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CIE · IGCSE · Mathematics

Vectors: Position vectors and geometric proofs using vectors
Practice Questions

20 CIE IGCSE Mathematics questions on Vectors: Position vectors and geometric proofs using vectors, each with instant feedback and a full examiner-style mark scheme.

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Question 1 · 1 mark · Difficulty 1/3

The position vector of point A is **a** and the position vector of point B is **b**. What is the vector $\overrightarrow{AB}$?

  1. **a** + **b**
  2. **a** − **b**
  3. **b** − **a**
  4. **b** + **a**
Show answer & explanation
✓ Answer: C — **b** − **a**
Award 1 mark for correct identification that $\overrightarrow{AB}$ = position vector of B − position vector of A. A is incorrect because **a** + **b** gives the sum of position vectors, not the displacement. B is incorrect because **a** − **b** gives $\overrightarrow{BA}$, the reverse direction. D is incorrect because addition does not give displacement between points.
Question 2 · 1 mark · Difficulty 2/3

In triangle OPQ, O is the origin, $\overrightarrow{OP}$ = **p** and $\overrightarrow{OQ}$ = **q**. M is the midpoint of PQ. What is the position vector of M?

  1. $\frac{1}{2}$(**p** − **q**)
  2. $\frac{1}{2}$(**p** + **q**)
  3. **p** + $\frac{1}{2}$**q**
  4. **q** − $\frac{1}{2}$**p**
Show answer & explanation
✓ Answer: B — $\frac{1}{2}$(**p** + **q**)
Award 1 mark for correct application of midpoint formula. The position vector of the midpoint is the average of the position vectors of the endpoints. A is incorrect — this gives half the vector from Q to P. C is incorrect — this does not represent the midpoint. D is incorrect — this is not the correct midpoint formula.
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CIE IGCSE Mathematics: Vectors: Position vectors and geometric proofs using vectors FAQ

How many CIE IGCSE Mathematics questions on Vectors: Position vectors and geometric proofs using vectors are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Vectors: Position vectors and geometric proofs using vectors 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 Vectors: Position vectors and geometric proofs using vectors 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 Vectors: Position vectors and geometric proofs using vectors 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 Vectors: Position vectors and geometric proofs using vectors typically tested on CIE IGCSE Mathematics papers?
Vectors: Position vectors and geometric proofs using vectors 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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