2022 XMS EMATH P2 PRELIM

XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Preliminary Examination 2022 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Secondary 4 Express/5 Normal (Academic) Setter: Ms Pang Hui Chin Vetter: Ms Low Yan Jin Moderator: Ms Yap Bee Leng 4048/02 25 August 2022 2 hours 30 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your name, register number and class in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . At the end of the paper, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised This document consists of 25 printed pages and 1 blank page. [Turn over For Examiner’s Use 100 Parent’s/Guardian’s Signature:

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c ABC== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff −  

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4 1 (a) Express 2 21 (2 3) 2 3 x xx −−− as a single fraction in its simplest form. Answer …………………………….. [2] (b) It is given that 22() 3 h r pV  −= . (i) Find the value of V when 4.5h= , 7r = and 3.4p=− . Answer V = …………………………. [1] (ii) Express r in terms of V, h and p. Answer …………………………….. [2]

5 [Turn over (c) (i) Simplify 2 3 6 729 x   . Answer …………………………….. [1] (ii) Given that 3 10 2 4 20 q r x px xyy = , where p, q and r are constants, find the value of p, q and r. Answer p = ………………………….. q = ………………………….. r = ………………………….. [3]

6 2 The diagram shows a circle PQRS, with centre O. SOP is a straight line. When pr