Geometry & MeasuresExam Tips

Exam Tips

Part of Vectors (Geometry Proofs) · GCSE GCSE Mathematics revision

This exam tips covers Exam Tips within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 11 of 12 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.

Topic position

Section 11 of 12

Practice

14 questions

Recall

12 flashcards

Exam Tips

Always show the route: write AB = AO + OB before substituting. Examiners want to see the path, not just the answer.
Factor out clearly: write ½(-a + b) rather than leaving it unexpanded — it makes the scalar multiple obvious.
State the conclusion: never let the algebra speak for itself. Write "Therefore PQ is parallel to AB" or "Therefore A, B, C are collinear."
Watch the direction of arrows: if the arrow in the diagram points from B to A but you need AB, that is -BA.
Collinearity needs two conditions: parallel direction AND a shared point. Say both explicitly.
Common error: writing OA = a when OA means the magnitude. Context matters — in vector geometry OA usually means the vector.

Keep building this topic

Read this section alongside the surrounding pages in Vectors (Geometry Proofs). That gives you the full topic sequence instead of a single isolated revision point.

Key Results to Remember Practice Questions Vectors in Geometry: Proving What You Can See Knowledge Organiser: Vectors — Geometry Proofs

Practice Questions for Vectors (Geometry Proofs)

Vector AB goes from point A to point B. Which of the following describes vector BA?

A. The same vector as AB
B. Twice the length of AB in the same direction
C. The same magnitude as AB but in the opposite direction
D. Half the length of AB in the opposite direction

1 markfoundation

A student says: 'I have shown that vector AB is parallel to vector CD, so A, B, C, D all lie on the same straight line.' Explain why the student's reasoning is incorrect.

2 marksstandard

Quick Recall Flashcards

If AB = a, what is BA?

BA = -a. Reversing the direction of travel negates the vector. In diagrams: if you travel against an arrow, write a negative sign in front of that vector.

When are two vectors parallel?

Two vectors p and q are parallel when one is a scalar multiple of the other: p = kq for some non-zero scalar k. They point in the same or exactly opposite direction.

14 questions on Vectors (Geometry Proofs) — practise free

Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.

Try PrepWise Free

Key Results to Remember

Practice Questions