Cambridge A Level Mathematics 9709 — 2019 Oct/Nov Paper 2 · Variant 1

1 (i) Solve the inequality 2x 2x . [3] −7 < −9 ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (ii) Hence find the largest integer n satisfying the inequality 2 ln n 2 ln n . [2] −7 < −9 ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mark scheme: 1(i) State or imply non-modular inequality 2 2 (2 7) (2 9) x x − < − or corresponding equation or linear equation (with signs of 2x different) M1 Obtain critical value 4 A1 State 4 x < only A1 3 1(ii) Attempt to find n from lnn = their critical value from part (i) M1 Obtain or imply 4 e n < and hence 54 A1 2

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