Section A Answer all questions in the spaces provided. 1 Line L has equation 5y = 4x + 6 Find the gradient of a line parallel to line L Circle your answer. [1 mark] – 5 4 – 4 5 4 5 5 4 2 One of the equations below is true for all values of x Identify the correct equation. Tick () one box. [1 mark] cos2 x = –1 – sin2 x cos2 x = –1 + sin2 x cos2 x = 1 – sin2 x cos2 x = 1 + sin2 x 3 Do not write outside the box (03) G/Jun24/7356/2 Turn over U 3 It is given that 3 loga x = loga 72 – 2 loga 3 Solve the equation to find the value of x Fully justify your answer. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7356/2 4 Curve C has equation y = 8sin x 4 (a) Curve C is transformed onto curve C1 by a translation of vector [ 0 ] 4 Find the equation of C1 [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (b) Curve C is transformed onto curve C2 by a stretch of scale factor 4 in the y direction. Find the equation of C2 [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (c) Curve C is transformed onto curve C3 by a stretch of scale factor 2 in the x direction. Find the equation of C3 [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 5 Do not write outside the box (05) G/Jun24/7356/2 Turn over U 5 A student suggests that for any positive integer n the value of the expression 4n2 + 3 is always a prime number. Prove that the student’s statement is false by finding a counter example. Fully justify your answer. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 6 Do not write outside the box (06) G/Jun24/7356/2 6 In the expansion of (3 + ax)n, where a and n are integers, the coefficient of x2 is 4860 6 (a) Show that 3n a2 n (n – 1) = 87480 [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 (b) The constant term in the expansion is 729 The coefficient of x in the expansion is negative. 6 (b) (i) Verify that n = 6 [1 mark]