 12
Topics Covered
Chapter 4: Integration (Part 2)
4.4 Integrating Expressions | 4.5 Integrating Inverse Trigonometric and Hyperbolic Functions | 4.6 Deriving and Using Reduction Formulae | 4.7 Finding the Length of an Arc of a Curve | 4.8 Finding the Area of a Surface of Revolution
Key Points to Learn
Reduction formulae: In in terms of In-2 or In-1
Arc length: L = ∫√(1 + (dydx)²) dx
Surface area: S = ∫2πy√(1 + (dydx)²) dx
Actions & Practice
Complete 30-35 practice questions
Focus on: Inverse functions (10 questions), Reduction formulae (12 questions), Arc length (8 questions), Surface area (5 questions)
Question types: Integration, applications
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 4 and Review Exercise 1
Week 6
|
of 12
Topics Covered
Chapter 5: Vectors (Part 1)
5.1 Vector Product | 5.2 Finding Areas | 5.3 Scalar Triple Product
Key Points to Learn
Vector product: a × b = |a||b|sin θ n̂, where n̂ is unit vector perpendicular to both
a × b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)
Area of parallelogram = |a × b|
Scalar triple product: a · (b × c) = volume of parallelepiped
Actions & Practice
Complete 30-35 practice questions
Focus on: Vector product (12 questions), Areas (10 questions), Scalar triple (13 questions)
Question types: Vector calculations, geometric applications
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 5
Week 7
|
of 12
Topics Covered
Chapter 5: Vectors (Part 2)
5.4 Straight Lines | 5.5 Vector Planes | 5.6 Solving Geometric Problems
Key Points to Learn
Line: r = a + λb, where a is point, b is direction vector
Plane: r · n = d, where n is normal vector
Distance from point to plane: |ax₀ + by₀ + cz₀ + d|√(a² + b² + c²)
Actions & Practice
Complete 30-35 practice questions
Focus on: Straight lines (12 questions), Planes (12 questions), Geometric problems (11 questions)
Question types: Vector equations, geometric applications
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 5
Week 8
|
of 12
Topics Covered
Chapter 6: Further Matrix Algebra (Part 1)
6.1 Transposing a Matrix | 6.2 The Determinant of a (3 × 3) Matrix | 6.3 The Inverse of a (3 × 3) Matrix (where it exists)
Key Points to Learn
Transpose: (AT)ij = Aji
3×3 determinant: use cofactor expansion or Sarrus' rule
Inverse: A-1 = 1det(A) × adj(A), where adj(A) is adjugate matrix
Actions & Practice
Complete 30-35 practice questions
Focus on: Transpose (8 questions), Determinant (12 questions), Inverse (15 questions)
Question types: Matrix operations, calculations
PAST PAPERS: Solve 25-30 individual questions from past papers
Review Chapter Review 6
Week 9
|
of 12
Topics Covered
Chapter 6: Further Matrix Algebra (Part 2)
6.4 Using Matrices to Represent Linear Transformations in 3 Dimensions | 6.5 Using Inverse Matrices to Reverse the Effect of a Linear Transformation | 6.6 The Eigenvalues and Eigenvectors of (2 × 2) and (3 × 3) Matrices | 6.7 Reducing a Symmetric Matrix to Diagonal Form
Key Points to Learn
3D transformations: rotation, reflection, scaling
Eigenvalues: solve det(A - λI) = 0
Eigenvectors: solve (A - λI)v = 0 for each eigenvalue
Diagonalization: A = PDP-1, where D is diagonal matrix of eigenvalues
Actions & Practice
Complete 30-35 practice questions
Focus on: Transformations (10 questions), Eigenvalues/eigenvectors (15 questions), Diagonalization (10 questions)
Question types: Matrix operations, transformations, eigenvalue problems
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Review Chapter Review 6 and Review Exercise 2
Week 10
|
of 12
Exam Preparation
Full Past Paper Practice
Complete full papers under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Mark strictly using mark schemes
Analyze mistakes and patterns
Review examiner reports
Practice presentation and working clearly
Week 11
|
of 12
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers (last 3-5 years)
Time yourself strictly
Review all incorrect answers
Practice difficult question types
Week 12
|
of 12
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 4, progress to full papers by Week 10.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.
Math With Fahim
Edexcel IAL Further Pure Mathematics 3 - 5 Month Study Plan
Student Name:
[Your Name]
Email:
[Your Email]
Subject:
Further Pure Mathematics 3
Duration:
20 Weeks (5 Months)
Recommended:
6-8 hours per week
Study Plan Overview
This 5-month comprehensive plan covers all 6 chapters of Further Pure Mathematics 3 at a more relaxed pace. The plan allows for deeper understanding, more practice, and gradual skill building. Past paper practice begins in Week 10 with individual questions, gradually increasing to full papers by Week 16.
Week 1
|
of 20
Topics Covered
Chapter 1: Hyperbolic Functions (Part 1)
1.1 Introduction to Hyperbolic Functions | 1.2 Sketching Graphs of Hyperbolic Functions
Key Points to Learn
sinh x = ex - e-x2, cosh x = ex + e-x2, tanh x = sinh xcosh x
Properties and graphs of hyperbolic functions
Actions & Practice
Complete 20-25 practice questions
Focus on: Definitions (12 questions), Graphs (13 questions)
Question types: Calculations, graph sketching
Review Chapter Review 1
Week 2
|
of 20
Topics Covered
Chapter 1: Hyperbolic Functions (Part 2)
1.3 Inverse Hyperbolic Functions | 1.4 Identities and Equations
Key Points to Learn
cosh²x - sinh²x = 1
1 - tanh²x = sech²x
Inverse functions: arsinh, arcosh, artanh
Actions & Practice
Complete 20-25 practice questions
Focus on: Inverses (12 questions), Identities (13 questions)
Question types: Solving equations, proving identities
Review Chapter Review 1
Week 3
|
of 20
Topics Covered
Chapter 2: Further Coordinate Systems (Part 1)
2.1 Ellipses | 2.2 Hyperbolas | 2.3 Eccentricity
Key Points to Learn
Ellipse: x²a² + y²b² = 1, foci at (±c, 0) where c² = a² - b²
Hyperbola: x²a² - y²b² = 1, foci at (±c, 0) where c² = a² + b²
Eccentricity: e = ca (ellipse: 0 < e < 1, hyperbola: e > 1)
Actions & Practice
Complete 20-25 practice questions
Focus on: Ellipses (8 questions), Hyperbolas (9 questions), Eccentricity (8 questions)
Question types: Curve sketching, geometric properties
Review Chapter Review 2
Week 4
|
of 20
Topics Covered
Chapter 2: Further Coordinate Systems (Part 2)
2.4 Tangents and Normals to an Ellipse | 2.5 Tangents and Normals to a Hyperbola | 2.6 Loci
Key Points to Learn
Tangents and normals: use differentiation
Loci: geometric paths
Actions & Practice
Complete 20-25 practice questions
Focus on: Tangents/normals (15 questions), Loci (10 questions)
Question types: Differentiation, geometric applications
Review Chapter Review 2
Week 5
|
of 20
Topics Covered
Chapter 3: Differentiation
3.1 Differentiating Hyperbolic Functions | 3.2 Differentiating Inverse Hyperbolic Functions | 3.3 Differentiating Inverse Trigonometric Functions
Key Points to Learn
ddx(sinh x) = cosh x, ddx(cosh x) = sinh x, ddx(tanh x) = sech²x
ddx(arsinh x) = 1√(1+x²), ddx(arcosh x) = 1√(x²-1), ddx(artanh x) = 11-x²
ddx(arcsin x) = 1√(1-x²), ddx(arccos x) = -1√(1-x²), ddx(arctan x) = 11+x²
Actions & Practice
Complete 20-25 practice questions
Focus on: Hyperbolic (8 questions), Inverse hyperbolic (8 questions), Inverse trig (9 questions)
Question types: Differentiation, chain rule applications
Review Chapter Review 3
Week 6
|
of 20
Topics Covered
Chapter 4: Integration (Part 1)
4.1 Standard Integrals | 4.2 Integration | 4.3 Trigonometric and Hyperbolic Substitutions
Key Points to Learn
Standard integrals: ∫sinh x dx = cosh x + C, ∫cosh x dx = sinh x + C
Substitutions: x = a sin θ, x = a cosh u, x = a sinh u
Actions & Practice
Complete 20-25 practice questions
Focus on: Standard integrals (10 questions), Integration techniques (8 questions), Substitutions (7 questions)
Question types: Integration, substitution methods
Review Chapter Review 4
Week 7
|
of 20
Topics Covered
Chapter 4: Integration (Part 2)
4.4 Integrating Expressions | 4.5 Integrating Inverse Trigonometric and Hyperbolic Functions | 4.6 Deriving and Using Reduction Formulae
Key Points to Learn
Partial fractions, integration by parts
Reduction formulae: In in terms of In-2 or In-1
Actions & Practice
Complete 20-25 practice questions
Focus on: Expressions (8 questions), Inverse functions (8 questions), Reduction formulae (9 questions)
Question types: Integration, reduction formulae
Review Chapter Review 4
Week 8
|
of 20
Topics Covered
Chapter 4: Integration (Part 3)
4.7 Finding the Length of an Arc of a Curve | 4.8 Finding the Area of a Surface of Revolution
Key Points to Learn
Arc length: L = ∫√(1 + (dydx)²) dx
Surface area: S = ∫2πy√(1 + (dydx)²) dx
Actions & Practice
Complete 20-25 practice questions
Focus on: Arc length (12 questions), Surface area (13 questions)
Question types: Integration, applications
Review Chapter Review 4 and Review Exercise 1
Week 9
|
of 20
Topics Covered
Chapter 5: Vectors (Part 1)
5.1 Vector Product | 5.2 Finding Areas | 5.3 Scalar Triple Product
Key Points to Learn
Vector product: a × b = |a||b|sin θ n̂
a × b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)
Area of parallelogram = |a × b|
Scalar triple product: a · (b × c) = volume of parallelepiped
Actions & Practice
Complete 20-25 practice questions
Focus on: Vector product (8 questions), Areas (8 questions), Scalar triple (9 questions)
Question types: Vector calculations, geometric applications
Review Chapter Review 5
Week 10
|
of 20
Topics Covered
Chapter 5: Vectors (Part 2)
5.4 Straight Lines | 5.5 Vector Planes | 5.6 Solving Geometric Problems
Key Points to Learn
Line: r = a + λb, where a is point, b is direction vector
Plane: r · n = d, where n is normal vector
Distance from point to plane: |ax₀ + by₀ + cz₀ + d|√(a² + b² + c²)
Actions & Practice
Complete 20-25 practice questions
Focus on: Straight lines (8 questions), Planes (9 questions), Geometric problems (8 questions)
Question types: Vector equations, geometric applications
START PAST PAPER PRACTICE: Solve 10-12 individual questions from past papers (Chapters 1-5 topics)
Review Chapter Review 5
Week 11
|
of 20
Topics Covered
Chapter 6: Further Matrix Algebra (Part 1)
6.1 Transposing a Matrix | 6.2 The Determinant of a (3 × 3) Matrix | 6.3 The Inverse of a (3 × 3) Matrix (where it exists)
Key Points to Learn
Transpose: (AT)ij = Aji
3×3 determinant: use cofactor expansion or Sarrus' rule
Inverse: A-1 = 1det(A) × adj(A)
Actions & Practice
Complete 20-25 practice questions
Focus on: Transpose (6 questions), Determinant (10 questions), Inverse (9 questions)
Question types: Matrix operations, calculations
PAST PAPERS: Solve 15-18 individual questions from past papers
Review Chapter Review 6
Week 12
|
of 20
Topics Covered
Chapter 6: Further Matrix Algebra (Part 2)
6.4 Using Matrices to Represent Linear Transformations in 3 Dimensions | 6.5 Using Inverse Matrices to Reverse the Effect of a Linear Transformation
Key Points to Learn
3D transformations: rotation, reflection, scaling
Inverse transformations: use inverse matrix
Actions & Practice
Complete 20-25 practice questions
Focus on: Transformations (12 questions), Inverse transformations (13 questions)
Question types: Matrix operations, transformations
PAST PAPERS: Solve 18-20 individual questions from past papers
Review Chapter Review 6
Week 13
|
of 20
Topics Covered
Chapter 6: Further Matrix Algebra (Part 3)
6.6 The Eigenvalues and Eigenvectors of (2 × 2) and (3 × 3) Matrices | 6.7 Reducing a Symmetric Matrix to Diagonal Form
Key Points to Learn
Eigenvalues: solve det(A - λI) = 0
Eigenvectors: solve (A - λI)v = 0 for each eigenvalue
Diagonalization: A = PDP-1, where D is diagonal matrix of eigenvalues
Actions & Practice
Complete 20-25 practice questions
Focus on: Eigenvalues/eigenvectors (15 questions), Diagonalization (10 questions)
Question types: Matrix operations, eigenvalue problems
PAST PAPERS: Solve 20-25 individual questions from past papers
Review Chapter Review 6 and Review Exercise 2
Week 14
|
of 20
Revision & Consolidation
Comprehensive Review - All chapters 1-6
Practice
Complete 30-40 mixed practice questions
PAST PAPERS: Solve 25-30 individual questions from past papers
Create error log, review formulas
Week 15
|
of 20
Revision & Consolidation
Focus on full paper practice
Practice
PAST PAPERS: Attempt 1 full past paper (timed - 1.5 hours)
Mark strictly, analyze mistakes
Week 16
|
of 20
Exam Preparation
Full past paper practice under exam conditions
Practice
PAST PAPERS: Complete 2 full past papers (timed - 1.5 hours each)
Focus on recent papers, time management
Mark strictly using mark schemes
Week 17
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Mark strictly, analyze mistakes
Week 18
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers, time management
Week 19
|
of 20
Intensive Exam Practice
Focus on full paper practice and exam technique
Practice
PAST PAPERS: Complete 3 full past papers (timed)
Focus on recent papers, time management
Week 20
|
of 20
Final Preparation
Final review and exam readiness
Practice
PAST PAPERS: Complete 2 full past papers (timed)
Final review of all formulas
Review error log
Light practice on weak areas
Mental preparation and exam strategy
Ensure you understand exam format and requirements
Study Tips
Time Management
Allocate specific times for each topic. Use a timer when practicing past papers.
Regular Review
Review previous topics weekly to maintain retention.
Past Papers
Start with individual questions in Week 10, progress to full papers by Week 16.
Mark Schemes
Always mark your work using official mark schemes to understand expectations.