Cambridge A Level Mathematics 9709 — 2016 Oct/Nov Paper 2 · Variant 1
9709/21/O/N/16 · 2 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q3 · A curve has equation y 2 sin 2x cos 2x 6 and is defined for 0 Find the x-coordinates of…
3 A curve has equation y 2 sin 2x cos 2x 6 and is defined for 0 Find the x-coordinates of the stationary points of= the curve,−5giving your+ answers correct to 3≤xsignificant≤0. figures. [6]
Mark scheme: 3 Differentiate to obtain 4cos2 x + 10sin 2 x B1 Equate first derivative to zero and arrange to tan 2 x = ... *M1 Obtain tan 2 x = − 0.4 A1 Carry out correct method for finding at least one value of x, dependent *M DM1 Obtain x = 1.38 A1 Obtain x = 2.95 and no others between 0 and π A1 [6] 2
Q5 · Cos 2x 9 cosx 5 5 (i) Show that 2 cos x 1
cos 2x 9 cosx 5 5 (i) Show that 2 cos x 1. [3] + + cosx 4 + + 0 cos 4x 9 cos 2x 5 (ii) Hence find the exact value of dx. [4] + + Ô cos 2x 4 −0 +
Mark scheme: 5 (i) Use cos2 x = 2cos 2 x − 1 and attempt factorisation of numerator M1 Obtain (2cos x + 1)(cos x + 4) A1 Confirm given result 2cos x + 1 A1 [3] (ii) Express integrand as 2cos2 x + 1 B1 Integrate to obtain sin 2 x + x B1 Apply limits correctly to integral of form k1 sin 2 x + k 2 x M1 Obtain 2π A1 [4] dy
What was in this paper
The subtopics covered by these 2 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 2016 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.