KS3 Maths Help
The 25 KS3 topics that bridge KS2 to GCSE. Every concept with worked examples and an embedded calculator where helpful.
KS3 (Years 7-9) is where pupils meet algebra, Pythagoras, basic trig and standard form. The topics below build directly into GCSE Foundation tier.
- Prime factor decompositionBreak a number into prime factors using a factor tree.
- LCM and HCFLowest common multiple and highest common factor methods.
- Squares and cubesSquare numbers, cube numbers and their roots.
- Indices (introduction)a&sup{n} notation; multiplying and dividing index numbers.
- Standard formNumbers as a×10&sup{n} where 1 ≤ a < 10.
- Operations with negativesAdding, subtracting, multiplying and dividing negative numbers.
- Fractions, decimals, percentagesConverting and calculating across all three notations.
- Percentage changeIncrease, decrease, profit, loss as percentages.
- Ratio and proportionSharing in a ratio, equivalent ratios.
- Direct and inverse proportiony ∝ x and y ∝ 1/x.
- Speed, distance, timeS=D/T triangle. Compound measure.
- Density, mass, volumeρ=m/V triangle. Compound measure.
- Algebraic expressionsVariables, terms, coefficients, simplification.
- Expanding bracketsa(b+c) = ab+ac and double brackets (a+b)(c+d).
- Factorising (single bracket)ax+ay = a(x+y) by spotting the common factor.
- Solving linear equationsInverse operations, balance method.
- Inequalities (introduction)<, >, ≤, ≥ and the number-line representation.
- Sequences and the nth termLinear sequences and finding a formula.
- Coordinates and graphsPlotting points and reading line graphs.
- y = mx + c (straight-line graphs)Gradient and y-intercept of linear graphs.
- Pythagoras' theorema² + b² = c² for right-angled triangles.
- SOHCAHTOA (basic trigonometry)Right-angled triangles: sin, cos, tan ratios.
- TransformationsTranslation, reflection, rotation, enlargement.
- Probability (KS3 introduction)Calculating simple probabilities and listing outcomes.
- Scatter graphs and correlationPositive, negative, no correlation; line of best fit.