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Unformatted text preview: ing: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 561 822. Consider y = sin x + π . 9 (a) (b) The graph of y intersects the x-axis at point A. Find the x-coordinate of A, where 0 ≤ x ≤ π. Solve the equation sin x + π = – 1 , for 0 ≤ x ≤ 2π. 9 2 Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 823. The table below shows some values of two functions, f and g, and of their derivatives f′ and g′. x 1 2 3 4 f(x) 5 4 –1 3 g(x) 1 –2 2 –5 f′(x) 5 6 0 7 g′(x) –6 4 –3 4 562 Calculate the following. (a) d (f(x) + g(x)), when x = 4; dx (b) ∫ (g' ( x) + 6)dx . 3 1 Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 824. The equation of a curve may be written in the form y = a(x – p)(x – q). The curve intersects the x-axis at A(–2, 0) and B(4, 0). The curve of y = f(x) is shown in the diagram below. y 4 2 –4 A –2 0 2 B 4 6x –2 –4 –6 563 (a) (i) Write down the value of p and of q. (ii) Given that the point (6, 8) is on the curve, find the value of a. (iii) Write the equation of the curve in the form y = ax2 + bx + c. (5) (b) dy . dx (i) Find (ii) A tangent is drawn to the curve at a point P. The gradient of this tangent is 7. Find the coordinates of P. (4) (c) The line L passes through B(4, 0), and is perpendicular to the tangent to the curve at point B. (i) Find the equation of L. (ii) Find the x-coordinate of the point where L intersects the curve again. (6) (Total 15 marks) 825. The table below shows the subjects studied by 210 students at a college. Year 1 Year 2 Totals History 50 35 85 Science 15 30 45 Art 45 35 80 Totals 110 100 210 564 (a) A student from the college is selected at random. Let A be the event the student studies Art. Let B be the event the student is in Year 2. (i) Find P(A). (ii) Find the probability that the student is a Year 2 Art student. (iii) Are the events A and B independent? Justify your answer. (6) (b) Given that a History student is selected at random, calculate the probability that the student is in Year 1. (2) (c) Two students are selected at random from the college. Calculate the probability that one student is in Year 1, and the other in Year 2. (4) (Total 12 marks) 826. The diagram shows a triangular region formed by a hedge [AB], a part of a river bank [AC] and ˆ a fence [BC]. The hedge is 17 m long and BAC is 29°. The end of the fence, point C, can be positioned anywhere along the river bank. (a) Given that point C is 15 m from A, find the length of the fence [BC]. 15 m A river bank C 29° 17 m B (3) 565 (b) The farmer has another, longer fence. It is possible for him to enclose two different ˆ triangular regions with this fence. He places the fence so...
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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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