2024 HYSS S4-5 G3 MA Prelim Paper 2 MS

[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. MARKING SCHEME . For Examiner’s Use 90 This document consists of 25 printed pages and 1 blank page. © 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_PRELIMINARY EXAMINATION_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_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over 1 (a) Express as a single fraction in its simplest form 21 7 3 6xx−−− . ( )( ) ( )( ) ( )( ) 2 1 2(6 ) (7 3 ) 7 3 6 6 7 3 12 2 7 3 1 [expand numerator correctly]6 7 3 5 16 7 3 xx x x x x xx Mxx x Axx − − −−=− − − − − − += −−−−− += −−−−− Answer ………………………. [2] (b) It is given that 35 92 wv w −=+ + . (i) Find v when 6w=− . ( )3 5 6 39 0.75 16 2 4v or B−−= + = −−−−+ Answer ………………………. [1] (ii) Rearrange the formula to make w the subject. ( )( ) 35 92 2 9 3 5 1 [remove bases] 9 2 18 3 5 4 21 2 1 [group - terms on 1 side] 21 2 4 21 2 14 wv w w v w M wv w v w wv w v A w vw v v Av −=+ + + − = − −−− − + − = − − = − −−− −= − −=− −−−−

4 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Answer w = .…………………. [3] (c) Solve the equation 2 5 3 1 2 4 7xx −=−− . Give your solutions correct to two decimal places. ( )( ) ( ) ( ) 2 2 2 2 53 1 24 7 5( 2) 3 1 1 [puts to common base]2 2 7 7(5 10 3) 4 35 53 0 1 [simplifies accurately quad. eqn.] 35 35 4(1)( 53) 12(1) 1.45389 36.45389 xx x Mxx xx x x M xM x or x −=−− +− = −−−+− + − = − − − = −−− − −  − − −= −−− =− = 1.45 1 36.45 1 [accept 2 d.p. only]x A or x A=− −−− = −−− Answer x = ……...… , x = …….…… [5]

5 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_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. ( ) ( ) 22 Length 9 7 1 4 1 265 16.3 1 CD M A = − − + − −−− = = −−− Answer ……………… units [2] (b) Determine the coordinates of point E. ( ) 29 81 11,9 1 CE OE OC OE EB =− −−   +=        − −−− 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. ( ) 4 9 5Gradient 1 ( ) 7 ( 11) 18 5 18 Subst. 7, 4 107 118 DE M ECF y x c D cM −= =− −−−−− =− + = −−− So, equation of line DE: 5 107 18 18 5 18 107 1 xy x y A += + = −−−

6 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Answer ………………………. [3] 3 (a) The first four terms of a sequence are 9 13 175 , , , .4 9 16 (i) State the fifth term of the sequence. 5th term = 21 125 B−−− Answer ………………………. [1] (ii) Find an expression, in terms of n, for the nth term, Tn , of this sequence. Rule for numerator = 41n+ Rule for base = 2n 2 41 1n nTB n += −−− 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  Award B1 for ANY 1 correct rule

7 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_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. 61pB+ −−− 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] ( )( ) ( ) 22 1 7 6 1 [form BOTH set of products, take dif ference] 7 7 6 1 [expand all terms correctly] 7 ( ) p p p p M p p p p p A shown − + − + −−− = + − − − − −−− =− ...…….………………………………………………………………………………….… (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] Sum 1 6 7 4 12 1 [simplied sum correctly] p p p p pM = − + + + + + = + −−− If sum = 199, then we must see that p is an integer, 4 12 199 4 187 1 [isolated - term] 46.75 p p M p p += = −−− = From above, we see that p is not an integer, so 199 cannot be the sum of four numbers on the grid. ----- A1 (attempt to explain and make relation to the workings)

8 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_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. Amount given to parents = 15% 6875 $1031.25= Amount left after giving parents = $5843.75 Amount put into her savings = 35% 5843.75 $2045.3125 1 M = −−− Amount left after giving parents and paid to savings 5843.75 2045.3125 3798.4375 $3798 (nearest dollar) 1 A −= = −−− 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. Total amount for sofa = ( )1 830 3 260 1 [both sets of computation to b e shown]4 $987.50 1 M A   +  −−− = −−−  Award M1 for any 1 correct computation

9 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Answer $ ……………………. [2] (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. 118% $3174.20 100100% 3174.20 1118 $2690 1 M A → →  −−− = −−− 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. NZD SGD 120.7206 100 940 100 940 778.657 495 1120.7206 M = −−− Total amount on credit card bill 102.6% 778.657 495 1 798.90 (nearest cent) 1 M SGD A =  −−− = −−−

10 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Answer SGD …………………. [3] 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. 237 151 86 sin sin86 1163 329 29.61924 BAD ABD M ABD  = − =   = −−−−  =  Bearing of D from B ( )360 180 151 1 360 29.61924 29 301.4 1 ABD M A − − −  −−−− = − −  =  −−−− 163 329 152