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GCSE Higher · grades 4–9 · 20% of marks

GCSE Higher — Geometry and measures

20% of a GCSE Higher entry is geometry and measures, spread across all three papers rather than gathered into one. The DfE lists 25 content statements for geometry and measures at this tier, and the question bank is organised by them rather than by chapter headings, so you can see exactly which one you are weak on. Expect geometric terms, notation and diagrams, ruler and compass constructions and loci, angle facts, parallel lines and polygons, properties of triangles and quadrilaterals, congruence criteria for triangles and geometric reasoning and simple proofs. Higher only: combinations of transformations and invariance, circle theorems, the sine rule and the cosine rule and area of a triangle: ½ab sin C. A Foundation entry is never asked for these. 40% of the marks are AO1, for applying a standard technique correctly, and the remaining 60% are for reasoning and for solving problems — so an answer with no working rarely scores everything that was available. Most of this area is natural Paper 1 material, so practise it without a calculator before you practise it with one.

  • G1 — Geometric terms, notation and diagrams
  • G2 — Ruler and compass constructions and loci
  • G3 — Angle facts, parallel lines and polygons
  • G4 — Properties of triangles and quadrilaterals
  • G5 — Congruence criteria for triangles
  • G6 — Geometric reasoning and simple proofs
  • G7 — Transformations: rotation, reflection, translation, enlargement (part Higher)
  • G8 — Combinations of transformations and invariance (Higher only)
  • G9 — Circle definitions and parts of a circle
  • G10 — Circle theorems (Higher only)
  • …and 15 more geometry and measures statements at this tier

Practise

GCSE Higher · Geometry and measuresQuestion 1 of 20 · 0 correct
Practice mode· no pressure · hints available

Geometry and measures

G5

Intermediate

A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

💡 Hints:
Printable worksheetNon-calculator sheetSample Paper 1Sample Paper 2

The 25 DfE statements in geometry and measures at Higher

G1Geometric terms, notation and diagramsnon-calculator
30 questions
G2Ruler and compass constructions and locinon-calculator
15 questions
G3Angle facts, parallel lines and polygonsnon-calculator
30 questions
G4Properties of triangles and quadrilateralsnon-calculator
30 questions
G5Congruence criteria for trianglesnon-calculator
30 questions
G6Geometric reasoning and simple proofsnon-calculator
30 questions
G7Transformations: rotation, reflection, translation, enlargementpart Highernon-calculator
Higher-only part: "and negative"32 questions
G8Combinations of transformations and invarianceHigher onlynon-calculator
28 questions
G9Circle definitions and parts of a circlenon-calculator
30 questions
G10Circle theoremsHigher onlynon-calculator
30 questions
G11Geometrical problems on coordinate axesnon-calculator
30 questions
G12Properties of 3D shapesnon-calculator
30 questions
G13Plans and elevationsnon-calculator
10 questions
G14Standard units of measureeither paper
30 questions
G15Measuring, scale drawings and bearingseither paper
30 questions
G16Area of 2D shapes and volume of prismseither paper
30 questions
G17Circles, composite shapes, spheres, pyramids and conescalculator
30 questions
G18Arc lengths and sector areascalculator
30 questions
G19Congruence and similarity: lengths, areas and volumespart Highereither paper
Higher-only part: "areas and volumes"30 questions
G20Pythagoras’ theorem and trigonometric ratiospart Highercalculator
Higher-only parts: "and, where possible, general triangles"; "and three dimensional figures"30 questions
G21Exact trigonometric valuesnon-calculator
30 questions
G22The sine rule and the cosine ruleHigher onlycalculator
30 questions
G23Area of a triangle: ½ab sin CHigher onlycalculator
30 questions
G24Translations as vectorsnon-calculator
30 questions
G25Vector arithmetic and vector proofpart Highernon-calculator
Higher-only part: "use vectors to construct geometric arguments and proofs"30 questions

Related

Geometry and measures at Foundation15% of Higher marksRatio, proportion and rates of changeHigher · 20% of marksAlgebraHigher · 30% of marksNumberHigher · 15% of marks

Questions people ask

How much of the GCSE Higher paper is geometry and measures?

20% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.

How many topics are there in geometry and measures at GCSE Higher?

25 DfE content statements, coded G1 to G25 within this area. Every question in the bank is tagged to one of them.

Which geometry and measures topics are Higher only?

Combinations of transformations and invariance (G8), Circle theorems (G10), The sine rule and the cosine rule (G22) and Area of a triangle: ½ab sin C (G23). A further 4 statements have a Higher-only part inside otherwise shared content.

Can I use a calculator for geometry and measures questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 25 statements in this area, 16 are naturally non-calculator and 5 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does geometry and measures carry?

The GCSE Higher split is 40% AO1 (use and apply standard techniques), 30% AO2 (reason, interpret and communicate) and 30% AO3 (solve problems in and out of context). Questions in this area are set across all three.

Are these past paper questions?

No. Every question at /gcse-higher is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.

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