EJC_9758_2025_Prelim_P2

2025 JC2 H2 Mathematics Preliminary Examination Paper 2 [Turn over EUNOIA JUNIOR COLLEGE JC2 Preliminary Examination 2025 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CIVICS GROUP INDEX NO. MATHEMATICS Paper 2 9758/02 18 September 2025 3 hours Additional Materials: Printed Answer Booklet List of Formulae (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 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 7 printed pages and 1 blank page.

2 Section A: Pure Mathematics [40 marks] 1 The curve C has equation 33 3x y xy k+ − = , where k is a positive constant. C intersects the x-axis at the point A. (a) Find the equation of the tangent to C at A. Give your answer in the form y px q=+ , where p and q are constants to be found in terms of k. [5] (b) There are two points on C where the tangents are parallel to the y-axis. Given that k = 3, find the exact y-coordinates of these two points. [3] 2 A sequence 1 2 3, , ,u uu  is defined by ( )1 2 1n n n uuu+ = − for all positive integers n. (a) Find the possible limits of the sequence, if the sequence is convergent. [2] (b) For each of the following, evaluate 2u and 3u , and state whether the sequence is convergent: • 1 0u = , • 1 0.01u = , • 1 0.01u =− . [6] 3 The curve 1C has equation 2 8 2 28 x xxy −+= − . The curve 2C has equation ( ) 2 26 116 25 xy− += . (a) Sketch 1C and 2C on the same diagram, stating the coordinates of any vertices, turning points, intersections with the x-axis and the equations of any asymptotes. [7] (b) Find the volume of solid obtained when the smaller region bounded by 1C and 2C is rotated through 2π radians about the x-axis. [4]

3 4 Relative to the origin O, point A has position vector given by 1 2 1  = a . The line 1l passes through the point A and is parallel to 23 1 t t   − . The plane p has equation 05 50 2 t         =+           r , ,  where t is a real constant. It is known that 1l and p are parallel and 1l is not on p. (a) Show that 1.t=− [4] (b) The line 2l passes through the origin and poin