GCSE Maths (9-1) H: Geometry

GCSE (9-1) Higher Mathematics is broken down into six main areas:

  • Number (NH)
  • Algebra (AH)
  • Ratio, proportions, rates of change (RH)
  • Geometry and Measures (GH)
  • Statistics (SH)
  • Probability(PH)
Geometry:know how to

1. 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

2. 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

3. Angles:

  • Apply the properties of angles at a point
  • at a point on a straight line
  • vertically opposite angles
  • alternate and corresponding angles on parallel lines
  • derive and use the sum of angles in a triangle

4. Derive and apply the properties and definitions of:

  • special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus;
  • triangles and other plane figures using appropriate language

5. Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

6. Angles and Sides

  • Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to find results about angles and sides
  • Know that the base angles of isosceles triangle are equal
  • obtain simple proofs

7. 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)



Geometry: know how to

8. Describe the changes and invariance achieved by combinations of rotations, reflections and translations

9. Identify and apply circle definitions and properties, including:

  • centre, radius, chord, diameter, circumference
  • tangent, arc, sector and segment

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

11. Solve geometrical problems on coordinate axes

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

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

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

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

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

17. 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

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

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

20. Know the formulae for: Pythagoras' theorem, a2 + b2 = c2
... and the trigonometric ratios
SOHCAHTOA

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

21. 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°

22. Know and apply the sine and cosine rule

sine rule  and   a2 = b2 + c2 – 2bcCosA

to find unknown lengths and angles

23. Know and apply : Area triangle = ½absinC
to calculate the area, sides or angles of any triangle.

24. Describe translations as 2D vectors

25. 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