2024 HYSS S4-5 G3 MA Prelim Paper 2 QP

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 4-G3 / 5-G2 NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 PAPER 2(XX) 19 August 2024 2 hour 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class, and index number on all the work you hand in. 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 the questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. For Examiner’s Use 90 This document consists of 24 printed pages. © HYSS 2024 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior permission of Hua Yi Secondary School. Setter: Ms Jasmine Tan

2 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 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 = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 1 (a) Express as a single fraction in its simplest form 21 7 3 6xx−−− . Answer ………………………. [2] (b) It is given that 35 92 wv w −=+ + . (i) Find v when 6w=− . Answer ………………………. [1] (ii) Rearrange the formula to make w the subject. Answer w = .…………………. [3]

4 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over (c) Solve the equation 2 5 3 1 2 4 7xx −=−− . Give your solutions correct to two decimal places. Answer x = ……...… , x = …….…… [5]

5 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 2 C is the point ( )9,1− and D is the point ( )7,4 . 2 8CE −= . (a) Calculate the length of the line CD. Answer …………….… units [2] (b) Determine the coordinates of point E. Answer E (………. , …….….) [1] (c) Find the equation of the line DE. Leave your answer in the form ax by c+= , where a, b and c are constants. Answer ………………………. [3]

6 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 3 (a) The first four terms of a sequence are 9 13 175 , , , .4 9 16 (i) State the fifth term of the sequence. Answer ………………………. [1] (ii) Find an expression, in terms of n, for the nth term, Tn , of this sequence. Answer Tn = …………………. [2] (b) Elijah finds a number grid from his board game. The diagram shows part of a number grid. A rectangle outlining four numbers, as shown, can be placed anywhere on the grid. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

7 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over (i) If p represents the number in the top right corner of the rectangle, write down an expression, in terms of p, for the number in the bottom left corner of the rectangle. Answer ………………………. [1] (ii) Show that the difference between the products of the numbers in the opposite corners of the rectangle is always 7− . Answer [2] ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… (iii) Elijah says it is impossible for the sum of the four numbers in the rectangle to be 199. Justify with relevant working, why he is correct. Answer [3] ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….… ...…….………………………………………………………………………………….…

8 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 4 (a) Sophie earns a monthly salary of $6875. She gives 15% of this amount to her parents. She puts 35% of the remainder into a savings account. Calculate the amount she has left after giving to her parents and p utting into her savings account. Leave your answer correct to the nearest dollar. Answer $ ……………………. [3] (b) The cash price of a sofa is $830. Sophie buys this sofa on credit. She pays a deposit of one quarter of the cash price. She then pays 3 monthly payments of $260. Calculate the total amount Sophie pays for the sofa. Answer $ ……………………. [2]

9 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over (c) Sophie pays a monthly rent of $3174.20. This is 18% more than her monthly rent last year. Calculate her monthly rent last year. Answer $ ……………………. [2] (d) During her vacation, Sophie visits her friend in Wellington. Sophie spends NZD 940 in New Zealand using her credit card. She is charged a 2.6% fee for the currency conversion. The exchange rate between Singapore dollars (SGD) and New Zealand dollars (NZD) is SGD 100 = NZD 120.7206. Calculate the total amount on Sophie’s credit card bill, including the fee. Give your answer in Singapore dollars, correct to the nearest cent. Answer SGD …………………. [3]

10 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn over 5 ABCD is a field on horizontal ground. AD = 163 m, BD = 329 m, CD = 152 m and angle BDC = 48o. The bearing of B from A is 151o and the bearing of D from A is 237o. (a) Calculate the bearing of D from B. Answer …………………… o [3] 163 329 152