Course Content – AQA Syllabus (7357).
Unit 1 – Pure mathematics 1
– Proof, proof by deduction, proof by exhaustion, & disproof
– Surds & rationalising the denominator
– Solving & graphing quadratic equations
– Graph transformations
– Simultaneous equations
– Inequalities
– Polynomials & the Factor Theorem
– Coordinate geometry, including straight line equations & intersection
– Circle theorems
Unit 2 – Pure mathematics 2
– Differentiation & integration
– Binomial expansion & approximations
– Trigonometry (sin, cosine & trig identities)
– Proving & solving trigonometry identities
– Exponentials & logarithms
– Laws of logarithms
Unit 3 – Mechanics 1
– Vectors
– Kinematics, motion graphs & non-uniform acceleration
– Constant acceleration & SUVAT equations
– Forces & Newton’s laws
Unit 4 – Statistics 1
- Population & sampling
- Representing qualitative & quantitative data
- Measure of location
- Dispersion
- Correlation & regression
- Elemental probability
- Solving probability problems
- Laws of Probability
- Probability distributions
- Statistical distribution
- Binomial distributions, including binomial coefficients, probability function, & cumulative distribution function
- Hypothesis tests
Unit 5 – Pure mathematics 3
- Proof by contradiction
- Simplifying expressions
- Division of polynomials
- Mapping & functions
- Composite & inverse functions
- The modulus
- Solving modulus equations & inequalities
- Graph transformations
- Partial & repeated fractions
- Arcs, sectors, & small angle approximations
- Inverse trig functions
- Cosec, Sec & Cot
- Addition & double angle formulas
- Binomial expansions as approximations
- Binomial expansions & partial fractions
- Series & sequences
- Unit 6 – Pure mathematics 4
- Points of inflection, convex, & concave curves
- Trigonometric identities & equations
- Rules of differentiation, including the product rule, the quotient rule, & implicit differentiation
- Rules of integration
- Differential equations
- Integrating complex functions
- Integration by substitution
- Integration by parts
- Integration of partial fractions
- Parametric integration & differentiation
- Parametric & cartesian equations
- Numerical methods
- Vectors & 3D vectors
Unit 7 – Mechanics 2
- Kinematics & projectile motion
- Dynamics
- Resultant forces, friction, & equilibrium
- Newton’s Laws of Motion
- Moments
Unit 8 – Statistics 2
- Correlation & regression
- The Product Moment Correlation Coefficient
- Probability
- The Normal Distribution
- Normal approximation to a binomial distribution
- Hypothesis testing
Preparing for the examinations
- Paper 1
- Paper 2
- Paper 3
