ACJC 2025 JC2 H2 Prelim Paper 1 QP

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 MATHEMATICS 9758/01 Paper 1 26 August 2025 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 . 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 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 2025 H2 MATHEMATICS 9758/01 1 (a) Without using a calculator, solve the inequality 2 22 x xx +− . [4] (b) Hence, solve the inequality 2 22 x xx +− . [2] 2 The graph of 2ax bx cy xd ++= + has a vertical asymptote with equation 1x=− and an oblique asymptote with equation 22yx=+ . It is given that 2c . (a) Write down the value of d and show that 2a= and 4b= . [3] (b) Hence find the range of values of c if the graph has no stationary points. [2] 3 It is given that xyyx= , where 0x , 0y . (a) Show that ( ) 2 1 lnd d 1 ln yxy xy += − . [3] (b) Hence find the coordinates of the point on the curve xyyx= whose tangent is parallel to the y-axis. [2] 4 The region R is bounded by the curve with equation lny x x= , the lines ex= , 2ex= and the x-axis. Find the exact volume of the solid formed when R is rotated about the x-axis by 2π radians. Give your answer in the form ( ) 3 3πe e27 ab + , where a and b are integers to be found. [6] 5 Relative to the origin O, the points A and B have non-zero and non-parallel position vectors a and b respectively. The plane p has equation 0=rn . (a) Given that 0 =  a n b n , show that AB is perpendicular to n. Hence, describe the geometrical relationship between AB and the plane p. [2] (b) Write down the equation of a line parallel to AB that is contained in the plane p. [1] (c) The point F is the foot of perpendicular from a point C with position vector c to the plane p. Find the position vector of point F, giving your answer in terms of c and n. [3]

3 ANGLO-CHINESE JUNIOR COLLEGE 2025 H2 MATHEMATICS 9758/01