2023 CCHY 4NA Prelim EM P1 Sol

* © CCHY 2023 [Turn_over 2023 Preliminary Examination Secondary Four Normal Academic CANDIDATE NAME MARKING SCHEME CLASS INDEX NUMBER MATHEMATICS 4045/01 Paper 1 27 July 2023 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on 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 paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. The number of marks is given in brackets [ ] at the end of each question or part question. Question Number Marks Possible Marks Obtained Question Number Marks Possible Marks Obtained 1 2 11 3 2 3 12 3 3 2 13 3 4 5 14 3 5 4 15 3 6 3 16 1 7 6 17 3 8 5 18 4 9 3 19 6 10 4 20 4 Presentation Deduction – 1 / – 2 TOTAL 70 This document consists of 15 printed pages and 1 blank page. CHUNG CHENG HIGH SCHOOL (YISHUN)

2 © CCHY 2023 [Turn_over Mathematical Formulae Compound Interest Total amount 1 100 n rP=+  Measurement Curved surface area of a cone πrl= 2Surface area of a sphere 4 πr= 21Volume of a cone 3 πr h= 34Volume of a sphere 3 πr= 1Area of triangle sin 2ABC ab C= , where is in radiansArc length r= 2 , where is in radians1Sector area 2 r = Trigonometry sin sin sin a b c A B C== 2 2 2 2 cos Aa c bcb += − Statistics Mean fx f=  22 Standard deviation fx fx ff  =−   

3 © CCHY 2023 [Turn_over Answer all the questions. 1 7 2 330% 2  0.325 12 15 Write these numbers in descending order. Answer: 7 2 , 330% , 2  , 12 15 , 0.325 [2] 2 (i) Solve 4 6 21x− − − and represent your answer on a number line. Answer: 4 6 21x− − − [2] 4 21 6x− − + 4 15x− − 15 4x − − 33 4x (ii) Hence, find the smallest integer that satisfies 4 6 21x− − − . Answer: ……………………………………… [1] 3 (a) Sarah mixes 0.4 kg of flour with 250 g of butter. Write the ratio of butter : flour in its simplest form. 250 : 400 5 : 8 Answer: ………………… : …………………… [1] 0 3 4 4 5 8

4 © CCHY 2023 [Turn_over (b) A bag contains only blue and pink bean bags. 3 11 of the bean bags are pink. Write the ratio pink bean bags : blue bean bags in its simplest form. Answer: ………………… : …………………… [1] 4 (a) Write 628 as a product of its prime factors. 2628 2 157= Answer: ……………………………………… [1] (b) Find the largest perfect square that is a factor of 600. 32600 2 3 5=   Largest square = 2225 = 100 Answer: ……………………………………… [2] (c) 3280 2 5 7=   Find the lowest common multiple (LCM) of 280 and 600. Give your answer as a product of its prime factors. LCM of 280 and 600 = 322 3 5 7   Answer: ……………………………………… [1] (d) Find the smallest positive integer of x such that 600x is a perfect cube. 32600 2 3 5=   3 2 2600 2 3 5 3 5x=     45x= Answer: ……………………………………… [1] 3 8 628 = 22  157 100 23  3  52  7 45

5 © CCHY 2023 [Turn_over 5 (a) Given that 2 2 dva=− , find the value of v when 5a= and 8d =− . ( ) ( ) 2 8 52v −=− 27v= Answer: ……………………………………… [2] (b) Make d the subject of the formula 2 2 dva=− . 2 2 d va=+ ( )2 2d v a=+ ( )2d v a= + Answer: ……………………………………… [2] 6 Simplify ( ) 2 3 0 5 6 2 ad ad x  . = 22 3 25 1 6 a d a x d  = 325 6 a dx Answer: ……………………………………… [3] 27 ( )2d v a= + 325 6 a dx

6 © CCHY 2023 [Turn_over 7 (i) Sheldon wanted to invest $18 000 in a saving plans with a compound interest of 5% half yearly for 4 years in Bank A. Calculate the total interest that he received at the end of the 4 years. 42 5 / 2$18000 1 100A  =+  $21931.25216A= $21931.25216 $18000I =− $3931.25216I = $3931.25I = (2 dp) Answer: $……………………………………… [3] (ii) Sheldon is also thinking of investing in Bank B with the same amount of $18 000 and the same duration of 4 years. However, Bank B charged simple interest with rate of 6% per annum. Which Bank should Sheldon invest in? Explain your answer with reasonings. ( )( )18000 6 4$ 100I = $4320I = BAII  Answer: Bank ……………………… This is because …………………………………………………………………...……………… …………….……………………………………………………………………..……………….. …………………………………………………………………………………….………..… [3] 8 Expand and simplify (i) ( ) ( )2 7 4c p p c+ − − + , 2 2 7 4c p p c++− = 92pc− Answer: ……………………………………… [2] 3931.25 B Bank B will allow Sheldon to earn more interest as compared to Bank A. 92pc−

7 © CCHY 2023 [Turn_over (i) )1)(35(2)32)(25( +−−+− xxxx . = ( ) ( )( ) 2210 15 4 6 2 5 5 3 3x x x x x x+ − − − + − − = ( )( ) 2210 11 6 2 5 2 3x x x x+ − − + − = 2210 11 6 10 4 6x x x x+ − − − + = 7x Answer: ……………………………………… [3] 9 (i) Expand 2 ( )( )p p a p a− + − . ( ) 2 2 2p p a−− = 2 2 2p p a−+ = 2a Answer: ……………………………………… [2] (ii) Hence, write down the value of 2123456 (123459)(123453)− . ( )( )2123456 123456 3 123456 3− + − = 23 = 9 Answer: ……………………………………… [1] 7x 2a 9

8 © CCHY 2023 [Turn_over 10 ( ) 22 16 8x x x a b− + = − + (a) Find the value of a and of b. ( ) ( ) 22 8 8 8x− − + ( ) 2 8 56x−− Answer: a = …………… , b = ……………… [2] (b) Hence, solve 2 16 8 0xx− + = , giving your answers correct to 2 decimal places. ( ) 2 8 56 0x− − = ( ) 2 8 56x−= ( )8 56x− = 56 8x=+ or 56 8x=− + x = 15.48331 or x = 0.51669 Answer: x = …………… or x = ……………… [2] 11 Janelle travels from Singapore to Thailand. She exchanged $400 into Thai Baht when the exchange rate was 1 Thai Baht = $0.03875. While in Thailand, she spent 6500 Baht. On her return, she exchanged the remaining Baht into dollars when the exchange rate was 1 Thai Baht = $0.03765. How much Singapore dollars did she receive? 1$1 Thai Baht0.03875= 1$400 400 Thai Baht0.03875= = 10322.58065 Thai Baht Remaining amount of Thai Baht = 10322.58065 – 6500 = 3822.58065 1 Thai Baht = $0.03765 3822.58065 Thai Baht = $0.03765 3822.58 065 = $143.92016 Answer: $……………………………………… [3] 8 -56 15.48 0.52 143.92

9 © CCHY 2023 [Turn_over 12 Point E is on the intersection point of the bisector of angle ACB and perpendicular bisector of BC. (a) Use only ruler and compass to locate and label E in the answer space below. [2] Answer: (b) Measure BE. Answer: ………………………………… cm [1] A B C 10.1

10 © CCHY 2023 [Turn_over 13 EFG and XYZ are similar triangles with all the length given in cm. (a) Find EFG . 44G =  (corresponding  in a triangle) 180 44 71EFG = − −  (  sum of a triangle) = 65 Answer: …………………………………  [1] (b) Triangle EFG is an enlargement of triangle XYZ. Find the scale factor. Scale factor = 2.25 0.25 = 9 Answer: ……………………………………… [1] (c) Hence, find x in terms of e.