Cambridge A Level Mathematics 9709 — 2018 Oct/Nov Paper 2 · Variant 2

2 Given that 9x 3x 240, find the value of 3x and hence, using logarithms, find the value of x correct to 4 significant+ figures.= [5] ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mark scheme: 2 2 (3 ) x or 2 B1 May be implied by 3 3 1 240 + = x x Attempt solution of quadratic equation in 3x *M1 Perhaps using substitution 3 = x u Obtain, finally, 3 15 = x only A1 Apply logarithms and use power law for 3 = x k where 0 > k M1 Dependent *M, need to see ln3 ln = x k , 3 log = x k oe Obtain 2.465 A1 May be done using 2 9 , x same processes 5

More questions on Logarithmic and exponential functions

3 y M x O The diagram shows the curve with equation y 5 sin 2x tan 2x = −3 for values of x such that 0 1 Find the x-coordinate of the stationary point M, giving your answer correct to 3 significant≤xfigures.< 40. [5] ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mark scheme: 3 B1 Differentiate to obtain 2 6sec 2 − x B1 Equate first derivative to zero and find value for 3 cos 2x M1 Use correct process for finding x from 3 cos 2 = x k M1 Obtain 0.284 nfww A1 Or greater accuracy 5

More questions on Differentiation