2023 Sec 3 Express E Math EOY Bukit Merah Secondary with Answer

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I Class I Index Number I Name BUKIT MERAH SECONDARY SCHOOL MATHEMATICS Paper1 END-OF-YEAR EXAMINATION 2023 SECONDARY 3 EXPRESS 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. BP-465 4052/01 4 October 2023 2 hours 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 re. 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 80. For Examiner's Use Calculator Model: This document consists of 20 printed pages. Setter: Ms Lim LE [Turn over 465

Compound Interest Mensuration 2 Mathematical Formulae r n Total amount= P ( 1 + 100 ) Curved surface area fa cone = rrrl Surface area of a sphere = 4rrr 2 1 Volume of a cone= 3rrr 2 h 4 Volume of a sphere= 3rrr 3 1 Area of triangle ABC = 2 a.b sin C Arc length = r0, where 0 is in radians 1 Sector area= 2r 20, where 0 is in radians Trigonometry a b C = sin A sin B sin C a.2 = b2 + c2 - 2bc cos A Statistics Ifx Mean=--If 2.,fx 2 Ifx ( ) 2 Standard deviation = V - If LLE/BMSS/2023/3E/EOY /4052/1 466 BP-466 [TURNOVER

BP-467 3 1 (a) Evaluate 4.9 x I 06 - 5 .64 x 104. Give your answer in standard form, correct to 2 significant figures. Answer [1] (b) 1.37 x 10-1 seconds can be written as k nanoseconds. Find the value of k. (1 nanosecond= 1 x 10-9 seconds) Answer k= ...................... .. .... [I] 2 Given that 0° -:::; 0-:,; 180°, find the value(s) of 0 for sin 0 = 0. 772 . Answer 0 = .. .. ...... ...... .... .. ...... [2] LLE/BMSS/2023/3E/EOY /4052/1 [TURNOVER 467

BP-468 4 3 Find the value of p in 3 25 - 3 2 4 = 2 x y+ 1 . Answer p = .. .. . .. . .. . .. . ..... .. .. ..... . .. [2] 4 (a) Express 1008 as a product of its prime factors. Answer. .... .... ... ............... .... ... ... [l] (b) Hence, find the smallest positive integer k such that 1008k is a perfect cube. Answer.. ............... .. .. ....... .... ... ... . [l] LLE/BMSS /2023/3E/EOY /4052/1 [TURNOVER 468

5 5 In country X, the Goods and Services Tax (GST) is predicted to rise from 7% to 8.5% in the future. Before the increase, the price of a tablet is $1391 including 7% GST. Calculate the new price inclusive of GST, after the GST has increased to 8.5%. Answer $....... ............ ..... .. . . . . [2] 6 3 ( )-2 Simplify m2n-5 --c- : , giving your answer in positive index notation. Answer . . .. . ... .. .. . .. . . . . .. . ..... .. . ...... .. [3] BP-469 LLE/BMSS/2023 /3E/EOY/4052/1 [TURN OVER 469

6 7 (a) Liquid is flowing out of the full container at a constant rate. After t seconds , the depth of water in the container is d cm. Sketch the graph of d against t. d 0 (b) Liquid is poured into the empty container at a constant rate. After t seconds , depth of water in the container is d cm. Sketch the graph of d against t. d ---------------~------------• t BP-470 [I] (1) LLE/BMS S/2023/3E/EOY /4052/1 [TURN OVER 470

8 Liquid detergent is sold in two sizes. $4.75 Which container is better value for money? Explain your answer. Answer LLE/BMSS/2023/3E/EOY /4052/1 471 7 $13.71 [3] [TURNOVER

BP-472 8 9 (a) S 1 I - 1.. • -~ l ") 9 - I 7 6' .. o vet 1e 1net"lun Jttes Yr - . < .... x+ .: ~ ·-· (, .v - ) . ·t 2 . ' Answer [3] (b) Show your solution in (a) on the number line below . Answer: [l] X LLE/BMSS /2023/3£ /EOY /4052/1 [TURNOVER 472

9 10 A map is drawn to a scale of I cm to 4 km. (a) Express the scale of the map in the form of I : n. Answer .............. ...... ... .... ...... [1] (b) The distance between two schools is 8.4 km. Find the distance, in centimetres , on the map. Answer ............. .............. cm [I] (c) One of the schools occupies an area of 2.5 cm2 on the map. Calculate its actual area in square kilometres. Answer ........................... km2 [2] BP-473 LLE/BMSS/2023/3E/EOY /4052/1 [TURNOVER 473