Outlined below are topics covered for OCR Pure Maths A-Level
It is advisable to check the official Pure Maths A-Level specification for any changes.
Contents for Pure Maths OCR
Prior Knowledge
Algebra Basics
Polynomials
Pythagoras’ Theorem
Trigonometry Introduction
Algebra and Functions : 1
Indices
Surds
Functions
Factorising
Completing the Square
Quadratic Equations
Quadratic Equations – Roots and Discriminant
Quadratic Graphs
Simultaneous Equations
Inequalities
Algebraic Long Division
Factor Theorem
Rational Expressions – Simplifying
Coordinate Geometry
Gradient of Straight Lines
Straight Lines
Intersection of Graphs
Exam Questions – Straight Lines
Circles
Parametric Equations
Algebra and Functions : 2
Sketching Cubic and Reciprocal Curves
Modulus Functions, Equations and Inequalities
Working with Functions
Graph Transformations
Asymptotes
Partial Fractions
Sequences and Series
Binomial Expansion
Working with Sequences and Series
Arithmetic Sequence and Series
Geometric Sequence and Series
Trigonometry
Trigonometric Ratios
Trigonometric Graphs and Transformations
Applications of Trigonometry
Trigonometric Equations
Trigonometric Identities
Sec θ, Cosec θ and Cot θ
Inverse trigonometric functions
Identities & Equations – Pythagorean Type
Small-angle Approximations
Identities – Addition type
Identities & Equations – Double angle type
Identities – Half angle type
Identities – Triple angle type
Identities & Equations – Harmonic Formulae
Exam Questions – Mixed trigonometry
Logarithmic and Exponential Functions
Exponential Functions and Logarithms
The Exponential Function ex and Natural Log Functions
Modelling Curves of the form y=kxn and y=kax
Differentiation
Differentiation – Introduction
Tangents and Normals
Stationary Points
Increasing and Decreasing functions
Standard Differentials
The Chain Rule
The Product and Quotient Rules
More Standard Differentials
The Reciprocal Function of dy/dx
Exam Questions – Differentiation
Exponential Functions
Parametric Functions
Implicit Functions
Connected Rates of Change
Integration
Integration – Introduction
Equations of Curves
Definite Integration
Integration – Common Functions
Integrals of Trigonometric Functions
Integrals involving Partial fractions
Integration by Substitution
Integrals of the form f[g(x)]g'(x) by inspection
Integration by Parts
General Methods – Integration
Applications of Integration – Area bound by a curve
Differential equations – Separating the variables
Differential equations – Forming differential equations
Numerical Methods
Solution of Equations by Numerical methods
Numerical Integration
Index
- circles
- chain rule
- change of sign
- completing the square
- connected rates of change
- coordinate geometry
- cosine rule
- cubic graph
- decreasing functions
- differential equations:
- solving
- forming
- differentiation:
- chain rule
- connected rates of change
- implicit
- parametric
- product rule
- quotient rule
- differentials:
- ax
- ex
- ln x
- sin, cos, tan(x)
- sec, cosec, cot(x)
- discriminant
- domain – functions
- implicit differentiation
- increasing functions
- indices
- inequalities
- integration
- by parts
- common functions
- general methods
- partial fractions
- substitution
- trigonometric
- definite
- integration applications
- area under a curve
- iteration
- intersection – graphs
- inverse functions
- parametric:
- differentiating
- equations
- partial fractions
- product rule
- proof
- quadrant rule
- quadratics:
- discriminant
- equations
- graphs
- quotient rule
-+
- tangents to curves
- transformations:
- graphs
- trapezium rule
- trigonometric:
- equations
- graphs
- ratios 30°, 60°, 45°
- trigonometry
- cosine rule
- cosec, sec and cot θ
- inverse functions
- sine rule
- small angles
- trigonometry – identities:
- addition formulae
- double angle formulae
- half angle formulae
- harmonic formulae
- Pythagorean
- triple angle formulae