ACJC_9758_2024_Promo_Qns

ANGLO-CHINESE JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION Higher 2 MATHEMATICS 9758/01 Paper 1 27 September 2024 QUESTION PAPER 3 hr 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. Fo llow the instructions on the front cover of the answer booklet. Give non-exact numerical answers corr ect 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 are required to 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. [Turn over

2 ANGLO-CHINESE JUNIOR COLLEGE 2024 H2 MATHEMATICS 9758/01 1 Solve exactly the inequality 32 4 12 x xx   . [3] Hence solve 32 4 12 x xx   . [2] 2 It is given that 1t a nyx . (i) Show that  22d21 1d yyy x   and  22 2 2 dd d 21dd d yy yyy yxx x     . [3] (ii) Hence find the first three terms in the Maclaurin expansion of y. [2] 3 The diagram below shows the graph of the curve fyx , with turning point at ,22 k  and asymptotes with equations xk and 0y . The curve undergoes the following sequ ence of transformations in succession A: Translate k units in the negative x-direction B: Reflection about the y-axis C: Translate k units in the positive x-direction (i) Sketch the curve after the transformations, indicating clearly the equations of the asymptotes and the coordinates of the turning point. [2] (ii) Find the equation of the curve after the transformations in the form fya x b where a and b are constants to be determined, in terms of k where appropriate. [1] (iii) Another curve gyx is such that   gg 4xx for all x. State the equation of a line of symmetry of this curve. [1] y x O

3 ANGLO-CHINESE JUNIOR COLLEGE 2024 H2 MATHEMATICS 9758/01 [Turn over 4 The diagram shows the graph of fyx  , which passes through the origin and has turning points at 2, 5 and 6, 0 . The graph of fyx  has a vertical asymptote 1x and a horizontal asymptote 5y . (i) Sketch the graph of fyx  , stating the equation of asymptote(s) and the coordinates of any intersection(s) with the axes where possible. [3] (ii) Write down the x-coordinate(s) of the stationary poi