GCSE maths · strand

Geometry & Measures

37 topics, each with printable practice questions and a full answer key. Every sheet is generated, so you can make a fresh one whenever you need it.

Foundation and Higher tier 19 topics

Part Foundation, part Higher only 10 topics

Higher tier only 7 topics

Other worksheets 1 topic

Vectors Proof Questions

All strands by tier: Foundation tier · Higher tier

GCSE subject content 31 DfE statements

work with coordinates in all four quadrants

Midpoint of a Line Segment

A17

solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

Cylinders

use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description

Shapes

use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line

Loci and Construction

apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

Angles · Angles in Parallel Lines · Angles in Polygons · Bearings · Circle Theorems · Congruent Triangles · Finding the Area of Any Triangle · The Sine Rule

derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language

Angles · Angles in Polygons · Shapes

use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

Congruent Triangles

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

Circle Theorems · Congruent Triangles · Proof of the Circle Theorems · Pythagoras

identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)

Enlarging with Negative Scale Factors · Similar Shapes (Lengths) · Transformations

describe the changes and invariance achieved by combinations of rotations, reflections and translations

Transformations

identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

Area and Circumference of Circles · Circle Theorems · Parts of a Circle

G10

apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

Circle Theorems · Proof of the Circle Theorems

G11

solve geometrical problems on coordinate axes

Midpoint of a Line Segment

G12

identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres

Faces, Edges and Vertices · Plans and Elevations · Surface Area

G13

construct and interpret plans and elevations of 3D shapes

Plans and Elevations

G15

measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

Bearings · Scale Drawings · Using a Ruler & Protractor

G16

know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

Area and Perimeter · Area of Compound Shapes · Cylinders · Faces, Edges and Vertices · Plans and Elevations · Surface Area · Volume of a Prism

G17

know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids

Area and Circumference of Circles · Area and Perimeter · Area of Compound Shapes · Cylinders · Frustums · Loci and Construction · Sector Areas and Arc Lengths · Spheres and Cones

G18

calculate arc lengths, angles and areas of sectors of circles

Sector Areas and Arc Lengths

G19

apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures

G20

know the formulae for: Pythagoras’ theorem, a² + b² = c², and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

3d Pythagoras and Trigonometry · Pythagoras · SOHCAHTOA (Trigonometry)

G21

know the exact values of sinθ and cosθ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tanθ for θ = 0°, 30°, 45° and 60°

Exact trig values

G22

know and apply the sine rule, a/sinA = b/sinB = c/sinC, and cosine rule, a² = b² + c² − 2bc cosA, to find unknown lengths and angles

Finding the Area of Any Triangle · The Cosine Rule · The Sine Rule

G23

know and apply Area = ½ ab sinC to calculate the area, sides or angles of any triangle

Finding the Area of Any Triangle

G24

describe translations as 2D vectors

Transformations · Vectors

G25

apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs

Vectors · Vectors Proof Questions

calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4×3) = √4 × √3 = 2√3) and rationalise denominators

Area and Circumference of Circles · Cylinders · Exact trig values · Frustums · Loci and Construction · Sector Areas and Arc Lengths · Spheres and Cones

N15

round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

Cylinders · Frustums

change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

Cylinders · Scale Drawings · Volume of a Prism

use scale factors, scale diagrams and maps

Scale Drawings · Similar Shapes (Lengths)

R12

compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors

Statements from the Department for Education's GCSE mathematics subject content. Contains public sector information licensed under the Open Government Licence v3.0.

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