TMJC 2024 JC1 H2 Maths Promo Solutions (with Questions and Markers Comments)

H2 MATHEMATICS 9758 3 hours Additional materials: Printed Answer Booklet List of Formulae and Results (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. TAMPINES MERIDIAN JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION

2 1 It is given that   3 2f , x ax bx cx d    where , , and a b c d are non-zero real constants. The graph of  fy x passes through the points  0,3 and  2,1 . It is also known that one of the stationary points of  fy x is  3,3 . Find the values of a, b, c and d. [4]   3 2f x ax bx cx d     f 0 3 3 d     3 2f 3x ax bx cx       2f ' 3 2x ax bx c   Since one of the stationary points of  fy x is 3,3 ,         2 f ' 3 3 3 2 3 0 27 6 0 ------- 1 a b c a b c            Since one of the stationary point of  fy x is  3,3 , it also means that  fy x passes through  3,3 .           3 2 f 3 3 3 3 3 3 3 27 9 3 0 ------- 2 a b c a b c                        3 2 f 2 1 2 2 2 3 1 8 4 2 2 ------- 3 a b c a b c              Using GC,     3 2 1, 6, 9 3 from above f 6 9 3 a b c d x x x x          Note that at stationary point,  f ' 0.x 

3 [Turn Over 2 (a) State a sequence of three transformations that will transform the curve with equation  fy x onto the curve with equation   2f 3 .y x   [3] (b) Without using a calculator, solve exactly the inequality 2 2 2 1.2 1 x x x    [4] (a)  fy x Replace x by 3x  f 3y x  Replace x by x  f 3y x   Replace y by 2 y     f 32 2f 3 y x y x        The sequence of 3 transformations are as follows: I. Translation of 3 units in the negative direction.x II. Reflection in the axis.y III. Stretch by factor 2 parallel to the axis.y Alternative Method  fy x Replace x by x  fy x  Replace x by 3x      f 3 f 3 y x y x        Replace y by 2 y     f 3