GCSE maths worksheets

Apply systematic listing strategies, including the product rule for counting.

Estimate the powers and roots of any given positive number.

Calculate with roots and with integer and fractional indices.

Calculate exactly with fractions, surds and multiples of pi; rationalise denominators.

Calculate with numbers in standard form.

Change recurring decimals into their corresponding fractions and back.

Partial Converts a terminating decimal. Does not handle a recurring one.

Identify and work with fractions in ratio problems.

Apply limits of accuracy when rounding or truncating, including upper and lower bounds.

Partial Chooses an accuracy to report to. Does not give the upper and lower bounds.

Factorise quadratics, including the difference of two squares, and use the laws of indices.

Know an equation from an identity and use algebra to construct arguments and proofs.

Interpret expressions as functions, and their inverse and composite functions.

Use y = mx + c for parallel and perpendicular lines; find a line through two points.

Interpret the roots, intercepts and turning points of a quadratic.

Sketch translations and reflections of the graph of a given function.

Plot and interpret graphs in real contexts, including simple kinematics.

Use the equation of a circle at the origin and find a tangent at a given point.

Partial Finds the center and radius from the equation. Does not find a tangent.

Solve quadratic equations by factorising, completing the square and the formula.

Solve two simultaneous equations, linear/linear or linear/quadratic.

Translate a situation into an equation, solve it and interpret the solution.

Solve linear and quadratic inequalities and represent the solution set.

Partial Solves the linear equation. Does not solve an inequality or shade its solution set.

Use triangular, square and cube numbers and arithmetic, geometric and Fibonacci sequences.

Deduce an expression for the nth term of linear and quadratic sequences.

Partial Writes the nth term of an arithmetic or geometric sequence. Does not cover quadratic sequences.

Compare lengths, areas and volumes using ratio and scale factors.

Convert between related compound units: speed, rates of pay, density, pressure.

Interpret equations that describe direct and inverse proportion.

Partial Solves direct proportion. Does not cover inverse proportion.

Interpret the gradient of a straight-line graph as a rate of change.

Solve growth and decay problems, including compound interest.

Use fractional and negative scale factors for enlargements.

Describe the invariance achieved by combining rotations, reflections and translations.

Partial Applies one transformation. Does not compose several or ask what stays fixed.

Identify circle parts: centre, radius, chord, diameter, tangent, arc, sector and segment.

Partial Relates inscribed and central angles. Does not name the tangent, chord or segment.

Apply and prove the circle theorems on angles, radii, tangents and chords.

Partial Applies the inscribed angle theorem. Does not cover tangents or chords, and does not ask for a proof.

Construct and interpret plans and elevations of 3-D shapes.

Partial Reads a cross-section off a drawn solid. Does not ask for a plan and elevation to be drawn.

Interpret and use bearings.

Calculate arc lengths, angles and the areas of sectors of circles.

Calculate the surface area and volume of spheres, pyramids, cones and composite solids.

Apply congruence and similarity, including the ratios of areas and volumes.

Partial Uses the similarity criteria on lengths. Does not scale areas or volumes.

Apply Pythagoras and trigonometric ratios in two and three dimensions.

Partial Solves right triangles in the plane. Does not work in three dimensions.

Know the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°.

Know and apply the sine rule and the cosine rule.

Know and apply Area = 1/2 ab sin C.

Describe translations as 2-D vectors.

Partial Applies the translation on a coordinate plane. Does not use vector notation for it.

Apply the property that an exhaustive set of mutually exclusive events sums to 1.

Partial Finds the probability of one outcome. Does not use the outcomes summing to 1 to find a missing one.

Use a probability model to predict outcomes as sample size increases.

Calculate the probability of independent and dependent combined events.

Calculate conditional probabilities using two-way tables, tree diagrams and Venn diagrams.

Infer properties of a population from a sample, knowing the limitations of sampling.

Interpret and construct tables and line graphs for time series data.

Partial Describes the shape of a graph. The graph is a function rather than data over time.

Construct histograms with unequal class intervals and cumulative frequency graphs.

Partial Reads a histogram with equal intervals. Does not cover unequal ones or cumulative frequency.

Compare distributions using graphs, measures of centre, quartiles and interquartile range.

Apply statistics to describe a population.

Use scatter graphs, lines of best fit and predictions; know correlation is not causation.