SAJC_9758_2024_Promo_Qns

[Turn Over ST ANDREW’S JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 MATHEMATICS 9758/01 Paper 1 4 October 2024 FINAL EXAMINATION 3 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) ______________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Answer all questions. Write your answers on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you must present the mathematical steps using mathematical notations and not calculator commands. You must show all necessary working clearly. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 7 printed pages and 1 blank page.

2 [Turn Over 1 The sum, nS , of the first n terms of a sequence 1 2 3, , ,... ...nu u u u is given by 5 5 24 ( 4)!n nS n    . (i) Determine with a reason, if the series converges and write down the value of the sum to infinity if it exists. [2] (ii) Find the exact value of 2 1 r r u     , expressing your answer in the simplest form. [2] (iii) Find a formula for nu in the form f ( ) ( 4)! n n where f ( )n is a quadratic polynomial. [4] 2 The parametric equation of a curve C are 2 , 1 1 where 0 1x t y t t      . (i) Find d d y x in terms of t. What can be said of the tangent to the curve as 1t ? [2] (ii) Sketch the curve C, showing clearly the coordinates of the endpoints. [3] (iii) Show that the equation of the tangent to C at the point 2 ,1 1T t t   is 2 1 2 2 1t y t x t     [2] (iv) The tangent to the curve at the point with x-coordinate 2 meets the x and y axis at the points P and Q respectively. Find the exact area of triangle OPQ. [4] 3 A curve 1C has equation 2 2 1, 05 4 y x x   . (i) Sketch the curve 1C, showing clearly the equations of any asymptotes and coordinates of any intersections with the axes. [3] A curve 2C has equation 2 3y x  . (ii) Sketch the curve 2C on the same diagram as 1C, showing clearly the coordinates of any intersections with the axes. Find and label the x-coordinates of the point(s) of intersections of 1C and 2C on this diagram. [3] (iii) Hence, state the range of values of x for which 2 2 3 5 1 4 xx       , where 0x . [2]

3 [Turn Over 4 (a) The abo