CJC Prelims 2025 H2 Math P2 Questions

9758/02/J2PRELIM/2025 [Turn Over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 9758/02 Paper 2 17 Sep 2025 3 hours Additional Materials: Printed Answer Booklet List of Formulae (MF27) READ THESE INSTRUCTIONS FIRST Answer all the 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 8 printed pages.

2 9758/02/J2PRELIM/2025 Section A: Pure Mathematics [40 marks] 1 The diagram shows the graphs of ( )fyx= and ( )f'yx= . The graph of ( )fyx= has turning points at ( )3, 4− and ( )3, 4 , crosses the x -axis at ( )2, 0− and ( )2, 0 , and the equations of asymptotes are 1x=− , 1x= and 2y= . The graph of ( )f'yx= crosses the x -axis at ( )3, 0 , and the equations of asymptotes are 1x= and 0y= . On separate diagrams, sketch the graphs of (a) ( )fyx= , [2] (b) ( ) 1 ,f 'y x= [3] (c) ( )f 1,yx= −− [3] labelling clearly the equation(s) of any asymptote(s), coordinates of any axial intercept(s) and turning point(s) where applicable. 2 Functions f and g are defined by ( ) 2 4f: , , 4 4 x xx x → ∈≠ −  , 1g : ln 1 , , 0x xx x →+ ∈>  . (a) Sketch the graph of ( )fyx= , stating the equations of any asymptotes, the coordinates of the points where it crosses the axes and the coordinates of the turning points, if any. [2] (b) Show that gf exists. Hence find the rule, domain and range of gf. [4] (c) If the domain of f is further restricted to xk< , state the largest value of k for which the function 1f − exists. [1] (d) Using the restricted domain found in part (c), find 1f − in a similar form. [3] y x O y =2 (−2, 0) (2, 0) (3, 4) (−3, 4) x = −1 x = 1 x y O y =0 (3, 0) x = 1

3 9758/02/J2PRELIM/2025 [Turn Over 3 Fig. 1 shows a net of a hexagonal pyramid folded from a star-shaped cardboard of equal edge length cma . The net consists of a hexagon with equal sides of cmx and six isosceles triangles with base cmx and side cma . The net is folded to form a right pyramid with