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Question 5 Total: 16 Marks) Jennie is a piano teacher who teaches nine pupils She records how many hours per week they practice the piano song with the most recent practical exam score Student Practice hours per week Practical exam score out of 100 Donovan 50 Va 6 71 3 55 Higgins Begum 25 47 1 80 Collins Coldridge 4 Nedalek 65 Carter 83 Whe 11 92 She plots a scatter dagram of in data, as shown below cam fout of 1001 10 20 30 Practice those erty to postre este potenton terre position on the காயா போனிய Jerne decante e o cutien Describe the corn on by the degree

Question 9 Total: [10 Marks) The number of matches in each of a sample of 85 boxes is summarised in the table. Number of matches Number of boxes Less than 239 1 239-243 244-246 1 2 247 3 248 4 249 6 250 10 251 13 252 16 253 20 5 3 254 255-259 More than 250 Total 1 85 (a) For these data: (1) state the modal value; (1) (W) determine values for the median and the interquartile range (3) (b) Given that, on investigation, the 2 extreme values in the above table are 227 and 271, calculate estimates of the mean and the standard deviation (4) (c) For the numbers of matches in the 85 boxes, suggest with a reason, the most appropriate measure of spread 12)

Question 7 Total: [6 Marks] A quadrilateral has vertices A, B, C and D with position vectors given by OA- 5.08 - 2.0C-7 and OD 10 VO (a) Write down the vector AB (1) (6) Show that ABCD is a parallelogram, but not a rhombus. (5)

Question 3 Total: [9 Marks) (a) The baggage loading time, X minutes, of a chartered aircraft at its UK airport may be modelled by a normal random variable with mean 55 and standard deviation 8. Determine: ( P(X < 60); (3) (P(55 < X < 60) (2) (b) The baggage kading time, Y minutes, of a chartered aircraft at its overseas airport may be modelled by a normal random variable with mean and standard deviation 16. Given that P(Y<90) = 0.95, find the value of Al. (4)

Question 10 Total: [3 Marks] The equation 13 - x2 + 4x - 900 = 0 has exactly one real root, a Taking x1 = 10 as a first approximation to a, use the Newton-Raphson method to find a second approximation, xz, to a Give your answer to four significant figures ~ End of Exam

Question 8 Total: [6 Marks] (a) Find the first three terms, in ascending powers of x of the expansion of (1 - 2030 (3) (b) Carly has lost her calculator. She uses the first three terms, in ascending powers of x, of the expansion of (1 - 2x)?° to evaluate 0.9980 Find Carly's value for 0.998 10 and show that it is correct to five decimal places. (3)

Question 6 Total: [10 Marks) (a) A geometric series begins 420 + 294 + 205.8 ..... 0 Show that the common ratio of the series is 0.7. (1) () Find the sum to infinity of the series. (2) (W) Write the nth term of the series in the form p *q", where p and q are constants. (2) (b) The first term of an arithmetic series is 240 and the common difference of the series is -8. The nth term of the series is ( Write down an expression for alle (1 (1) (6) Given that 14 = 0, find the value of (4)

Question 5 Total: 16 Marks Jennie is a plano teacher who teaches nine pupils She records how many hours per week they practice the piano song with the most recent practical exam score Student Practice hours per week Practical exam score out of 100 54 6 7 Donovan Var Higgins Begum 3 55 25 47 Colin 1 80 4 61 Coldridge Nedak Cart 8 83 Whe 11 She plots a scatter diagram of this, as shown below am com fout of 100 10 20 30 Practice house de poste este posible non for the position on the foram Jerne decade it to outien Describe the come on by the

Question 1 Total: [7 Marks) A curve is defined for 0sxs by the equation y = x cos 2x, and is sketched below. M dy (a) Find 2) (2) (b) The point A, where x = a, on the curve is a stationary point. (0) Show that 1 - 2a tan 2a = 0. (2) () Show that 0.4 <a<0.5. (2) (H) Show that the equation 1 - 2x tan 2x = 0 can be rearranged to become tan- (1)

Question 2 Total: [10 Marks] The first term of a geometric series is 12 and the common ratio of the series is (a) Find the sum to finity of the series. ) (2) (b) Show that the sixth term of the series can be written in the form (3) (c) The nth term of the series is un Write down an expression for Un in terms of n. (1) (1) Hence show that loga un an loga 3- (31 – 5) loga 2 () (4)