O-LevelMathematicsVectors and transformations4024/12 · Oct/Nov 2025 · Q215 Marks

OPQR is a parallelogram. OP = a and OR = 2b. M is the midpoint of QR. N is a point on PQ and PN : NQ = 1 : 3. [Figure: Parallelogram OPQR. Vectors OP=a, OR=2b shown. Points M and N marked. NOT TO SCALE]

(a)(i)Find, as simply as possible, in terms of a and/or b MQ[1]
(a)(ii)Find, as simply as possible, in terms of a and/or b NM.[2]
(b)Line OP is extended to point X. MNX is a straight line. Find the position vector of X.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[1] (a)(i) (1/2)a
[2] (a)(ii) (3/2)b - (1/2)a final answer
[2] (a)(ii) B1 for PN = (1/2)b oe or NQ = (3/2)b oe
[2] (b) (7/6)a
[2] (b) B1 for PX = (1/6)a soi or for NMQ to NXP scale factor = 1/3 soi

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Vectors and transformations, O-Level Mathematics (syllabus 4024). Structured question, 5 marks.
Source: O-Level Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 21.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content