Year 13 maths topics

A-level · ages 17 to 18 · 14 topics first taught in Year 13. Earlier topics keep coming back in review.

Algebra

Binomial expansion coefficients: Find the coefficient of a term when a bracket is raised to a power.
Parametric equations: Find points on a curve from x(t) and y(t), and find dy/dx using the chain rule.
Sum to infinity of a geometric series: Find what a geometric series adds up to when it goes on for ever.

Forces and moments: Resolve forces, use F = ma, and balance moments.
Projectile motion: Split projectile motion into horizontal and vertical parts, with g = 9.8 m s⁻².

Vectors in three dimensions: Work with 3-D vectors: their length, the scalar product and the distance between points.

Differential equations: Solve simple differential equations by integrating, using a given point.
Differentiating exponentials and trig: Differentiate eᵏˣ, sin kx, cos kx and ln x, and find the gradient at a point.
Differentiating with the chain rule: Differentiate a function of a function, such as (2x+1)3.
Implicit differentiation: Find the gradient of a curve whose equation mixes x and y.
Integration by substitution: Integrate a function when part of it is the derivative of another part.
Kinematics using calculus: Differentiate displacement to find velocity and acceleration.
Newton-Raphson iteration: Use Newton-Raphson to improve an estimate of a root.
The trapezium rule: Estimate the area under a curve by splitting it into trapeziums.