6 marks 340 513 part of the graph of y p q cos x is

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Unformatted text preview: ................................... (Total 6 marks) 360 539. The function f is given by f(x) = 2 – x2 – ex. Write down (a) the maximum value of f(x); (b) the two roots of the equation f(x) = 0. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) ˆ ˆ 540. In the triangle ABC, A = 30°, BC = 3 and AB = 5. Find the two possible values of B . Working: Answers: …....………………………………………….. …….................................................................. (Total 6 marks) 361 541. The independent events A, B are such that P(A) = 0.4 and P(A ∪ B) = 0.88. Find (a) P(B) (b) the probability that either A occurs or B occurs, but not both. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 542. A curve has equation x3 y2 = 8. Find the equation of the normal to the curve at the point (2, 1). Working: Answer: …....………………………………………….. (Total 6 marks) 362 543. The complex number z satisfies the equation z= 2 + 1 – 4i 1– i Express z in the form x + iy where x, y ∈ . Working: Answer: …....………………………………………….. (Total 6 marks) 544. Find the exact value of x satisfying the equation (3x)(42x+1) = 6x+2. Give your answer in the form ln a where a, b ∈ ln b . Working: Answer: …....………………………………………….. (Total 6 marks) 363 545. Solve the inequality x – 2 ≥ 2x + 1. Working: Answer: …....………………………………………….. (Total 6 marks) 546. The random variable X is normally distributed and P(X ≤ 10) = 0.670 P(X ≤ 12) = 0.937. Find E(X). Working: Answer: …....………………………………………….. (Total 6 marks) 364 547. The point A is the foot of the perpendicular from the point (1, 1, 9) to the plane 2x + y – z = 6. Find the coordinates of A. Working: Answer: …....………………………………………….. (Total 6 marks) 548. A particle moves in a straight line. Its velocity v ms–1 after t seconds is given by v = e – t sin t. Find the total distance travelled in the time interval [0, 2π]. Working: Answer: …....………………………………………….. (Total 6 marks) 365 549. The function f is defined for x ≤ 0 by f(x) = x2 –1 . x2 +1 Find an expression for f–1(x). Working: Answer: …....………………………………………….. (Total 6 marks) 550. Using the substitution y = 2 –x, or otherwise, find ∫ 2 x dx. 2– x Working: Answer: …....………………………………………….. (Total 6 marks) 366 551. A teacher drives to school. She records the time taken on each of 20 randomly chosen days. She finds that 20 ∑x 20 i = 626 and i =1 ∑x i 2 = 19780.8, where xi denotes the time, in minutes, taken on the ith i =1 da...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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