RI_9758_2024_Promo

© RI 2024 [Turn Over RAFFLES INSTITUTION 2024 YEAR 5 PROMOTION EXAMINATION Higher 2 MATHEMATICS 9758 3 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (MF26) 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. RAFFLES INSTITUTION Mathematics Department

2 H2 MA 9758/2024 RI Year 5 Promotion Examination 1 A curve D has equation ln , 0,cy ax b x x x= + +  where ,a b and c are constants. It is given that D has a stationary point at 3 2x= and the tangent to D at the point where 1x= is 5.yx=− Find the values of ,a b and .c [4] 2 With respect to the origin O, the fixed points A and B have position vectors a and b respectively, where a and b are non-zero and non-parallel. (a) The variable point R has position vector ( )1,= + −r a b where  is a real parameter. Describe geometrically the set of all possible positions of R. [1] It is given that the angle AOB is 90 . (b) Explain why 0.=a.b [1] (c) Among the set of all possible points R, the point *R is the closest to the origin O. Find the position vector of *.R Hence state the ratio **:AR BR in t erms of magnitudes of a and b. [4] 3 Do not use a calculator in answering this question. Solve the inequality ( ) 26 2 3 2 1 .21 xx xx +− +− [4] Hence solve ( ) 26 2 3 2 1 .21 xx xx +− +− [3]

3 H2 MA 9758/2024 RI Year 5 Promotion Examination [Turn over 4 A curve C has parametric equations 31x  = + and 2 31y  = + , for 0. The point P is a variable point on .C (a) With reference to the