Oxford Cambridge and RSA AS Level Mathematics A H230/01 Pure Mathematics and Statistics Question Paper and Marking Scheme

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Section A: Pure Mathematics Answer all the questions. 1 In this question you must show detailed reasoning. (i) Express 32 7 in the form a b, where a is an integer and b is a prime number. [2] (ii... ) Express 1 2 2 - in the form c + d e , where c and d are integers and e is a prime number. [3] 2 (i) The equation x2 +3x+k = 0 has repeated roots. Find the value of the constant k. [2] (ii) Solve the inequality 6+x-x2 2 0. [2] 3 (i) Solve the equation sin 0.25 for º º 0360 2i = G i 1 . [3] (ii) In this question you must show detailed reasoning. Solve the equation tan 3z = 3 for 0º G z 1 90º. [3] 4 (i) It is given that y = x2 +3x. (a) Find x y d d . [2] (b) Find the values of x for which y is increasing. [2] (ii) Find y^3-4 xhdx. [5] 5 N is an integer that is not divisible by 3. Prove that N2 is of the form 3p+1, where p is an integer. [5] 6 Sketch the following curves. (i) y x 2 = [2] (ii) y = x3 -6x2 +9x [Show More]

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