Year 12 maths topics

A-level · ages 16 to 17 · 22 topics first taught in Year 12. Earlier topics keep coming back in review.

Algebra

Arithmetic sequences and series: Find a term, or the sum of the first terms, of an arithmetic sequence.
Exponential growth and logarithms: Use exponential models, and logarithms to solve for the time.
Logarithms and their laws: Evaluate logarithms and combine them using the laws.
Partial fractions: Split an algebraic fraction into two simpler fractions.
Proof by counter-example: Disprove a statement with a counter-example.
Sigma notation: Evaluate sums written with sigma notation, using the standard results.
The factor theorem and remainders: Use f(a) to find remainders and factors of polynomials.
The modulus function: Evaluate and solve equations and inequalities with a modulus.

Motion with constant acceleration: Choose and use a constant-acceleration equation.

Radians: Convert between degrees and radians, and find arc lengths and sector areas in radians.
Solving trigonometric equations: Solve simple trigonometric equations for angles between 0° and 360°.
Trigonometric identities: Use sin²θ + cos²θ = 1 and tan θ = sin θ ÷ cos θ to find missing values.

Hypothesis testing: the ideas: Write hypotheses, say whether a test is one-tailed or two-tailed, and decide whether to reject H₀.
Regression lines and residuals: Use a regression line to predict, read its gradient in context, and find a residual.
Sampling methods: Name a sampling method from how it works, and spot where it could be biased.
The binomial distribution: Use X ~ B(n, p): the mean, the variance and the probability of exactly k successes.
The normal distribution: Use the mean, standard deviation, z-scores and the 68-95-99.7 rule.

Definite integrals of linear functions: Find an antiderivative and evaluate it at two limits.
Differentiating polynomials: Use the power rule to find gradients.
Finding stationary points: Connect a zero derivative with a horizontal tangent.
Integrating polynomials: Integrate powers of x, and evaluate definite integrals, including areas under curves.
The product and quotient rules: Differentiate products and quotients, and find the gradient at a point.