RI Post+Prelim+Revision+P1 Qns

RAFFLES INSTITUTION H2 Mathematics 9758 2025 Year 6 Term 4 Post-Prelim Revision Paper 1 (Source: A level questions) Total number of marks: 100 3 hour Please attempt this paper in one sitting under exam conditions within 3 hours before the lesson on 17 October 2025. 1 The graph of 2 1xy ax bx c   , where ,ab and c are non-zero constants, has an asymptote at 1 2x . The graph also has a turning point at 12, 9  . Find the values of ,ab and c . [4] 2 Find the exact equation of the tangent to the curve  2 ln 11 5yx at the point where 2.x [5] 3 (a) Without using a calculator, solve the inequality 43 .2 x xx  [4] (b) Hence, solve the inequality 34 .2 x xx  [2] 4 A gardener designs a flower bed ABCDE in the shape of a rectangle with an equilateral triangle on one of the shorter sides. Side AE is of length a m and side ED is of length b m (see diagram). The total perimeter of the flower bed is 20 m. Find the maximum possible area of the flower bed, showing that it is a maximum value. Give your answer correct to 4 significant figures. [6]

Raffles Institution H2 Mathematics 2025 Year 6 _______________________________________________________________________________________________ _____________________________________ Y6 H2 Math Term 4 Post Prelim Revision: Paper 1 Page 2 of 4 5 Vectors a and b are such that 1a.b . It is also given that  ab + a is perpendicular to  ab + b . (a) Show that 1ab [3] (b) Hence find the angle between the direction of a and direction of b. [3] 6 (b) Given that 0n , show that 2 sin coscos d , xn x n xx nx x c nn  where c is an arbitrary constant. [3] (c) Using the result in part (b) show that, for all positive integers, n , the value of π 0 cos dx nx x can be expressed as 2 k n , where the possible value(s) of k are to be determined [2] (d) Using the result in part (b) find the exact value of π 2 0 cos 2 d .x xx [3] 7 (a) Use double angle formula, show that  4 1cos cos 4 4 cos 2 3 .8   [2] (b) The region R lies in the first quadrant and is bounded by the curve   342 9yx , the x- axis and the lines 1.5x and 3.x R is rotated about the x-axis through 2π radians. Using the substitution 3sinx  , find the exact volume generated. [6] 8 (a) The complex number 2i is denoted by z and the complex number 13 i is denoted by .w Without using a calculator, evaluate .wwz z . Give your answer in the form i,cd where c and d are real numbers. [4] (b) The equation 32 0za zb z c   , where ,ab and c are constants, has roots 3 and w where w is a complex number. (i) State a condition on ,ab and c for the third root to be w*. [1] (ii) G iven that the condition in part (bi) holds, and that 12 iw  , find the values of ,ab and c . [3]

Raffles Institution H2 Mathematics 2025 Year 6 _______________________