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Category: Geometry Key stage 4  

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Abbreviation: MG KS4

See also: Pre-curriculum/National curriculum descriptions. Category lists.


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, a/sinA = b/sinB = c/sinC , and cosine rule, a2 = b2 + c2 - 2bc cos A, to find unknown lengths and angles}
  • {know and apply Area = 1/2 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}

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