Swiss Cottage WA2 Revision Paper.QP

1 Swiss Cottage Secondary School 2024 WA2 Practise Paper MATHEMATICAL FORMULAE 1. ALGEBRA Quadratic Equation For the equation 2ax bx c 0   , 2 4 2 b b acx a    . Binomial Theorem 1 2 2 1 2 n n n n n r r n n n n(a b) a a b a b ..... a b .... b r                          where n is a positive integer and      1 ........ 1! ! ! ! n n n n rn r n r r r          . 2. TRIGONOMETRY Identities 2 2sin cos 1A A  2 2sec 1 tanA A  2 2cosec 1 cotA A   sin sin cos cos sinA B A B A B    cos cos cos sin sinA B A B A B     tan tantan 1 tan tan A BA B A B    sin 2 2sin cosA A A 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A      2 2 tantan 2 1 tan AA A  Formulae for ABC sin sin sin a b c A B C  2 2 2 2 cosa b c bc A   1 sin2 bc A Home of Thoughtful Leaders: Serve with Honour, Lead with Humility 30

2 1 Given that     2 3 3 4f 2 3 4 xx x   , find  f . x [3]

3 2 The total surface area of a spherical ball of ice is decreasing at a rate of /scm2 2 . Find the rate of change of the volume when its radius is 0.5 cm. [Volume of sphere = 34 3 r ; total surface area of sphere = 24 r ] [5]

4 3 It is given that  3 1 2 1.y x x   (i) Show that d d y x can be written in the form 2 1 mx n x   where m and n are integers. [3] (ii) Show that y is increasing for 1 .2x [2]

5 4 A curve has the equation 2 ,3 4 xy x   4 .3x (i) Find an expression for d .d y x [2] (ii) Find the coordinates of the points on the curve where the normal is parallel to the line 2 16 3.y x  [3]

6 5 The diagram shows part of a straight line graph drawn to represent the equation 3y cx dx  . Find the value of c and of d. [4] x2 (4, 5) (7, 8)

7 6 The following table shows the population density, d, of a colony of bacteria , taken at various time, t, in minutes, during an experiment. t 16 32 48 64 80 d 0.0364 0.0603 0.0998 0.165 0.273 It is believed that d, can under certain circumstances be modelled by ektd A , where A and k are constants. (i) On a graph paper, p lot ln d against t and draw a straight line graph. The vertical ln d-axis should have a scale of 2 cm to 0.5 unit, and the horizontal t-axis should start at 0 and have a scale 2 cm to 10 minutes. [3] (ii) Use the graph to estimate the value of A and of k. [3] (iii) Estimate the population density at the 50th minute. [2] End of Paper