2025 JPJC H2 Math Prelim P2 QP

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC2 Preliminary Examination 2025 MATHEMATICS 9758/02 Higher 2 16 Sept 2025 Paper 2 3 hours Additional materials: Printed Answer Booklet List of Formulae and Results (MF27) READ THESE INSTRUCTIONS FIRST This document consists of 7 printed pages and 1 blank page. [Turn over 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 co rrect 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 by [ ] at the end of each question or part question .

2 Section A: Pure Mathematics [40 Marks] 1 To prepare for the General Election, a political party studies the effectiveness of spreading information on Instantglam , a social media platform , by uploading a particular video. The number of Instantglam users who have viewed the video increases at a rate that is directly proportional to the number of Instantglam users who have yet to view the video. The number of Instantglam users who have viewed the video t hours after the video is uploaded is x. The total number of Instantglam users is P, assumed to be fixed. (i) Write down a differential equation and show that ( )1e ktxP −=− , where k is a positive constant. [4] It is known that 12 hours after the video is uploaded, half the total number of Instantglam users have viewed the video. (ii) Estimate to the nearest hour, the time needed for 80% of the total number of Instantglam users to have viewed the video. [3] (iii) Sketch the graph of x against t. [2] 2 With reference to the origin O, the points A, P and Q have position vectors a, p and q respectively. A straight line l through the point A is parallel to a unit vector e. (i) The point Q lies on l. Show that ( )−  =q a e 0 . [2] (ii) Given that P is not on l, give the geometrical meaning of ( )−p a e . [1] It is also given that 3=pq and AQ is 2 units. (iii) Using the results in (i) and (ii), or otherwise, show that the area of triangle APQ can be written as k qe , where k i