Year 10 Mathematics: Higher Tier

4 operations, directed number, LCM/HCF, prime factors. GCSE problem solving.

Speed, density and pressure. Upper and lower bounds, error intervals and calculations using bounds.

Substitution, simplifying, solving all types of linear equations.

All notation, at a point, straight line, vertically opposite and with parallel lines.

Special quadrilaterals, angles in polygons, exterior and interior.

Apply and prove the 8 circle theorems.


Calculate using indices, use index laws including negative and fractional indices, simplify surds.

Place value, calculate and interpret standard form (calculator and non-calculator).

Plot y = mx + c, identify parallel and perpendicular lines, find equations of lines.

Order fractions, use all 4 operations, mixed/improper and problem solving.


Basic percentage, percentage change, increase/decrease, reverse and multipliers for growth and decay.

Solving problems using ratio, combined ratios.

Expanding two/three binomials, factorise quadratics, change the subject, complete the square. Solve by factorising and drawing quadratic graphs.

Argue mathematically to show equivalence, use algebra to prove.

Simplifying algebraic fractions by factorising and using the four operations with equivalence.

Review: Perimeter and Area of all shapes, including circles and sectors and arc lengths.

Volumes of prisms, cones, spheres and pyramids.


All probability. Single events, combined events, relative frequency, tree diagrams, conditional probability, venn diagrams.

Reflect, rotate, translate and enlarge (positive and negative scale factors). Invariance

Revisit all previous representations including boxplots, cumulative frequency, histograms and all measures of average and spread. Compare distributions.

Revisit all Pythagoras' Theorem and Trigonometry including exact values.

Perpendicular bisector, angle bisect, and loci problems.