Year 10 maths topics

GCSE · ages 14 to 15 · 23 topics first taught in Year 10. Earlier topics keep coming back in review.

Number

Reverse percentages: Recover an original price after a percentage change.
Simplifying surds: Simplify surds by taking out square factors, and add them.
Standard form: Interpret powers of ten in standard form.

Direct and inverse proportion: Use y = kx and y = k/x to solve proportion problems.

Completing the square: Write x² + bx + c as (x + p)² + q, and find the minimum point.
Expanding double brackets: Expand and simplify pairs of brackets.
Factorising quadratics: Write quadratics as pairs of brackets.
Quadratic sequences: Use the second difference to spot a quadratic sequence, and find later terms.
Rearranging formulae: Change the subject of a formula, and use it to find a missing value.
Simplifying algebraic fractions: Simplify algebraic fractions by factorising and cancelling.
Simultaneous equations: Solve two equations with two unknowns.
Solving quadratics: Solve quadratic equations by factorising.
The quadratic formula: Use the discriminant, and solve quadratics with the formula.

Density and pressure: Use density = mass ÷ volume and pressure = force ÷ area.
Volume of cones and spheres: Use the formulae for the volume of a cone and a sphere.

Arc length and sector area: Find the length of an arc and the area of a sector.
Area of a circle: Use radius or diameter to calculate the area of a circle.
Circle theorems: Use the angle at the centre, angles in a semicircle, cyclic quadrilaterals and tangents.
Exact trigonometric values: Know the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°.
Right-angled trigonometry: Use sin, cos and tan to find sides and angles.
Sine and cosine rules: Use the sine rule, the cosine rule and ½ab sin C in any triangle.
Vectors: Add and scale column vectors, and find the length of a vector.

Histograms and frequency density: Use frequency density = frequency ÷ class width to read and draw histograms.