# Type ii error 16 total 24 marks 794 using demorgans

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Unformatted text preview: on of the vertical asymptote of y = f(x). (1) (b) 2 Find f(x). Give your answer in the form ax + bx where a and b ∈ (5 x − 1) . (4) (Total 5 marks) 831. The function g(x) is defined for –3 ≤ x ≤ 3. The behaviour of g′(x) and g″(x) is given in the tables below. x –3 < x < –2 –2 –2 < x < 1 1 1<x<3 g′(x) negative 0 positive 0 negative x –3 < x < – 1 2 –1 2 –1<x<3 2 g″(x) positive 0 negative Use the information above to answer the following. In each case, justify your answer. 569 (a) Write down the value of x for which g has a maximum. (2) (b) On which intervals is the value of g decreasing? (2) (c) Write down the value of x for which the graph of g has a point of inflexion. (2) (d) Given that g(–3) = 1, sketch the graph of g. On the sketch, clearly indicate the position of the maximum point, the minimum point, and the point of inflexion. (3) (Total 9 marks) − 2 4 832. Let C = 1 7 and D = 5 2 −1 a. The 2 × 2 matrix Q is such that 3Q = 2C – D (a) Find Q. (3) (b) Find CD. (4) (c) Find D–1. (2) (Total 9 marks) 570 2 2 833. The position vectors of points P and Q are − 3 and 2 respectively. The origin is at O. 1 − 4 Find (a) ˆ the angle POQ ; (b) the area of the triangle OPQ. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 571 834. Solve the equation e 2 x − 1 = 2. x+2 Working: Answer: ....…………………………………….......... (Total 6 marks) 572 835. The table below shows the probability distribution of a discrete random variable X. x 0 1 2 3 P(X = x) 0.2 a b 0.25 (a) Given that E(X) = 1.55, find the value of a and of b. (b) Calculate Var(X). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 573 3 2 836. Given that A = 1 − 2 and B = 2 0 0 find X if BX = A – AB. − 3 Working: Answer: ....…………………………………….......... (Total 6 marks) 10 837. Consider the 10 data items x1, x2, ... x10. Given that ∑x 2 i = 1341 and the standard deviation is i =1 6.9, find the value of x . Working: Answer: ....…………………………………….......... (Total 6 marks) 574 5 838. The function f is given by f(x) = x + 2 , x ≠ 0. There is a point of inflexion on the graph of f at x the point P. Find the coordinates of P. Working: Answer: ....…………………………………….......... (Total 6 marks) 839. Let P(z) = z3 + az2 + bz + c, where a, b, and c ∈ (–3 + 2i). Find the value of a, of b and of c. . Two of the roots of P(z) = 0 are –2 and Working: Answer: ....…………………………………….......... (Total 6 marks) 575 840. A team of five students is to be chosen at random to take part in a debate. The team is to be chosen from a group of eight medical students and three law students. Find the probabil...
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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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