AQA 7356 AS June 2019 Paper 1 Pure and Mechanics.

State the number of solutions to the equation tan 4y ¼ 1 for 0 y 180 Circle your answer. [1 mark] 1 24 8 2 Dan believes that for every positive integer n, at least one of 2n 1 and 2n þ 1 is prime. Which value of n shown below is a counter example to Dan’s belief? Circle your answer. [1 mark] n ¼ 3 n ¼ 4 n ¼ 5 n ¼ 6 Jun19/7356/1 Do not write outside the box (02) 3 3 It is given that (x þ 1) and (x 3) are two factors of f (x), where f (x) ¼ px3 3x2 8x þ q 3 (a) Find the values of p and q. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 3 (b) Fully factorise f (x). [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Jun19/7356/1 Turn over s (03) 4 4 Show that ffiffiffi 6 p ffiffiffi 3 p ffiffiffi 2 p can be expressed in the form m ffiffiffi n p þ n ffiffiffiffi mp , where m and n are integers. Fully justify your answer.