Math - Sec2 - SA2 - 2023 - Bukit Merah Sec

I Class I Index Number I Name BUKIT MERAH SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2023 SECONDARY 2 EXPRESS MATHEMATICS Paper1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your class , index number and name 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 . 4052/01 6 October 2023 1 hour 15 minutes 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 rr, use either your calculator value or 3.142, unless the question requires the answer in terms of rr. 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 50. For Examiner's Use Calculator Model: 21 BPN21

1 /,, 54 2.1 Calculate {/ -'3. ----. V 0.03 2 Part A -Answer alll question s A nsiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1] 2 A television screen has sides in the ratio width : height = 4 : 3. A laptop screen has sides in the ratio width : h,eight = 16 : 9. An image exactly fills the television screen. The same image only fills the height of the laptop screen and not the width, as shown in the diagram. Image Find the fraction of the laptop screen not covere d by the image. Give your answer in its lowest tenm . A.ns,ver . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. [2] TSX/BMSS /2023/2E/EOY IP 1 !TURN OVER 22

3 3 The table gives information about a box of books. Hardcover Paperback Fictional 14 12 Non-fictional 6 18 One book is selected at random from the box. Find, as a fraction in its simplest form, the probability that the book is (a) a hardcover book, Ans1,ver ......... ........... ............................ [l] (b) a non-fictional book, Ans,ver .................. ,. ............................ [I] (c) a fictional paperback book. Answer [1] TSX/BMSS/2023/2E/EOY/Pl !TURNOVER 23

4 4 The table shows some correspon ding values of two quantities x and y . (a) With out doing any calcu lation, explain why x and y are inversely proportional. Ans)ver .... ..... .... .. ........ .... ...... ... .............. ...... .. ....... ........... .... ....... ........ . . [1] (b) Express _v in terms of x. Annver y = . . ......... .. . ........ ...... .. .... [l] (c) Hence , find the value of p . Answer p = . ........ .. . . ...... ... . ........... [l] TSX/BMSS /2023/2E1EOY IP 1 !TURNOVER 24

---------------- -- -- ------------ BP-25 5 5 A map has a scale of 1 : 500 000. (a) The distance between Singapore and Bali on the map is 332 cm. Calculate the actual distance, in kilometres, between Singapore and Bali. Answer ............. .......... ...... .. . km [2] (b) The area of Bangkok is 1569 km2. Calculate the area, in square centimetres , of Bangkok on the map. Answer ....... .... .... .... .............. cm2 [2] TSX/BMSS /2023/2E/EOY IP l [TURN OVER 25

6 B A Triangle ABC is congruent to triangle DAE . ACE is a straight line. 6 8.7 cm E Tuition 6.8 cm • wit Given that AD = 8. 7 cm, CE = 2. 2 cm, DE = 6. 8 cm, angle ADE = 70° and angle A CB = 65 °. (a) Find AE. Answer .......................................... cm [l] (b) Find angle EAD. Ans,ver . . . .. . . . ... . . . . . . .. . . .. .. . . . . . . . . . . .. . . . . . . . . . . . [ 1] {c) Tom states that AB is parallel to DE. Show, with calculations , whether you agree v,·ith Tom. Ans.ver I ........ .. .... ..... ........ with Tom b1:!cause .. .. ... ... .... ..... ...... ..... .... .... .... .... . [2] TSX/BMSS /2023/2£/EOY/Pl (TURN.OVER 26

7 7 D C Triangle ABD is similar to triangle BCD. Given that angle BAD= 28°, angle EDA = 35°, AD= 13.8 cm and CD= 5 cm. (a) Find angle ABC. Ans1-ver ..... ...... ...... .... ...... .... ..... ............ [2] (b) Find BD. Answer .......................................... cm [2] TSX/BMSS/ 2023/2£/EOY IP I (TURN OVER 27

8 12.8 The diagram shows a quadrilate ral WXYZ. Angle WXZ = angle YZX = 90°. 8 z -~---~Y 10.3 Given that WZ= 12.8 cm,XY= 10.3 cm and angleXWZ= 34°. (a) FindXZ. Ans-wer ........ .................. ........ ........ cm [2] (b) Find angle YXZ. Ans,ver ....... . ......... ... ...... ... ......... ... ... . . . . [2] (c) \\'hat is the mathematical name of quadrilatt:'.ral WXYZ? Answer ....... ............. ...... ... ........... .. .. .... [l] TSX/BMSS /2023/2E/EOY/Pl (TURNOVER 28

- --------------- - ----- -- - - - - - - - ------ --- 9 9 Jade hires a car during a business trip in France. She drives a total distance of 738 km. The car uses fuel at an average rate of 6 litres/ 100 km. Tu 1· t1· 0 n She pays €1 .54 per litre of fuel. .A She pays using her credit card and is charged a fee of 1.5% for the currency CJ.)nv The exchange rate for Singapore dollars and euros is $1 = €0.68. WI t (a) Calculate the total amount of fuel used by Jade. Answer ............................. ................. l [1] (b) Calculate the total amount , including credit card fee, Jade is charged for fuel. Give your answer in Singapore dollars correct to the nearest cent. Answer $ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . [3] TSX/BMSS/2023/2£/EOY IP 1 (TURN OVER 29

10 Part B - Answer alll questions 10 (a) Solve5x+ 9> 7x-13. Answer ....... ... ..... . .... ............. ..... [1] (b) State the largest prime nu ber that satisfies your solution in (a). Answer . . . . . . ... . .. . . . . . .. . ... .. ..... . .. . .... [l] 11 Show that ( Sn -1 )2 + 4 is a multiple of 5 for all integer values of n. 12 Answer 2x-1 It is given that v == --. " x-3 (a) Findy when x = -2 . (b) Rearrange the fonnula to make x the subject TSX/BMSS /2023/2E/EOY IP 1 30 (2] A11s1i1er y = .. ... ... . . . . . . .. .. ..... .. . . .. .... [l] Answ er x = ... . . . . . . . . . . . . . ..... ......... .... [3] [TURN OVER