Cambridge A Level Mathematics 9709 — 2014 May/June Paper 1 · Variant 1
9709/11/M/J/14 · 1 question · 75 marks · ≈84 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper4 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q8 · Relative to an origin O, the position vectors of points A and B are given by ` a ` a 3p…
8 Relative to an origin O, the position vectors of points A and B are given by ` a ` a 3p −p −−→ −−→ OA = 4 and OB = −1 . p2 p2 (i) Find the values of p for which angle AOB is 90Å. [3] −−→ (ii) For the case where p = 3, find the unit vector in the direction of BA. [3]
Mark scheme: 8 (i) OA.OB = –3p2 – 4 + p4 soi M1 (p2 + 1)(p2 – 4) = 0 oe e.g. with substitution M1 Put = 0 (soi) and attempt to solve p = ±2 and no other real solutions A1 [3] 9 − 3 12 (ii) BA = 4 − − 1 = 5 M1 Reversed subtraction can score M1M1A0 9 9 0 BA = 12 2 + 5 2 = 13 and division by their 13 M1 12 1 Unit vector = 5 cao A1 13 0 [3] sin2 θ − (1 − cos θ )
What was in this paper
The subtopics covered by these 1 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2014 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.