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MATHEMATICS A LEVEL PAPER 3 QUESTIONS AND COMPLETE SOLUTIONS

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MATHEMATICS A LEVEL PAPER 3 QUESTIONS AND COMPLETE SOLUTIONS MATHEMATICS A LEVEL PAPER 3 Given that ð10 0 f (x) dx ¼ 7 deduce the value of ð10 0 f (x) þ 1 dx Given that 6 ... cos y þ 8 sin y Rcos (y þ a) find the value of R. Determine which one of these graphs does not represent y as a function of x. Tick (3) one box p(x) ¼ 4x3 15x2 48x 36 4 (a) Use the factor theorem to prove that x 6 is a factor of p(x) 4 (b) (i) Prove that the graph of y ¼ p(x) intersects the x-axis at exactly one point. The number of radioactive atoms, N, in a sample of a sodium isotope after time t hours can be modelled by N ¼ N0ekt where N0 is the initial number of radioactive atoms in the sample and k is a positive constant. The model remains valid for large numbers of atoms. (b) (ii) State the coordinates of this point of intersection. Determine the number of days required for at least 90% of the number of atoms in the original sample to decay. Find the percentage of the atoms remaining after the first week. Give your answer to two significant figures. Explain why the model can only provide an estimate for the number of remaining atoms. [Show More]

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