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Find the coefficient of x7 in the expansion of (2x ÿ 3)7 Circle your answer. [1 mark] ÿ2187 ÿ128 2 128 2 Given that y ¼ 2x3 find dy dx Circle your answer. [1 mark] dy dx ¼ 5x2 dy dx ¼ 6x2 dy dx ¼ x4 2 dy dx ¼ 6x

Simplify log2 8a Circle your answer. [1 mark] a3 2a 3a 8a 2 It is given that sin y ¼ 4 5 and 90° < y < 180° Find the value of cos y Circle your answer. [1 mark] ÿ 3 4 ÿ 3 5 3 5 3 4 Jun23/7356/2 Do not write outside the box (02)3 3 (a) Find ð  2x3 þ x82 dx [3 marks

At a point P on a curve, the gradient of the tangent to the curve is 10 State the gradient of the normal to the curve at P Circle your answer. [1 mark] ÿ10 ÿ0.1 0.1 10 2 Identify the expression below which is equivalent to 2x   5 ÿ3 Circle your answer. [1 mark] 8x3 125 125x3 8 125 8x3 8 125x3 Jun23/7356/1 Do not write outside the box (02)3 3 The coefficient of x2 in the binomial expansion of (1 þ ax)6 is 20 3 Find the two possible values of a [3 marks] ___________...

The discrete random variable A takes only the values 0, 2 and 4, and has cumulative distribution function F(a) ¼ P(A  a) a 0 2 4 F(a) 0.2 0.6 1 Find P(A ¼ 2) Circle your answer. [1 mark] 0 0.4 0.6 0.8 2 The time, T days, between rain showers in a city in autumn can be modelled by an exponential distribution with mean 1.25 Find the distribution of the number of rain showers per day in the city. Tick (3) one box. [1 mark] Distribution Mean Exponential 0.8 Exponential 1.25 Poisso...

State the dimensions of power. Circle your answer. [1 mark] ML2T ÿ3 ML3T ÿ3 ML3T ÿ2 ML2T ÿ2 2 The force (3i þ 4j) N acts at the point with coordinates (0, 2) The unit vectors i and j are directed along the x-axis and the y-axis respectively. Calculate the magnitude of the moment of this force about the origin. Circle your answer. [1 mark] 6 N m 8 N m 10 N m 14 N m

The simple-connected graph G is shown below. The graph G has n faces. State the value of n Circle your answer. [1 mark] 2 3 4 5 2 Jonathan and Hoshi play a zero-sum game. The game is represented by the following pay-off matrix for Jonathan. Hoshi Strategy H1 H2 H3 Jonathan J1 ÿ2 3 2 J2 3 2 0 J3 4 ÿ1 3 J4 3 1 0 The game does not have a stable solution. Which strategy should Jonathan never play? Circle your answer. [1 mark] J1 J2 J3 J4 Jun23/7367/3D Do not write outside the...

Given that y ¼ sin x þ sinh x , find d2y dx2 þ y Circle your answer. [1 mark] 2 sin x ÿ2 sin x 2 sinh x ÿ2 sinh x 2 Which one of the expressions below is not equal to zero? Circle your answer. [1 mark] lim x ! 1 (x2eÿx) lim x ! 0 (x5 ln x) lim x ! 1 ex   x5 xlim ! 0(x3ex)

Find the number of solutions of the equation tanh x ¼ cosh x Circle your answer. [1 mark] 0 1 2 3 2 The diagram below shows a locus on an Argand diagram. 2 Re Im –3 O Which of the equations below represents the locus shown above? Circle your answer. [1 mark] jz ÿ 2 þ 3ij ¼ 2 jz þ 2 ÿ 3ij ¼ 2 jz ÿ 2 þ 3ij ¼ 4 jz þ 2 ÿ 3ij ¼ 4

A particle moves along the x‑axis under the action of a force, F newtons, where F = 3x2 + 5 Find the work done by the force as the particle moves from x = 0 metres to x = 2 metres. Circle your answer. [1 mark] 12 J 17 J 18 J 34 J 2 Two particles are moving directly towards each other when they collide. Given that the collision is perfectly elastic, state the value of the coefficient of restitution. Circle your answer. [1 mark] e = –1 e = 0 e = 1 2 e = 1 3 A stone of mass 0.2 kg...

The continuous random variable X has variance 9 The discrete random variable Y has standard deviation 2 and is independent of X Find Var(X + Y ) Circle your answer. [1 mark] 5 11 13 85 2 The random variable T has a discrete uniform distribution and takes the values 1, 2, 3, 4 and 5 Find the variance of T Circle your answer. [1 mark] 15 43 2 13 6 Turn over for the next question