GCSE Maths practice papers

The exam

GCSE Maths in England has two tiers, each with three papers of 1 hour 30 minutes and 80 marks: Paper 1 without a calculator, Papers 2 and 3 with a calculator. Foundation leads to grades 1 to 5, Higher to grades 4 to 9 (3 is allowed). Our papers follow the AQA 8300 layout and timing; Edexcel and OCR papers have the same length and marks.

How the marking works

• The right answer gets all the marks of a part.
• Wrong answer? Each right line of your working gets a method mark, and a line that follows from a wrong one still counts (follow-through), as in the exams.
• Drawings, constructions and proofs: you see the mark scheme and tick the marks your work earns.

Learn the topics

Every question links to the lesson that teaches it.

Number

Bounds in calculations · Converting units · Decimals · Exchange rates · Factors and multiples · Fractions · Fractions and decimals · From scientific notation · Integers · Order of operations · Percent · Powers, square roots, absolute value · Rational exponents · Rationalising a two-term bottom with its partner · Repeating decimals to fractions · Scientific notation · Significant figures and estimating · Simplifying square roots · Upper and lower bounds of a measurement · Venn diagrams with numbers

Algebra

Adding and subtracting rational expressions · Average rate of change · Changing the subject when it appears twice · Circle from the general form · Completing the square · Composition and inverse functions · Equation of a line through two points · Evaluate expressions · Expanding three brackets · Exponent rules · Exponential equations and logarithms · Exponential models from words · Factor by grouping · Factoring · Factoring completely · Graph transformations · Graphing with a table · Inequalities · Linear equations · Linear equations · Literal equations · Nonlinear systems · Parallel and perpendicular lines · Polynomials · Quadratic equations · Quadratic inequalities · Quadratic sequences · Rational equations · Rational expressions · Sequences · Simplify expressions · Slope from two points · Systems of equations · Tangent lines · Trig equations · Two-column proofs · Vertex form by completing the square · Word problems part 1 · Word problems part 2 · Write Ax + By = C as y = mx + b

Ratio, proportion and rates of change

Compound and continuous interest · Density, pressure, population density · Direct and inverse variation · Exchange rates · Exponential models from words · Motion with an unknown speed · Percent · Percent · Percent change twice · Percents and money · Ratios with units · Ratios, unit rates, compare deals · Sharing in a ratio · Simple interest · Speed-time graphs · Word problems part 2 · Work-rate

Geometry and measures

Angle facts · Angles in a polygon · Angles of elevation and depression · Arc length, sector area and perimeter as a part of the circle · Area of a triangle with sine · Bearings with trigonometry and Pythagoras · Circle rules · Composite shapes · Cones · Constructions with a ruler and compasses · Converting area units · Dilations about the origin · Distance between two points · Equation of a circle · Exterior angles · Isosceles triangles · Midpoint · More composite shapes · Parallel lines and a transversal · Parallelogram and trapezoid · Perimeter and area · Perpendicular bisector of a segment · Prisms · Pythagoras · Pythagoras in 3D · Reflections · Right-triangle trigonometry · Rotation about a point · Rotations about the origin · Scale drawings and maps · Similar shapes and solids · Similar triangles · Spheres and hemispheres · Tangents · The law of cosines · The law of sines · Three-figure bearings and back bearings · Trigonometry in 3D · Volume and surface area · Volume of a frustum

Probability

Binomial probability · Conditional probability · Experimental probability · Probability with and · Probability with counting · Probability with or · Sample spaces · Samples and predictions · Two-way tables · Venn and tree diagrams

Statistics

Box plots · Cumulative frequency · Histograms with unequal class widths · IQR and outliers · Mean of grouped data · Mean, median, mode, range · Scatter plots and correlation