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.
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.
Practice questions for Vectors (Geometry Proofs)
Vector AB goes from point A to point B. Which of the following describes vector BA?
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.
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.