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Maths A Level

OCR Maths A level H240

This new A Level qualification builds on the skills, knowledge and understanding set out in the new GCSE (9-1) 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 non-uniform 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 
Co-ordinate 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
  • Two-way 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
  • Multi-stage 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