Cambridge A Level Mathematics 9709 — 2020 Oct/Nov Paper 2 · Variant 3
9709/23/O/N/20 · 4 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 paper12 pages
Mark scheme11 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q3 · Y A B x O 1 2 The diagram shows the curve y The curve crosses the y-axis at the point A…
3 y A B x O 1 2 The diagram shows the curve y The curve crosses the y-axis at the point A, and the point B = + e−2x. on the curve has x-coordinate 1. The shaded region is bounded by the curve and the line segment AB. Find the exact area of the shaded region. [5] ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Mark scheme: 3 Integrate to obtain form 2 e x ax b − + M1 Obtain correct 2 1 2 e 2 x x − − A1 Apply limits to obtain 2 5 1 e 2 2 − − A1 Attempt to find area of relevant trapezium M1 Obtain 2 5 1 e 2 2 − + and subtract to obtain 2 e− or exact equivalent A1 5
Q4 · Solve the equation 2x x 6
4 (a) Solve the equation 2x x 6 . [3] −5 = + ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 6 . Give your answer correct to 3 significant (b) Hence find the value of y such that 21−y −5 = 2−y + figures. [2] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Mark scheme: 4(a) State or imply non-modulus equation 2 2 (2 5) ( 6) x x − = + or pair of linear equations B1 Attempt solution of 3-term quadratic equation or of pair of linear equations M1 Obtain 1 3 − and 11 A1 3 Question Answer Marks Guidance 4(b) Apply logarithms and use power law for 2 y k − = where 0 k > from (a) M1 Obtain 3.46 − A1 AWRT 2
Q5 · 8xn5 The sequence of values given by the iterative formula + with initial value 2…
6 8xn5 The sequence of values given by the iterative formula + with initial value 2 converges xn+1 = 8 x2 x1 = n + to !. (a) Use the iterative formula to find the value of correct to 4 significant figures. Give the result of ! each iteration to 6 significant figures. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (b) State an equation satisfied by and hence determine the exact value of [2] ! !. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Mark scheme: 5(a) Use iteration correctly at least once M1 Need to see 3 values including the starting values Obtain final answer 1.817 A1 Answer required to exactly 4 significant figures Show sufficient iterations to 6 significant figures to justify answer or show sign change in interval [1.8165, 1.8175] A1 3 5(b) State equation 2 6 8 8 x x x + = + or equivalent using α B1 Obtain 3 6 or exact equivalent B1 2
Q6 · It is given that 3 sin cos where is an angle such that 21 = 1 1 0Å < 1 < 90Å
6 It is given that 3 sin cos where is an angle such that 21 = 1 1 0Å < 1 < 90Å. (a) Find the exact value of sin [2] 1. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (b) Find the exact value of sec [2] 1. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (c) Find the exact value of cos [2] 21. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Mark scheme: 6(a) Use sin2 2sin cos = θ θ θ B1 Obtain 1 sin 6 θ = B1 2 6(b) Use correct identity or identities to find value of secθ M1 Obtain 6 35 or exact equivalent A1 2 6(c) Use correct identity or identities to find value of cos2θ M1 Obtain 17 18 or exact equivalent A1 2
What was in this paper
The subtopics covered by these 4 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 2020 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.