# Of any maximum or minimum points 4 d find the value of

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Unformatted text preview: ks) 402. A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. (a) The first two apples are green. What is the probability that the third apple is red? (b) What is the probability that exactly two of the three apples are red? Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 273 403. The diagram shows part of the graph of y = a (x – h)2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0). y P 2 1 A –1 (a) 1 x Write down the value of (i) h; (ii) (b) 0 k. Calculate the value of a. Working: Answers: (a) (i) …………………………………….. (ii) …………………………………….. (b) ................................................................. (Total 6 marks) 274 404. Figure 1 shows the graphs of the functions f1, f2, f3, f4. Figure 2 includes the graphs of the derivatives of the functions shown in Figure 1, e.g. the derivative of f1 is shown in diagram (d). Figure 1 Figure 2 y y f1 (a) O O x x y y f2 (b) O O x y x y f3 (c) O x O y x y f4 (d) O x O x y (e) O x 275 Complete the table below by matching each function with its derivative. Function Derivative diagram f1 (d) f2 f3 f4 Working: (Total 6 marks) 405. Consider the following statements A: log10 (10x) > 0. B: –0.5 ≤ cos(0.5x) ≤ 0.5. 276 π π ≤ arctan x ≤ . 2 2 C: – (a) Determine which statements are true for all real numbers x. Write your answers (yes or no) in the table below. Statement (a) Is the statement true for all real numbers x? (Yes/No) (b) If not true, example A B C (b) If a statement is not true for all x, complete the last column by giving an example of one value of x for which the statement is false. Working: (Total 6 marks) 277 2 ˆ , BC = 6, ABC = 45°. 2 406. The diagram shows a triangle ABC in which AC = 7 A 2 72 Diagram not to scale B (a) Use the fact that sin 45° = 45° C 6 6 2 ˆ to show that sin BAC = . 2 7 (2) ˆ The point D is on (AB), between A and B, such that sin BDC = (i) ˆ ˆ Write down the value of BDC + BAC . (ii) Calculate the angle BCD. (iii) (b) 6 . 7 Find the length of [BD]. (6) (c) Show that Area of ∆BDC BD = . Area of ∆BAC BA (2) (Total 10 marks) 407. Ashley and Billie are swimmers training for a competition. (a) Ashley trains for 12 hours in the first week. She decides to increase the amount of time she spends training by 2 hours each week. Find the total number of hours she spends training during the first 15 weeks. (3) 278 (b) Billie also trains for 12 hours in the first week. She decides to train for 10% longer each week than the previous week. (i) Show that in the third week she trains for 14.52 hours. (ii) Find the total number of hours she spends training during the first 15 weeks. (4) (c) In which week will the time Billie spends training first exceed 50 hours? (4) (Total 11 marks) 4...
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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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