OCR Maths A level H240
This new A Level qualification builds on the skills, knowledge and understanding set out in the new GCSE (91) subject content for mathematics for 2015. The content is separated into three areas: Pure Mathematics, Statistics and Mechanics with all elements being
assessed through a written examination. All pupils must study all three topic areas.
Year 12
Manipulation of Indices and Surds. Advanced algebraic techniques. Exploration of graphical representation with links to coordinate geometry and transformations. Binomial expansion. Introduction to Calculus. Advanced Trigonometry and an introduction to trig
identities. Exponentials and Logarithms. Vectors. Representation of data – statistical measures and diagrams. Outliers. Probability of mutually exclusive and independent events. The Binomial distribution and hypothesis testing. SI units. Constant and nonuniform acceleration. Newton’s Laws. Weight and Frictional forces.
Year 13
Extension of algebraic and numerical techniques including fractions & parametric equations. Iterative methods. Functions and graphs involving exponentials and logs. Sequences and sigma notation. Proof by contradiction. Further trigonometry. Further Calculus. Extension of the Binomial theorem. Differential equations. Set notation. Extension
of the Binomial Distribution. The Normal distribution leading to Central Limit Theorem. Correlation and hypothesis testing. Extension of work on acceleration, frictional forces and Newton’s Laws. Gravity. Application of vectors in a plane. Statics.
Topics Covered per Half Term
Pure & Stats 
Year 12 
Coordinate geometry 
 Midpoint and distance between two points
 Equation of a straight line
 Parallel and perpendicular lines
 Equation of a circle
 Solving problems with lines and circles

Logarithms 
 Introducing Logarithms
 Laws of logarithms
 Solving exponential equations
 Disguised quadratics

Exponential models 
 Graphs of exponential functions
 Graphs of logarithms
 Exponential functions and mathematical modelling

Binomial Expansion 
 Fitting models to data
 The Binomial theorem
 Calculating binomial coefficients
 Applications of binomial theorem

Triangle Geometry 
 The Sine rule
 The Cosine rule
 Area of a Triangle
 Sketching dervatives

Differentiation 
 Differentiation from first principles
 Rules of differentiation
 Simplifying into terms of the form axn
 Interpreting derivatives and second derivatives

Applications of differentiation 
 Tangents and normals
 Stationary points
 Optimisation

Integration 
 Rules of integration
 Simplifying into terms of the form axn
 Finding the equation of a curve
 Definite integration
 Geometric significance of definite integration

Probability 
 Combining probabilities
 Probability distributions
 The Binomial Distribution

Working with data 
 A reminder of statistical diagrams
 Standard deviation
 Calculations from frequency tables
 Scatter diagrams and correlation
 Outliers and cleaning data
 Populations and samples

Statistical hypothesis testing 
 Introduction to hypothesis testing
 Critical region for a hypothesis test

Conditional Probability 
 Set notation and Venn diagrams
 Twoway tables
 Tree diagrams
 Modelling with probablity

Normal Distribution 
 Introduction to normal probabilities
 Inverse Normal distribution
 Finding unknown mean and standard deviation
 Modelling with the Normal Distribution

Topics Covered per Half Term
Pure & Mechs 
Year 13 
Indices and surds 
 Using the laws of indices
 Working with surds

Quadratic functions 
 Review of quadratic equations
 Graphs of quadratic functions
 Completing the square
 Quadratic inequalities
 The discriminant

Polynomials 
 Disguised quadratics
 Working with polynomials including division
 Factor theorem
 Sketching polynomials

Using Graphs 
 Intersections of graphs
 Transforming graphs (inc discriminant revisited)
 Direct and indirect proportion (inc Graphs of a/x and a/xsquared)
 Sketching inequalities in two variables

Proof 
 Mathematical structures and arguments
 Inequality notation
 Disproof by counterexample
 Proof by deduction
 Proof by exhaustion

Trig functions and equations 
 Definitions and graphs of sine and cosine functions
 Tangent functions and exact values
 Trigonometric identities
 Introducing trigonometric equations
 Transformations of trig graphs
 More complex trigonometric equations

Vectors 
 Describing Vectors
 Operations with vectors
 Position and displacement vectors
 Using vectors to solve geometrical problems

Introduction to kinematics 
 Introduction to displacement, velocity and acceleration
 Kinematics and calculus
 Using travel graphs
 Solving problems in kinematics

Motion with constant acceleration 
 Deriving the constant acceleration formula
 Using the constant acceleration formulae
 Vertical motion under gravity
 Multistage problems

Force and motion 
 Newton's law of motion
 Combining forces
 Types of forces
 Gravity and weight
 Forces in equilibrium

Objects in contact 
 Newton's third law
 Normal reaction force
 Further equilibrium problems
 Connected particles
 Pulleys
