GCSE Mathematics₈₃₀₀

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

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

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 (eg to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

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

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

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

identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement

including fractional scale factors

including negative scale factors

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

identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference

including: tangent, arc, sector and segment

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

solve geometrical problems on coordinate axes

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

interpret plans and elevations of 3D shapes

construct and interpret plans and elevations of 3D shapes

use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.)

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

know and apply formulae to calculate: area of triangles, parallelograms, trapezia;

volume of cuboids and other right prisms (including cylinders)

know the formulae: circumference of a circle = $\mathsf{2}\mathit{\pi }\mathit{r}\mathsf{=}\mathit{\pi }\mathit{d}$

area of a circle = $\mathit{\pi }{\mathit{r}}^{\mathsf{2}}$

calculate perimeters of 2D shapes, including circles

areas of circles and composite shapes

surface area and volume of spheres, pyramids, cones and composite solids

calculate arc lengths, angles and areas of sectors of circles

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

including the relationships between lengths, areas and volumes in similar figures

know the formulae for: Pythagoras’ theorem, ${\mathit{a}}^{\mathsf{2}}\mathsf{+}\mathit{ }{\mathit{b}}^{\mathsf{2}}\mathsf{=}\mathit{ }{\mathit{c}}^{\mathsf{2}}$ and the trigonometric ratios, $\mathit{sin}\mathit{\theta }\mathit{}\mathsf{=}\mathit{}\frac{\mathit{opposite}}{\mathit{hypotenuse}}$ , $\mathit{cos}\mathit{\theta }\mathit{}\mathsf{=}\frac{\mathit{adjacent}}{\mathit{hypotenuse}}$ and $\mathit{tan}\mathit{\theta }\mathit{}\mathsf{=}\mathit{}\frac{\mathit{opposite}}{\mathit{adjacent}}$

apply them to find angles and lengths in right-angled triangles in two dimensional figures

apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

know the exact values of $\mathsf{sin}\mathsf{}\mathit{\theta }$ and $\mathsf{cos}\mathsf{}\mathit{\theta }$ for $\mathit{\theta }$ = 0°, 30°, 45° , 60° and 90°

know the exact value of $\mathsf{tan}\mathsf{}\mathit{\theta }$ for $\mathit{\theta }$ = 0°, 30°, 45° , 60°

know and apply the sine rule, $\frac{\mathit{a}}{\mathsf{sin}\mathsf{}\mathit{A}}\mathsf{=}\mathit{ }\frac{\mathit{b}}{\mathsf{sin}\mathsf{}\mathit{B}}\mathsf{=}\mathit{ }\frac{\mathit{c}}{\mathsf{sin}\mathsf{}\mathit{C}}$

and cosine rule,

${\mathit{a}}^{\mathsf{2}}\mathsf{=}{\mathit{b}}^{\mathsf{2}}\mathsf{+}{\mathit{c}}^{\mathsf{2}}\mathsf{-}\mathsf{2}\mathit{b}\mathit{c}\mathsf{cos}\mathsf{}\mathit{A}$

to find unknown lengths and angles

know and apply

$\mathit{A}\mathit{r}\mathit{e}\mathit{a}\mathsf{=}\mathit{}\frac{\mathsf{1}}{\mathsf{2}}\mathit{}\mathit{a}\mathit{b}\mathsf{sin}\mathsf{}\mathit{C}$

to calculate the area, sides or angles of any triangle

describe translations as 2D vectors

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