- 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 Fi 1 (23.67 KiB) Viewed 20 times
- 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 Fi 2 (23.67 KiB) Viewed 20 times
- 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 Fi 3 (23.67 KiB) Viewed 20 times
- 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 Fi 4 (18.35 KiB) Viewed 20 times
- 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 Fi 5 (21.52 KiB) Viewed 20 times
- 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 Fi 6 (22.68 KiB) Viewed 20 times
- 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 Fi 7 (26.88 KiB) Viewed 20 times
- 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 Fi 8 (19.95 KiB) Viewed 20 times
- 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 Fi 9 (19.95 KiB) Viewed 20 times
- 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 Fi 10 (13.67 KiB) Viewed 20 times
- 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 Fi 11 (14.48 KiB) Viewed 20 times
- 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 Fi 12 (37.05 KiB) Viewed 20 times
- 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 Fi 13 (14.93 KiB) Viewed 20 times
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)
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 4 Total: [7 Marks] The diagram shows the curve y = cos-ix for-13XS1 (a) Write down the exact coordinates of the points A and B. (2) (b) The equation cos- x= 3x + 1 has only one root. Given that the root of this equation is a show that 0.1 Sas 0.2. 12) (C) Use the iteration cos' x - 1) with x = 0.1 to find the values of x2, 13 and X. giving your answers to three decimal places. 3 (3)
Question 5 Total: 16 Marks) Jennie as 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) 50 54 Donovan Varer Higgins 6 7 3 55 25 47 Begum Colles 1 80 Coldridge 4 61 Nechalk 45 65 Carter 8 We 11 92 She plot a scatter diagram of it, as shown below am fout of 100 19 81 20 90 Pradehouse eroposte diesen pottle on the position on the fram och Jerne decade to orien Describe the common by weather
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 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 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 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 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 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