Hua Yi Sec Sch P2 2020

\I ' I.' I la .I,, : ' I Name: I Index Number: I c ·1ass: 'I il trlUA. YI S~CONDARY SCHOOL I ' ., MA 'FHEMATICS PAPER '2 Prelin:ainary Examination Candidates answer on the Question Paper. ReAD TMESE INSTRUCTIONS FIRST 4NA 4045/2 6 Aug 2020 2h '.Wfite yo&:Jr Name, Class aAd Index Number on all the work you hand in. Write 'iA darik blue or black pen . . . You may use an HB-,pencil'for any diagrams or graphs. ' ' Section A Answer .all questions. Se.ction B Ans~er one question . Write your answers on separate answer pap.er provided. Omission of essential working will result in loss of marks . . The use of a scientific calculator is expected, where appropriate. For 1! , use either your calculator value or 3.142. 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. At th'e en'd of the examination, fasten all your work securely together . . The number of marks· is given in brackets [ ] at the end of each question or part 'question. For Examiner's Use The total number of marks for this paper is 60. I This document consists of 14· printed pages including the cover page. ©HYSS2020 No part of thjs d0.cumen~ mc!'Y reprod1:1ced in alily fem, or transmitted in any form or by any means without the P"1dr,f>·ermjssion of Hua Yi Secondary School. [Tum Over

Compound Inter~t Mensuration Trigonometry Statistics 2 Mathematical Formulae r Total amount= P(l+-Y 100 Curved surface area of a cone = 1D"l Surface area of a sphere = 4nr 2 1 Volume of a cone= -TTT 2h 3 Volume of-a sphere = i nr3 3 Area of triangle ARC= .!..absinC 2 AI:c~ . = -r-8, .where O· is-m-radians Sector area= .!..r20, where (} is in radians 2 a b c --=--=--sinA sinB sine a 2 =b 2 +c2 -2bccosA Mean= "'I.ft "'i.f . . "i,fx ~fx 2 (~ )2 Standard Deviation= "i.f - "'i.J Sec 4NA Preliminary Examination 2020 -Mathematics Paper 2

3 Section A (52 marks) Answer all the questions in this section. 1 (a) (i) Write 0.000 00265 in standard form. Answer (ii) The population of India in 2013 was 1.25 x 109 • The area of India is 3.3 x 106 square kilometres. Calculate the number of people per square kilometre in India. Give your answer in standard form. Answer Js.8+41.2 (b) By writing each value correct to 1 significant figure, estimate the value of 2 3 - . ~ITT-. Answer 2 a2 (2a)z (a) Simplify -x--. ab 3 b Answer (b) Write J;1 x c as a single power of c. Answer (c) Solve 2x-i = 1. Answer Sec 4NA Preliminary Examination 2020 Mathematics Paper 2 [1] [2] [2] [2] [I] [I]

3 4 4 (a) Express x2 +6x-27 in the form (x+ h) 2 + k • Answer [I] (b) Hence or otherwise, solve x2 + 6x- 27 = 0 . Answer x = ___ or __ _ [2] A 0 .____._ ____ ____J B 50cm The diagram shows a sector OAB of a circle centre 0, radius 50 cm and angle AOB = 80°. The sector is folded, joining the edges OA and OB resulting in the cone as shown above. Find (a) the length of arc AB, Answer cm [2] (b) the radius of the circular base of the cone, Answer ____ cm [2] (c) the vertical height of the cone. Answer ___ cm [2] Sec 4NA Preliminary Examination 2020 Mathematics Paper 2

.,. 5 5 The diagram below shows the first four figures of a sequence. Fig. 1 Fig.2 Fig. 3 Fig. 4 (a) Complete the table. Fig. Number, n Number of small triangles, t 1 4 2 7 3 10 4 13 5 (b) Find an expression, in terms of n, for the number of small triangles in Fig. n. Answer (c) Find the total number of small triangles in Fig. 50. Answer (d) Amy said a figure in this sequence can be formed using 64 small triangles. Do you agree with her? Show your working to support your answer. ········· · ···························································· · ················ · ······ · ··· · [I] [I] [I] . . . ... . . . . . . . . . .. ... . . . . . .. . . . . . . . . . . . . . . . . . . . . ... . ... . . ... . . . . . . . . . . . . . . . . . . . .. .. . . . . . . . . . . . . . .... [I] Sec:: 4NA Preliminary Examination 2020 Mathematics Paper 2

6 6 th fi t l20 tan, Andrew drove · 205 Ian. for e trS · b 12 km/h The distance between two towns, P and Q, 1~ . 85 km he increased bis speed Y at an average speed of x km/h. For the remammg ' and maintained this speed for the rest of the journey. (a) Write down an expression, in terms of x, for 120 km (i) the number of hours taken to travel the firSt ' Answer h [l] ------ (ii) the number of hours taken to travel the rest of the journey. Answer ____ h [I] (b) The first Pw:1 of the journey took 30 minutes more than the second part of the journey. Write down an equation in x, and show that it reduces to x2 -58x- 2880 = 0 · Answer ( c) Solve the equation x2 - 58x- 2880 = O . [3] Answer x= or --- ---- [2] (d) Calculate, in terms of minutes, the time he took to travel for the first 120 km. Answer ____ min [l] Sec 4NA Preliminary Examination 2020 Mathematics Paper 2

7 7 (a) Write 4 km/h as a speed in mis. Answer ____ mis [l] (b) Mr Tan received a prize of $50 000. He used some of the money to pay for a holiday in Japan, which cost ¥380 000. The exchange rate was S$1 = ¥76 .9. (i) Calculate the amount of Mr Tan had left after paying for the holiday. Give your answer in dollars, correct to the nearest dollar. Answer $ ---- (ii) He has plans to purchase a laptop for his son. In a recent electronics sale, there is a 20% discount off the laptops. If Mr Tan pays $850 for the laptop, what is its original price? Answer $ ---- 8 In 1 hour, 3 chefs in a restaurant prepared 16 meals. Assuming all the chefs work at the same rate, calculate the number of chefs needed to prepare 112 meals in 3 hours. Answer Sec 4NA Preliminary Examination 2020 Mathematics Paper 2 [2] [2] [2]

9 8 . . _ d BCDE is a parallelogram. In the diagram, ABC is a straight hne, EA - EB, an LAEB = 40° and LBCE = 20°. E D A B C (a) What is the mathematical name of quadrilateral EDCA? Answer (b) Find the values of x, y and z, stating your reasons clearly. Answer x = --- y= __ _ z= ___ _ (c) Jennie claims that /l.EBCis an isosceles triangle. Do you agree? Explain your answer clearly. ·········· · ···· · ··········· · ······· ·· ··········· · ······· · ······················ ····· ············ · ·· ·· · ····· · ····· · ·· · ··· · ····· ·· ····· · ·· · · · ·········· · ···· · ··· ·· ··· · ···· · ····· · ·· · ····· · ·············· Sec 4NA Preliminary Examination 2020 Mathematics Paper 2 [I] [3] [l]

9 10 This table of values is for y = xi _ 34x. X -5 0 5 10 15 20 25 30 35 Y-X2 34x 195 0 -145 -240 -285 p -225 -120 35 (a) Find the value of p. Answer p = ----- (b) Draw the graph of y = x 2 -34x for -5 x 35. -·- -t---,-- • -· ....... ....:--=----•-- ....:.. _ i----:---:-, - 1-- --=- ~---______... -L.:. ·- ,_.;__ I ' • • ~...L.1--- - - ~ I----;- --- ·~ f- ·--- - - - --. -1------- '- I-- - - -~1. - ;- -r - r-. - - 1-- ;--- -- - - -0------'-- - - - --I----- - _ _ .,__ -- -'-- 1---- - --1---1-- -I---".---;-- 1-- ---~ - - ~--±....-· - --· - - + - --- --:::-..:... t-=" - ~ -- --~- ~~ ~- t=~: ---- J.....---.. 1-------- I-- - ·- .:. ::.:...:....- = 1------ - -I-- -;---_ - -- ----- - - -:-i-------- - I - _- - ·r - ~-. - - L -- - ..... - :_-:=- ~t:-~--=:-:---:J ----~ ---- --!-- -- _ _t- - - - --- . l . -1 L I .· t ( c) Use your graph to find the values of x when y = - l 00. Answer x= t - r -- I 1 -I ----- Sec 4NA Preliminary Examination 2020 Mathematics Paper 2 or ----- [l] [3] [2]

10 11 The figure shows a closed hemisphere with centre O and volume of 134 cm 3 • Calculate (a) the radius r of the hemisphere. Answer _____ cm [2] (b) the surface area of the hemisphere. Answer ----- cm 2 [2] Sec 4NA Prcl" · · · urunary Examination 2020 Mathematics Paper 2