Pure Mathematics — Papers 1 & 2
1. Proof
Yr 1 & 2
1.1
Proof by Deduction
Notes Practice
1.2
Proof by Exhaustion
Notes Practice
1.3
Disproof by Counter Example
Notes Practice
1.4
Proof by Contradiction
Notes Practice
2. Algebra and Functions
Yr 1 & 2
2a
Algebraic Expressions (Yr 1)
Notes Practice
2b
Quadratics (Yr 1)
Notes Practice
2c
Equations & Inequalities (Yr 1)
Notes Practice
2d
Graphs & Transformations (Yr 1)
Notes Practice
2e
Algebraic Methods (Yr 2)
Notes Practice
2f
Functions & Graphs (Yr 2)
Notes Practice
2g
Partial Fractions (Yr 2)
Notes Practice
2h
Modulus Function (Yr 2)
Notes Practice
2i
Composite & Inverse Functions (Yr 2)
Notes Practice
2j
Parametric Equations (Yr 2)
Notes Practice
3. Coordinate Geometry
Year 1
3a
Straight Line Graphs
Notes Practice
3b
Circles
Notes Practice
3c
Circles and Lines
Notes Practice
4. Sequences and Series
Yr 1 & 2
4a
Binomial Expansion (Yr 1)
Notes Practice
4b
Arithmetic Sequences & Series (Yr 2)
Notes Practice
4c
Geometric Sequences & Series (Yr 2)
Notes Practice
4d
Sigma Notation & Recurrence (Yr 2)
Notes Practice
4e
Binomial Expansion: Negative & Fractional (Yr 2)
Notes Practice
5. Trigonometry
Yr 1 & 2
5a
Trigonometric Ratios (Yr 1)
Notes Practice
5b
Trigonometric Identities & Equations (Yr 1)
Notes Practice
5c
Radians (Yr 2)
Notes Practice
5d
Trigonometric Functions: sec, cosec, cot (Yr 2)
Notes Practice
5e
Addition Formulae (Yr 2)
Notes Practice
5f
Double Angle Formulae (Yr 2)
Notes Practice
5g
Harmonic Form: R cos/sin (Yr 2)
Notes Practice
5h
Proving Trigonometric Identities (Yr 2)
Notes Practice
6. Exponentials and Logarithms
Year 1
6a
Exponential Functions & y = eˣ
Notes Practice
6b
Logarithms & Laws of Logs
Notes Practice
6c
Solving Equations Using Logarithms
Notes Practice
6d
Logarithms & Non-Linear Data
Notes Practice
7. Differentiation
Yr 1 & 2
7a
Differentiation from First Principles (Yr 1)
Notes Practice
7b
Differentiating xⁿ, Tangents & Normals (Yr 1)
Notes Practice
7c
Stationary Points & Modelling (Yr 1)
Notes Practice
7d
Chain, Product & Quotient Rules (Yr 2)
Notes Practice
7e
Differentiating Trig, Exponentials & Logs (Yr 2)
Notes Practice
7f
Implicit & Parametric Differentiation (Yr 2)
Notes Practice
7g
Connected Rates of Change (Yr 2)
Notes Practice
8. Integration
Yr 1 & 2
8a
Integrating xⁿ & Indefinite Integrals (Yr 1)
Notes Practice
8b
Definite Integrals & Areas (Yr 1)
Notes Practice
8c
Integrating Standard Functions (Yr 2)
Notes Practice
8d
Integration by Substitution (Yr 2)
Notes Practice
8e
Integration by Parts (Yr 2)
Notes Practice
8f
Trapezium Rule (Yr 2)
Notes Practice
8g
Differential Equations (Yr 2)
Notes Practice
9. Numerical Methods
Year 2
9a
Locating Roots (Change of Sign)
Notes Practice
9b
Iteration: x = g(x)
Notes Practice
9c
The Newton–Raphson Method
Notes Practice
9d
Applications to Modelling
Notes Practice
10. Vectors
Yr 1 & 2
10a
2D Vectors & Position Vectors (Yr 1)
Notes Practice
10b
Solving Geometric Problems (Yr 1)
Notes Practice
10c
3D Vectors & Coordinates (Yr 2)
Notes Practice
10d
Vectors in Mechanics (Yr 2)
Notes Practice
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Statistics — Paper 3, Section A
S1. Statistical Sampling
Year 1
S1a
Populations, Samples & Sampling Methods
Notes Practice
S1b
Types of Data
Notes Practice
S1c
The Large Data Set
Notes Practice
S2. Data Presentation & Interpretation
Yr 1 & 2
S2a
Measures of Central Tendency & Spread (Yr 1)
Notes Practice
S2b
Representations of Data (Yr 1)
Notes Practice
S2c
Correlation & Regression (Yr 1)
Notes Practice
S2d
Exponential Models & PMCC (Yr 2)
Notes Practice
S2e
Hypothesis Testing for Correlation (Yr 2)
Notes Practice
S3. Probability
Yr 1 & 2
S3a
Venn Diagrams & Probability Rules (Yr 1)
Notes Practice
S3b
Tree Diagrams & Independence (Yr 1)
Notes Practice
S3c
Conditional Probability (Yr 2)
Notes Practice
S3d
Set Notation & Probability Formulae (Yr 2)
Notes Practice
S4. Statistical Distributions
Yr 1 & 2
S4a
Probability Distributions (Yr 1)
Notes Practice
S4b
The Binomial Distribution (Yr 1)
Notes Practice
S4c
The Normal Distribution (Yr 2)
Notes Practice
S4d
Approximating a Binomial (Yr 2)
Notes Practice
S5. Hypothesis Testing
Yr 1 & 2
S5a
Binomial Hypothesis Testing (Yr 1)
Notes Practice
S5b
Critical Values & Critical Regions (Yr 1)
Notes Practice
S5c
Hypothesis Testing with Normal Distribution (Yr 2)
Notes Practice
Mechanics — Paper 3, Section B
M1. Quantities and Units
Year 1
M1a
SI Units & Base Quantities
Notes Practice
M1b
Scalars and Vectors
Notes Practice
M2. Kinematics
Yr 1 & 2
M3. Forces and Newton’s Laws
Yr 1 & 2
M3a
Force Diagrams & Forces as Vectors (Yr 1)
Notes Practice
M3b
F = ma & Acceleration (Yr 1)
Notes Practice
M3c
Connected Particles & Pulleys (Yr 1)
Notes Practice
M3d
Resolving Forces & Inclined Planes (Yr 2)
Notes Practice
M3e
Friction (Yr 2)
Notes Practice
M3f
Statics & Dynamics on Slopes (Yr 2)
Notes Practice
M4. Moments
Year 2
M4a
Moments
Notes Practice
M4b
Resultant Moments
Notes Practice
M4c
Equilibrium
Notes Practice
M4d
Centres of Mass
Notes Practice
M4e
Tilting
Notes Practice
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