Marks 82 118 discuss the convergence or divergence of

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Unformatted text preview: x ≤ 360°, giving your answers to the nearest degree. Working: Answers: ....…………………………………….......... (Total 4 marks) 87 126. Find a vector equation of the line passing through (–1, 4) and (3, –1). Give your answer in the form r = p + td, where t ∈ . Working: Answers: ....…………………………………….......... (Total 4 marks) 127. Find the coordinates of the point on the graph of y = x2 – x at which the tangent is parallel to the line y = 5x. Working: Answers: ....…………………………………….......... (Total 4 marks) 88 128. If f ′(x) = cos x, and f π = – 2, find f(x). 2 Working: Answers: ....…………………………………….......... (Total 4 marks) 129. Find the sum of the infinite geometric series 2 − 4 + 8 − 16 + ... 3 9 27 81 Working: Answers: ....…………………………………….......... (Total 4 marks) 89 130. Find the coefficient of a5b7 in the expansion of (a + b)12. Working: Answers: ....…………………………………….......... (Total 4 marks) 131. If A is an obtuse angle in a triangle and sin A = 5 , calculate the exact value of sin 2A. 13 Working: Answers: ....…………………………………….......... (Total 4 marks) 90 132. The quadratic equation 4x2 + 4kx + 9 = 0, k > 0 has exactly one solution for x. Find the value of k. Working: Answers: ....…………………………………….......... (Total 4 marks) 133. The diagram shows three graphs. B y A C x A is part of the graph of y = x. B is part of the graph of y = 2x. C is the reflection of graph B in line A. Write down 91 (a) the equation of C in the form y =f(x); (b) the coordinates of the point where C cuts the x-axis. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 134. Let f (x) = x3. (a) Evaluate f (5 + h) − f (5) for h = 0.1. h 92 (b) What number does f (5 + h) − f (5) approach as h approaches zero? h Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 135. The Acme insurance company sells two savings plans, Plan A and Plan B. For Plan A, an investor starts with an initial deposit of $1000 and increases this by $80 each month, so that in the second month, the deposit is $1080, the next month it is $1160 and so on. For Plan B, the investor again starts with $1000 and each month deposits 6% more than the previous month. (a) Write down the amount of money invested under Plan B in the second and third months. (2) Give your answers to parts (b) and (c) correct to the nearest dollar. (b) Find the amount of the 12th deposit for each Plan. (4) 93 (c) Find the total amount of money invested during the first 12 months (i) under Plan A; (2) (ii) under Plan B. (2) (Total 10 marks) 136. The main runway at Concordville airport is 2 km long. An aeroplane,...
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