# Using a confidence interval for the mean determine

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Unformatted text preview: A ∪ B) = 1. Find (a) p(A∩B) (b) p ( A ∪ B) Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 47 66. At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100 mathematicians. Working: Answers: ....…………………………………….......... (Total 4 marks) 67. The diagram shows part of the graph of y = 12x2(1 – x). y 0 (a) x Write down an integral which represents the area of the shaded region. 48 (b) Find the area of the shaded region. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 68. Differentiate with respect to x: (a) (x2 + l)2 (b) 1n(3x – 1). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 49 25 69. The mean of the population x1, x2, ........ , x25 is m. Given that ∑x i = 300 and i =1 25 ∑ ( x – m) i 2 = 625, find i =1 (a) the value of m; (b) the standard deviation of the population. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 70. Solve the equation 3 sin2x = cos2x, for 0° ≤ x ≤ 180°. Working: Answers: ....…………………………………….......... (Total 4 marks) 50 71. 5 2 A and B are 2 × 2 matrices, where A = and BA = 2 0 11 2 44 8 . Find B. Working: Answers: ....…………………………………….......... (Total 4 marks) 72. The quadrilateral OABC has vertices with coordinates O(0, 0) A(5, 1) B(10, 5) and C(2, 7). (a) Find the vectors OB and AC . (b) Find the angle between the diagonals of the quadrilateral OABC. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 51 73. Find the coefficient of a3b4 in the expansion of (5a + b)7. Working: Answers: ....…………………………………….......... (Total 4 marks) 74. Three of the following diagrams I, II, III, IV represent the graphs of (a) y = 3 + cos 2x (b) y = 3 cos(x + 2) (c) y = 2 cos x + 3. 52 Identify which diagram represents which graph. y I y II 4 2 1 2 1 – –π 2 –π x 1 – –π 2 –π 1 –π 2 π 3 –π 2 3 π 5 2 4 1 –π x 3π – 2 y IV 1 – –π 2 π x 3π – 2 –2 y III –1 1 –π 2 3 1 –π 2 π x 3π – 2 2 1 –3 –π 1 – –π 2 1 –π 2 Working: Answers: (a) ………………………………………….. (b) .................................................................. (c) …………………………………….......... (Total 4 marks) 53 75. Solve the equation 43x–1 = 1.5625 × 10–2. Working: Answers: ....…………………………………...
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