Integers, factors and multiples, HCF and LCM, fractions and decimals, surds, and upper and lower bounds.
The laws of indices, fractional and negative indices, roots, and standard form arithmetic.
Sharing in a ratio, direct and inverse proportion, percentage change, reverse percentages and compound interest.
Simplifying, expanding brackets, factorising, algebraic fractions and changing the subject of a formula.
Solving linear equations, simultaneous equations by elimination and substitution, and linear inequalities including number lines.
Solving quadratics by factorising, the quadratic formula, completing the square, and the discriminant.
Linear and quadratic sequences, the nth term, function notation, composite and inverse functions.
Gradient, the equation y = mx + c, midpoint and length of a line, and parallel and perpendicular lines.
Recognising and sketching quadratic, cubic, reciprocal and exponential graphs, and solving equations graphically.
Angle facts, angles in parallel lines, interior and exterior angles of polygons, and the circle theorems.
Perimeter and area of 2D shapes, circles and sectors, surface area and volume of prisms, cylinders, cones and spheres.
Pythagoras' theorem, SOHCAHTOA, the sine and cosine rules, area of a triangle, bearings and 3D problems.
Column vectors, vector arithmetic and geometry, and the four transformations: translation, reflection, rotation and enlargement.
Averages and spread, frequency charts, cumulative frequency, and probability including combined events and tree diagrams.