AQA GCSE Mathematics Paper 3 (Higher), June 2025: Question 3

3 marks · Easy difficulty · Short Answer

Match the labelled parts of a circle, including a sector, a tangent, and a segment, to their correct terms.

Practise this question

Question

A circle with centre O showing four labelled features: A points to a radius from the centre to the circumference; B points to a shaded region enclosed by two radii and an arc; C points to a line that touches the top of the circle at a single point; D points to a shaded region enclosed by a chord and an arc. Below, boxes labelled A, B, C, and D are listed on the left, and terms Arc, Chord, Diameter, Radius, Sector, Segment, and Tangent are listed on the right, with A already joined to Radius by a line.

Mark scheme

Show the mark scheme Mark scheme for Question 3 showing that B matches to Sector, C matches to Tangent, and D matches to Segment, awarding 1 mark for each correct match (B3 total). A matching diagram is also provided showing lines connecting A to Radius, B to Sector, C to Tangent, and D to Segment, with additional guidance noting that two lines drawn from a single left-hand box is treated as choice.

How to answer it

Circle Parts & Terminology

AQA GCSE Mathematics • Geometry • 3 Marks

What this question tests

This question assesses your visual recall and vocabulary of the standard geometric properties and parts of a circle. You need to distinguish clearly between:

  • One-dimensional features (lines & boundaries): Radius, Diameter, Chord, Tangent, and Arc.
  • Two-dimensional features (enclosed regions/areas): Sector vs. Segment.

Question Walkthrough & Solutions

Identify the correct circle term for labels B, C, and D

Letter Visual Description in Diagram Correct Term Mark Awarded
A Line segment from centre O to the circumference Radius Given in question
B Shaded "slice" enclosed by two radii and an arc Sector 1 mark [B1]
C Straight line touching the outside curve at exactly one point Tangent 1 mark [B1]
D Shaded region bounded by a straight chord and an arc Segment 1 mark [B1]
Total: 3 Marks • Awarded as independent marks ( B1 for each correct single match).

✅ Mark Scheme Matching

  • B → Sector: Enclosed like a pizza slice.
  • C → Tangent: A line touching the circumference externally.
  • D → Segment: Region between a chord and an arc.

💡 How to Tell Sector vs Segment

This is the most common point of confusion:

  • Sector: Starts with S like Slice of cake or pizza. Must meet at the centre O via two radii.
  • Segment: Starts with S like a Segment of an orange (flat chord back, curved arc front). Formed by cutting with a chord.

🧠 Exam Technique & Guidance

  • Rule of Single Lines: The mark scheme states: "Two lines from a left-hand box is choice". If you draw two lines from letter B to different words, you will score 0 marks for that letter, even if one is correct.
  • Use a Ruler: Draw clean, clear straight lines connecting the boxes to prevent ambiguity.
  • Elimination: Cross off distractors you know are wrong (e.g. Arc is a curve, Chord is a line inside, Diameter spans centre edge-to-edge).

❌ Common Errors to Avoid

  • Swapping Sector and Segment: Mixing up the two 2D regions is the #1 reason students drop marks on this topic.
  • Confusing Chord with Tangent: A chord stays inside the circle (joins two boundary points). A tangent stays outside and brushes the circle at exactly one point.
  • Label D matched to Chord: The arrow points into the shaded area (Segment), not directly to the straight boundary line itself (Chord).

📐 Circle Geometry Quick Reference Card

Lines (1D)

  • Radius: Centre to circumference ( r ).
  • Diameter: Edge to edge through centre ( 2r ).
  • Chord: Any line joining two points on the circle.
  • Tangent: Straight line touching the circle at 1 point (meets radius at 90°).
  • Arc: A fraction of the curved circumference.

Regions (2D)

  • Sector: Area between two radii and an arc (Area = θ/360 × πr²).
  • Segment: Area between a chord and an arc (Area of sector − Area of triangle).

Topics

Geometry and measures · 3.4.1 Properties and constructions

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.