AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 11

1 mark · Easy difficulty · Short Answer

Use a pair of compasses to draw a circle given its diameter and centre X.

Practise this question

Question

A horizontal line segment is shown with a marked point labelled X at its centre. The question states: 'In this question use a pair of compasses. The line shown is the diameter of a circle, centre X. Draw the circle.'

Mark scheme

Show the mark scheme Mark scheme table for question 11. Answer: 'Correct circle drawn' awards 1 mark (B1). Comments state: 'mark intention, but must have been an attempt with compasses and not free-hand'.

How to answer it

Drawing a Circle from its Diameter

📌 What this question tests

Using geometric construction equipment (a pair of compasses) accurately, identifying the centre and radius of a circle when given the diameter, and drawing a complete circle that passes neatly through the endpoints of the given diameter line.

Question 11

AQA Foundation Tier • Geometry and Construction • 1 Mark

💡 Key Knowledge

  • Centre (X): The exact middle point of the circle where the sharp point of your compass must rest.
  • Diameter: The full straight line passing from one side of the circle to the other through the centre X.
  • Radius: The distance from the centre X to either outer endpoint of the line. The radius is exactly half of the diameter ( radius = diameter ÷ 2 ).

📐 Step-by-Step Construction

  1. Place the needle point of your compass firmly on point X.
  2. Adjust the compass pencil tip so it aligns precisely with one end of the drawn line segment (setting the compass width equal to the radius).
  3. Rotate the compass smoothly 360° to draw the complete circle.
  4. Verify that the drawn circumference passes through both ends of the original line.

✅ Correct Answer & Award Criteria

Full Circle Drawn (B1):

  • A single, clean, circular arc drawn completely around centre X.
  • The circle must pass through both outer ends of the given horizontal line segment.
  • Examiners look for intention and accurate compass use (within standard exam tolerance, typically ±2 mm of the endpoints).

🧠 Exam Technique

  • Check compass tightness: Tighten the hinge screw before entering the exam so the arms do not slip or widen while rotating.
  • Lean and rotate: Tilt the compass slightly forward in the direction of the turn and hold only the top spindle rather than the legs.
  • Sharp pencil: Keep your compass pencil sharp to ensure a thin, precise line that hits the endpoints cleanly.

❌ Common Errors

  • Free-hand drawing: Drawing the circle by hand without a pair of compasses scores 0 marks immediately (explicitly stated in mark scheme).
  • Wrong compass setting: Setting the compass width to the entire length of the line (the diameter) instead of from the centre X to an end (the radius).
  • Incomplete circle: Drawing only a semicircle or leaving large gaps along the circumference.
  • Wobbly or double lines: Going over the pencil line multiple times or letting the needle slip off point X.
Mark Scheme Note: Award B1 for a correct circle drawn. Examiners mark intention, but there must have been an attempt using a pair of compasses and not drawn free-hand.

Topics

Geometry and measures · 3.4.1 Properties and constructions

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.