Mathematics > Higher Education > A Level Mathematics A H240/02 Pure Mathematics and Statistics. Download to Score A. 100% Proven pass (All)

A Level Mathematics A H240/02 Pure Mathematics and Statistics. Download to Score A. 100% Proven pass Rate.

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Answer all the questions. 1 Differentiate the following with respect to x. (a) e-4x [2] (b) x 1 x 2 + [2] 2 The diagram shows part of the graph of y x = f( ), where f(x) is a cubic polynomial ... in x. 0 0.5 1 x y Explain why one of the roots of the equation f(x) = 0 cannot be found by the sign change method. [2] 3 The 15th term of an arithmetic sequence is 88. The sum of the first 10 terms is 310. Determine the first term and the common difference. [6]5 © OCR 2021 H240/02 Oct21 Turn over 4 The size, P, of a population of a certain species of insect at time t months is modelled by the following formula. P = 5000 - 1000cos (30t)° (a) Write down the maximum size of the population. [1] (b) Write down the difference between the largest and smallest values of P. [1] (c) Without giving any numerical values, describe briefly the behaviour of the population over time. [1] (d) Find the time taken for the population to return to its initial size for the first time. [2] (e) Determine the time on the second occasion when P = 4500. [4] A scientist observes the population over a period of time. He notices that, although the population varies in a way similar to the way predicted by the model, the variations become smaller and smaller over time, and P converges to 5000. (f) Suggest a change to the model that will take account of this observation. [1] 5 In this question you must show detailed reasoning. Points A, B and C have coordinates (0, 6), (7, 5) and (6, −2) respectively. (a) Find an equation of the perpendicular bisector of AB. [3] (b) Hence, or otherwise, find an equation of the circle that passes through points A, B and C. [Show More]

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