Pearson Edexcel Level 3 GCE [Mathematics Advanced Subsidiary PAPER 1: Pure Mathematics]

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1. Find 8 3 2 5 3 x x − + x       ∫ d giving your answer in simplest form. (4) _____________________________________________________________________________________ ... _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ __________________________________ 2. f(x) = 2x3 + 5x2 + 2x + 15 (a) Use the factor theorem to show that (x + 3) is a factor of f(x). (2) (b) Find the constants a, b and c such that f(x) = (x + 3)(ax2 + bx + c) (2) (c) Hence show that f(x) = 0 has only one real root. (2) (d) Write down the real root of the equation f(x – 5) = 0 (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________ [Show More]

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