TJC_9758_2024_Promo

1 TEMASEK JUNIOR COLLEGE 2024 JC1 END OF YEAR EXAMINATION Higher 2 MATHEMATICS 9758 27 Sep 2024 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 6 printed pages and 2 blank pages. [Turn over

2 1 The equation of a curve C is ( ) 2 2 7425− − =x y . State precisely a sequence of transformations by which the curve C may be obtained from the graph of 22 1xy−= . [3] 2 Mr Chan started selling three types of roasted meat rice in a hawker centre. For each plate of chicken rice, duck rice and pork rice, he makes a profit of exactly 50 cents, 80 cents and $1.10 respectively. On a particular day, Mr Chan made a profit of $167.40, and he earned $28.80 more in profit from the sale of pork rice than the chicken rice. The total number of plates of rice sold that day is found to be 3 times the plates of duck rice sold on that day. Find the number of plates of chicken rice, duck rice and pork rice that Mr Chan sold that day. [4] 3 The diagram below shows the graph of ( )fyx= . The curve intersects the x-axis and y-axis at ( 4, 0)−A and (0,11)C respectively and has a maximum point at ( )1,13B − . The lines 5=y and 5x=− are asymptotes of the curve. Sketch, on separate diagrams, the graphs of (a) f '( )yx= , [2] (b) 1 f ( )= −y x . [3] x y = 5 B(−1,13) A(−4,0) C(0,11) x = −5 y 1 ( )f=yx

3 4 (a) Find 2 2 4 d25 x xxx + −+ . . [4] (b) Find 2d sec 3d xx . [1] Hence find 2tan3 sec 3 dx x x x . [3] 5 (a) Differentiate with respect to x, (i) 1 sinln 1 sin x x +  − , leaving your result in a form involving a single trigonometric function. [3] (ii) 1 1tan 1 x −   − where 1x , simplifying your answer. [3] (b) It is given that 3xyx= for x > 0. By taking logarithm first, find an expression for d d y x in terms of x. [3]