6 marks 274 404 figure 1 shows the graphs of the

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Unformatted text preview: …….. (Total 6 marks) 422. When John throws a stone at a target, the probability that he hits the target is 0.4. He throws a stone 6 times. (a) Find the probability that he hits the target exactly 4 times. (b) Find the probability that he hits the target for the first time on his third throw. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 288 423. The angle θ satisfies the equation tanθ + cotθ = 3, where θ is in degrees. Find all the possible values of θ lying in the interval [0°, 90°]. Working: Answers: ……………………………………………….. (Total 6 marks) 424. The weights of a certain species of bird are normally distributed with mean 0.8 kg and standard deviation 0.12 kg. Find the probability that the weight of a randomly chosen bird of the species lies between 0.74 kg and 0.95 kg. Working: Answer: ……………………………………………….. (Total 6 marks) 289 425. The function f is defined on the domain [0, π] by f(θ ) = 4 cos θ + 3 sin θ. π . 2 (a) Express f(θ ) in the form R cos (θ – α) where 0 &lt; α &lt; (b) Hence, or otherwise, write down the value of θ for which f(θ ) takes its maximum value. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 290 426. The figure below shows part of the curve y = x3 – 7x2 + 14x – 7. The curve crosses the x-axis at the points A, B and C. y 0 A (a) Find the x-coordinate of B. (c) x Find the x-coordinate of A. (b) C B Find the area of the shaded region. Working: Answers: (a) ………………………………………….. (b) .................................................................. (c) ………………………………………….. (Total 6 marks) 291 427. The 80 applicants for a Sports Science course were required to run 800 metres and their times were recorded. The results were used to produce the following cumulative frequency graph. 80 Cumulative frequency 70 60 50 40 30 20 10 120 130 140 Time (seconds) 150 160 Estimate (a) the median; (b) the interquartile range. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 292 428. The one-one function f is defined on the domain x &gt; 0 by f(x) = (a) State the range, A, of f. (b) 2x – 1 . x+2 Obtain an expression for f –1(x), for x ∈ A. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 429. Find the set of values of x for which (ex – 2) (ex – 3)″ 2ex. Working: Answer: ……………………………………………….. (Total 6 marks) 293 430. A curve has equation xy3 + 2x2y = 3. Find the equation of the tangent to this curve at the point (1, 1). Worki...
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