GCSE Maths Help
Every topic in the GCSE 9-1 specification — Number, Algebra, Geometry, Probability, Statistics, Ratio & Proportion. Worked examples for AQA, Edexcel/Pearson, OCR and WJEC/Eduqas.
The GCSE 9-1 specifications across the four boards differ in question style but share the same content. Foundation tier covers the first ~80 percent of topics; Higher tier covers all of them, including surds, circle theorems, the cosine rule, conditional probability and histograms with frequency density. Below: every topic with a clear method and worked examples.
- Place value and roundingSignificant figures, decimal places, estimation.
- Upper and lower boundsError intervals from rounded measurements.
- Standard forma×10n; arithmetic in standard form.
- SurdsSimplify, rationalise the denominator (Higher).
- Indices (negative + fractional)Index laws including negative and fractional powers.
- Recurring decimalsConvert recurring decimals to fractions (Higher).
- PercentagesIncrease, decrease, multiplier method.
- Compound interestRepeated multiplication; growth and decay.
- Reverse percentagesFind the original from the percentage-changed value.
- Ratio (GCSE)Sharing, simplifying, ratio ↔ fraction.
- Expanding brackets (GCSE)Single, double and triple brackets.
- FactorisingSingle bracket, double bracket (quadratic), DOTS.
- Quadratic formulax = (-b ± √(b²-4ac))/(2a).
- Completing the square(x+a)² + b form. Higher tier.
- Solving quadratic equationsBy factorising, formula, or completing the square.
- Simultaneous equationsLinear (elimination, substitution) and linear+quadratic.
- Algebraic fractionsSimplify, add/subtract, multiply/divide. Higher.
- Inequalities (GCSE)Linear and quadratic; number-line and set notation.
- Sequences (GCSE)Linear, quadratic, geometric, Fibonacci-like.
- Functionsf(x), composite f(g(x)), inverse f−1(x).
- Iterationxn+1 from xn for numerical solutions.
- GraphsLinear, quadratic, cubic, reciprocal, exponential, trig.
- Pythagoras (GCSE)GCSE-level Pythagoras with worked exam questions.
- SOHCAHTOA (GCSE)GCSE right-angled trig; finding angles and sides.
- Sine rulea/sin A = b/sin B = c/sin C. Higher.
- Cosine rulea² = b² + c² - 2bc·cos A. Higher.
- Exact trig valuessin 30 = 1/2, cos 30 = √3/2, etc. Higher.
- 3D Pythagoras and trigPythagoras and trig applied to 3D shapes. Higher.
- Circle theoremsEight key circle theorems. Higher.
- Vectors2D vectors, addition, scalar multiplication, parallelism.
- Transformations (GCSE)Translation, reflection, rotation, enlargement.
- Similarity and congruenceSame shape (similar) vs same shape and size (congruent).
- Loci and constructionCompass-and-ruler constructions; loci of points.
- BearingsThree-figure bearings (000-359°) measured from north.
- Area and perimeter (GCSE)Triangles, parallelograms, trapezia, compound shapes.
- Volume and surface areaPrisms, pyramids, cylinders, cones, spheres.
- Circle area and circumferenceπr² for area; 2πr for circumference.
- Probability (GCSE)Calculating probabilities; AND/OR rules.
- Tree diagramsIndependent and dependent (without replacement) events.
- Venn diagramsSet notation: union, intersection, complement.
- Conditional probabilityP(A|B) = P(A∩B) / P(B). Higher.
- Cumulative frequencyMedian, quartiles, IQR from a CF curve.
- HistogramsFrequency density (Higher) for unequal class widths.
- Box plotsMedian, quartiles, IQR, comparing distributions.
- Scatter graphs and correlationLine of best fit; positive/negative correlation.
- Direct proportiony = kx with worked algebraic problems.
- Inverse proportiony = k/x; product xy is constant.
- Compound measuresSpeed, density, pressure; rates of flow.
- Growth and decayExponential growth (compound interest) and decay.
- Best buysUnit pricing for value comparison.