Cambridge A Level Mathematics 9709 — 2015 May/June Paper 4 · Variant 1
9709/41/M/J/15 · 3 questions · 50 marks · ≈56 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
Q1 · A block B of mass 2.7 kg is pulled at constant speed along a straight line on a rough…
1 A block B of mass 2.7 kg is pulled at constant speed along a straight line on a rough horizontal floor. The pulling force has magnitude 25 N and acts at an angle of 1 above the horizontal. The normal component of the contact force acting on B has magnitude 20 N. (i) Show that sin 1 = 0.28. [2] (ii) Find the work done by the pulling force in moving the block a distance of 5 m. [2]
Mark scheme: 1 Distance = × 6 × 500 = 1500 m or
Q2 · Y F N 25 N 1 tan−1 0.75 x O 63 N Three horizontal forces of magnitudes F N, 63 N and 25 N…
2 y F N 25 N 1 tan−1 0.75 x O 63 N Three horizontal forces of magnitudes F N, 63 N and 25 N act at O, the origin of the x-axis and y-axis. The forces are in equilibrium. The force of magnitude F N makes an angle 1 anticlockwise with the positive x-axis. The force of magnitude 63 N acts along the negative y-axis. The force of magnitude 25 N acts at tan−1 0.75 clockwise from the negative x-axis (see diagram). Find the value of F and the value of tan 1. [5]
Mark scheme: 2 1 1 distance = (0+6)×200+ (6+0)×300 2 2 2 1
Q3 · A block of weight 6.1 N slides down a slope inclined at tan−1 11 to the horizontal
3 A block of weight 6.1 N slides down a slope inclined at tan−1 11 to the horizontal. The coefficient of 60 friction between the block and the slope is 1 The block passes through a point A with speed 2 m s−1. 4. Find how far the block moves from A before it comes to rest. [5]
Mark scheme: 2 3 500 0.05t 0.0001t − A1 2 3 0 Distance = 0.025 × 5002 – 0.0001 × 5003 ÷ 3 = 2083 m A1 Accept 2080 For using area property of graph or 1 1 s = (u + v)t or s = ut + at2 2 2 M1 to find distance travelled by B
What was in this paper
The subtopics covered by these 3 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 2015 May/June, Paper 4 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.