ACJC 2025 JC1 H2 Math Promo QP

ANGLO-CHINESE JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION Higher 2 MATHEMATICS 9758/01 Paper 1 3 October 2025 QUESTION PAPER 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 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 8 printed pages and 2 blank page. [Turn over

2 ANGLO-CHINESE JUNIOR COLLEGE 2025 H2 MATHEMATICS 9758/01 1 Given that cos sin 2xxyx = , find the exact value of d d y x at x = . [5] 2 It is given that 11 tan 2yx −=+ where 11 22 x−   . Show that 22 2 2 2 d d 8 0d d (1 4 ) y y xy x x x + + = + . Hence find the Maclaurin series for y, up to and including the term in 3x . [5] 3 Given that ( )1 1 11 n r n r r n= =++ . (a) Show that ( )2 11 11 n r r r n= =−− . [2] (b) Find ( )2 11 21r r rr  =  + −  . [3] 4 (a) The diagram shows the graphs of y a bx=− and 6y mx=− where a, b and m are positive constants. The graph of y a bx=− meets the x-axis at the point 9 ,04   . The solution set of the inequality 6mx a bx−  − is given as { : , 1 or 3}x x x x   . Find the values a, b and m. [4] (b) Given that is a constant andk 1k  , solve the inequality 2 2 1 1,( 1) kx x k x k + −+ + + giving your answer in terms of k. [4] y x y a bx=− 6y mx=−

3 ANGLO-CHINESE JUNIOR COLLEGE 2025 H2 MATHEMATICS 9758/01 5 A curve 1C has parametric equation 23sec , 2 tan , 0 . 2xy   = =   (a) Sketch the curve 1C , stating the coordinates of the endpoint(s). [1] (b) Show that d1 d 3tan y x = . [2] 1L and 2L are tangents to curve 1C . (c) Find (i) the equation of 1L which is parallel to the y-axis. [2] (ii) the gradient of 2L which is tangent to the curve 1C at the point ( )3.75,1 . [2] (d)  is the acute angle between 1L and 2L . State the value of tan  . [1] (e) Describe a transfor