Category: Geometry Key stage 4

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Abbreviation: MG KS4

Description

In addition to consolidating subject content from key stage 3, pupils should be taught to:

interpret and use fractional {and negative} scale factors for enlargements
{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, 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}
construct and interpret plans and elevations of 3D shapes
interpret and use bearings
calculate arc lengths, angles and areas of sectors of circles
calculate surface areas and volumes of spheres, pyramids, cones and composite solids
apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures
apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures
know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45°, 60°
{know and apply the sine rule, = = , and cosine rule, a² = b² + c² - 2bc cos A, to find unknown lengths and angles}
{know and apply Area = ab sin 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}