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
- Expanding a single bracket
- Expanding two or more brackets
- Squaring a bracket
- Terms in expressions and equations
- Identity or equation - what is the difference?
- Linear Equations with a positive x term
- Linear equations with a negative x-term
- Linear equations with two x-terms
- Linear equations with brackets
- Fractional linear equations
- f(x) notation
- Polynomials
Polynomials
Pythagoras’ Theorem
Trigonometry Introduction
Algebra and Functions : 1
Indices
Surds
Factorising
Completing the Square
Quadratic Equations
Quadratic Equations – Roots and Discriminant
Quadratic Graphs
Simultaneous Equations
Inequalities
Algebraic Long Division
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
Partial Fractions
Sequences and Series
Binomial Expansion
- Binomial expansion
- Exam Questions - Binomial expansion for positive integer powers
- Exam Questions - Binomial expansion, comparing coefficients
- Exam Questions - Binomial expansion, estimating a value
- Exam Questions - Binomial expansion, other
- Exam Questions - Binomial expansion for rational and negative powers
- Exam Questions - Partial fractions with the 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
- Exponential functions: what they are and their graphs
- What do we mean by a log?
- Rules of logs
- Logarithms - Change of Base
- Simplifying and expanding
- Converting between Logarithmic and Power (Exponential) equations
- Modelling exponential growth and decay
- Modelling exponential equations | Exam Questions
- Exponential and log equations
- Simultaneous equations
- Solving inequalities
- Exam Questions - 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
Connected Rates of Change
Integration
Integration – Introduction
Equations of Curves
Definite Integration
Integration – Common Functions
- Integration:(ax+b)n types
- Exam Questions - Integration:(ax+b)n types
- Integrating exponential functions ex, eax and e(ax+b)
- Exam Questions - Integrating exponential functions ex, eax and e(ax+b)
- Integrating reciprocal functions 1/x and 1/(ax+b)
- Exam Questions - Integrating reciprocal functions 1/x and 1/(ax+b)
- Integrals of the form : f '(x)/f(x)
- Integrals of the form : f'(x)ef(x)
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
Vectors
Vectors
- What is a vector and a scalar quantity?
- Vector notation 2d
- Vector notation
- Position vectors 2d
- Position vectors
- Equal and negative vectors
- Multiplying a vector by a scalar 2d
- Multiplying a vector by a scalar
- Addition and subtraction of vectors 2d
- Addition and subtraction of vectors
- Magnitude of a 2 dimensional vector
- Magnitude of a 3 dimensional vector
- How to solve vector geometry problems
- Vector Methods in Geometry - Parallelogram problem
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