2025+Y5+H2+Math+Promo+_28Qn_29

_________________________________________________________________________ This document consists of 8 printed pages. RAFFLES INSTITUTION  RI2025 Mathematics Department [Turn over RAFFLES INSTITUTION 2025 YEAR 5 PROMOTION EXAMINATION Higher 2 MATHEMATICS 9758 3 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (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.

2 H2 MA 9758/2025 RI Year 5 Promotion Examination 1 Fig. 1 A tablet is dissolving in water and is modelled as a cylinder, as shown in Fig. 1. At t seconds after being dropped into the water, the radius of the tablet is x mm, and its thickness is 1 3 x mm. The circular cross-sectional area of the tablet is decreasing at a constant rate of 0.5 mm² per second. When x = 5, find the exact value of (a) d d x t , [2] (b) the rate of change of the volume of the tablet. [2] 2 Do not use a calculator in answering this question. Showing your working, find the complex numbers z and w which satisfy the simultaneous equations ( ) * 2i 5 7i, 4 i 3i. zw wz +=+ −= − [5]

3 H2 MA 9758/2025 RI Year 5 Promotion Examination [Turn over 3 The point A on the Argand diagram below represents the complex number 1w with modulus r and argument θ. It is given that the complex numbers 2w and 3w satisfy the equations 21ww=− and 32 iww= . Let B, C and D represent the complex numbers 2w , 3w and 23ww+ respectively. (a) On the copy of the Argand diagram in the Printed Answer Book, plot the points B, C and D, indicating clearly the modulus and argument of 2w and 3w . [3] (b) State, in radians, the angle BOC. [1] (c) By considering the quadrilateral OBDC , find 23ww+ in terms of r and 23arg ( )ww+ in terms of θ. [2] Im Re r

4 H2 MA 9758/2025 RI Year 5 Promotion Examination 4 (a) The diagram shows the curve f( )yx= , with turning points at (3, 2.5)A and (0, 1)B . The lines 1y= and 2x=− are asymptotes of the curve. On separate