2024 Prelim P1 asr

[Turn Over ANDERSON SERANGOON JUNIOR COLLEGE H2 MATHEMATICS JC2 Prelim Paper 1 (100 marks) 9758 9 Sept 2024 3 hours Additional Material(s): List of Formulae (MF 26) CANDIDATE NAME CLASS / READ THESE INSTRUCTIONS FIRST Write your name and class in the boxes above. Please write clearly and use capital letters. Write in dark blue or black pen. HB pencil may be used for graphs and diagrams only. Do not use staples, paper clips, glue or correction fluid. Answer all the questions and write your answers in this booklet. Do not tear out any part of this 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. 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. All work must be handed in at the end of the examination. If you have used any additional paper, please insert them inside this booklet. The number of marks is given in brackets [ ] at the end of each question or part question. Question number Marks 1 2 3 4 5 6 7 8 9 10 11 Total This document consists of 23 printed pages and 5 blank pages.

2 1 (a) Sketch the graphs of 3exy= and 3yx=+ on the same diagram. Indicate clearly the coordinates of the points of intersection between the 2 graphs. Solve the inequality 3e 3.x x+ [3] (b) Hence find 2 2 3e 3 d ,x xx − −− giving your answer in an exact form. [2] 2 (i) Find ( ) 1 2sind 1d e x xx − − . [1] (ii) Hence using integration by parts, find 1 2 sin d 1 e x xx x − − . [3] 3 The curve C has parametric equations 2 12xt t=− , 12yt t=+ , ,0tt . The point P on the curve has parameter 1.t = (i) Find the equation of tangent and normal to C at the point P. [4] (ii) The tangent at P meets the y-axis at B. The normal at P meets the x-axis at A. If O is the origin, find the area of the quadrilateral OAPB. [2] 4 A sequence is such that 0 2u = and 3 1 1 2 n nnu u n − = + +  for 1n . (a) It is given that ( )3 22 1 4 1 n r nnr = += . By considering ( )1 1 n rr r uu − = − , find a formula for nu in terms of n. [4] (b) Hence, using the formula of nu found in (a), find ( ) 2 3 9 12 2 rn r r + =  ++    exactly. [3]

3 [Turn Over 5 (a) It is given that a , b and c are non-zero vectors. If + = −a b a b , show that the two vectors a and b are perpendicular to each other. [4] (b)