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HomeCIE IGCSE MathematicsGeometry: Constructions and loci
CIE · IGCSE · Mathematics

Geometry: Constructions and loci
Practice Questions

20 CIE IGCSE Mathematics questions on Geometry: Constructions and loci, each with instant feedback and a full examiner-style mark scheme.

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Try 2 sample questions on Geometry: Constructions and loci

Question 1 · 1 mark · Difficulty 1/3

Which of the following correctly describes the locus of points equidistant from two fixed points A and B?

  1. A circle with centre at the midpoint of AB
  2. The perpendicular bisector of the line segment AB
  3. A line parallel to AB
  4. Two parallel lines either side of AB
Show answer & explanation
✓ Answer: BThe perpendicular bisector of the line segment AB
Award 1 mark for identifying the perpendicular bisector of AB. A is incorrect — a circle would represent points equidistant from a single point, not two points. C is incorrect — a parallel line would not include all equidistant points. D is incorrect — this describes the locus equidistant from a single line.
Question 2 · 1 mark · Difficulty 2/3

A surveyor needs to construct an angle of 60° using only a ruler and compasses. Which construction should be used as the first step?

  1. Construct a perpendicular bisector
  2. Construct an equilateral triangle
  3. Bisect a right angle
  4. Draw a semicircle
Show answer & explanation
✓ Answer: BConstruct an equilateral triangle
Award 1 mark for recognising that an equilateral triangle has interior angles of 60°. A is incorrect — a perpendicular bisector creates 90°, not 60°. C is incorrect — bisecting 90° gives 45°. D is incorrect — a semicircle alone does not create a 60° angle.
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20 questions · 25 min · free

CIE IGCSE Mathematics: Geometry: Constructions and loci FAQ

How many CIE IGCSE Mathematics questions on Geometry: Constructions and loci are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Geometry: Constructions and loci for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Geometry: Constructions and loci practice with other Mathematics topics or even switch to a totally different CIE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Geometry: Constructions and loci questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CIE.
How is Geometry: Constructions and loci typically tested on CIE IGCSE Mathematics papers?
Geometry: Constructions and loci appears across multiple question types on real CIE IGCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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