Cambridge A Level Mathematics 9709 — 2018 Feb/March Paper 2 · Variant 2

1 Solve the inequality 5x 2 4x 3 . [4] + > + ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mark scheme: 1 EITHER: State or imply non-modular inequality 2 2 (5 2) (4 3) + > + x x or corresponding equation or pair of linear equations (B1 Attempt solution of 3-term quadratic equation or of 2 linear equations M1 Obtain critical values 5 9 − and 1 A1 And no others State answer 5 9 , 1 < − > x x A1) OR: Obtain critical value 1 = x from graph, inspection, equation (B1 Obtain critical value 5 9 = − x similarly B2 State answer 5 9 , 1 < − > x x B1) 4

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2 A curve has equation y 4x sin 2x.1 Find the equation of the tangent to the curve at the point for which = x [4] = 0. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mark scheme: 2 Differentiate using product rule *M1 Obtaining form 1 1 1 2 2 2 sin cos + k x k x x Obtain correct 1 1 2 2 4sin 2 cos + x x x or unsimplified equivalent A1 Attempt equation of tangent with numerical value for gradient DM1 Dependent on first M1 Obtain 4 = y x A1 4

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