In year 12, the students will study four units for the full A Level Mathematics qualification.

AS Unit 1 (Pure Mathematics A)

AS Unit 2 (Applied Mathematics A)

U2 Unit 3 (Pure Mathematics B)

U2 Unit 4 (Applied Mathematics B).

Pure Mathematics A

Understand and use the structure of a mathematical proof, algebra and functions, coordinate geometry in (x,y) plane, sequences and series (including the Binomial Theorem), trigonometry, exponential functions and logarithms, differentiation, integration, vectors.

Examination 2 hours 30 minutes (120 marks)

25% of the full U2 Mathematics qualification (62.5% of the AS qualification)

Applied Mathematics A

Statistics - Statistical sampling, presentation and data interpretation including probability distributions, statistical distributions, statistical hypothesis testing.

Mechanics - Quantities and units in Mechanics, kinematics including deriving and using the formulas for constant acceleration of motion in a straight line, using calculus in kinematics, forces and Newton's laws, vectors.

Examination 1 hour 45 minutes (75 marks)

15% of the full U2 Mathematics qualification (37.5% of the AS qualification)

Pure Mathematics B

Proof by contradiction, algebra and further functions (including simplifying proportional expressions, factoring, cancellation, algebraic division, sketching curves defined by modulus linear function, composite functions and

inverse), further coordinate geometry, further sequences and series, further trigonometry, further differentiation and integration, numerical methods.

2 hours 30 minutes exam (120 marks)

35% of the full U2 Mathematics qualification

Applied Mathematics B

Statistics - Conditional probability, branch diagrams, Venn diagrams, two-way tables, modelling with probability (including critiquing assumptions made and the impact of assumptions more realistic), further statistical distributions, further statistical hypothesis testing.

Differential Equations and Mechanics – use trigonometric functions to solve problems in context, differentiation and integration, form differential equations in context, evaluate analytical solutions of differential equations and find specific solutions, interpret the solution of a differential equation in the context of problem solving, further quantities and units, moments, kinematics, vectors.

Examination 1 hour 45 minutes (80 marks)

25% of the full U2 Mathematics qualification

In year 13, the students will study five units for the full A Level Further Mathematics qualification.

AS Unit 1 (Further Pure Maths A)

AS Unit 2 (Further Statistics A)

AS Unit 3 (Further Mechanics A)

A2 Unit 4 (Further Pure Maths B)

Either

A2 Unit 5 (Further Statistics B)

Or

A2 Unit 6 (Further Mechanics B)

Unit 1- Further Pure Maths A

Construct mathematical proofs using mathematical induction, solve quadratic, cubic and quartic equations, complex numbers, matrices, understand and use the relationship between roots and coefficients of polynomial equations, sums of series, further vectors.

Exam 1 hour 30 minutes (70 marks)

13.3% of full A2 Further Mathematics qualification

Unit 2 – Further Statistics A

Random variables and the Poisson process, mean/variance/standard deviation of linear combinations of independent random variables, discrete and continuous probability distributions, probability density function, cumulative distribution function, expectation, Poisson, Exponential and Chi-squared distributions, correlation and linear regression, goodness of fit tests.

Exam 1 hour 30 minutes (70 marks)

13.3% of full A2 Further Mathematics qualification

Unit 3 – Further Mechanics A

Momentum and impulse, Principle of Conservation of Momentum, Newton’s Experimental Law, Hooke’s Law, work, energy and power, gravitational, kinetic and elastic energy, conservation of energy, the Work-Energy Principle, horizontal and vertical circular motion, differentiation and integration of vectors. 

Exam 1 hour 30 minutes (70 marks)

13.3% of full A2 Further Mathematics qualification

Unit 4 – Further Pure Maths B

Further complex numbers, de Moivre’s Theorem, further Trigonometry, solving trig. equations, further matrices, further algebra and functions including Maclaurin series of a function, further calculus, volumes of revolution, mean value of a function, integrate partial fractions, differentiate inverse trig. functions, Polar coordinates, Hyperbolic functions, differential equations. 

Exam 2 hours 30 minutes (120 marks)

35% of full A2 Further Mathematics qualification

Unit 5 – Further Statistics B

Samples, populations, unbiased estimators, mean, variance, standard errors, linear combination of independent normal distributions, Central Limit Theorem, Normal approximations, hypothesis testing, Student’s t-distribution, Mann-Whitney and Wilcoxon signed-ranks test, estimation, confidence intervals.

Exam 1 hour 45 minutes (80 marks)

25% of full A2 Further Mathematics qualification

Unit 6 – Further Mechanics B

Rectilinear motion, further solving of equations of motion using calculus, momentum and impulse in 2D using vectors, moments of forces and centre of mass of a coplanar system of particles, laminae, or system of particles connected by light rods, equilibrium of rigid bodies, 1st and 2nd order differential equations, simple harmonic motion.

Exam 1 hour 45 minutes (80 marks)

25% of full A2 Further Mathematics qualification