Cambridge A Level Mathematics 9709 — 2012 Oct/Nov Paper 1 · Variant 3
9709/13/O/N/12 · 2 questions · 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 scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q2 · 2 It is given that f(x) = x3 −x3, for x > 0
1 2 It is given that f(x) = x3 −x3, for x > 0. Show that f is a decreasing function. [3]
Mark scheme: (x) M1 1 7C3 × 24 × – 2 powers 4 and 3 35 seen or implied B1 –70 A1 [3] 2 f′(x) = – 3x–4– 3x2 B1 B1 0 ⇒ decreasing function B1 Dependent upon minus signs & even [3] powers 3 7 cos x +5=2(1–cos2x) M1 Use of c2 + s2=1 2 cos x + 1 ( cos x + 3) =0 cos = –0.5 A1 x=120°, 240° A1 A1 ft for 360 –1st solution [4] 4 area ∆ = 2√3 B1 2√3 π tan A= ⇒A= 3 B1 Accept 60° 2
Q3 · Solve the equation 7 cos x + 5 = 2 sin2x, for 0◦≤x ≤360◦
3 Solve the equation 7 cos x + 5 = 2 sin2x, for 0◦≤x ≤360◦. [4]
Mark scheme: 1 1 3 M1 A1 =55 (i) 2 4 3 9 3 27
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 2012 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.