2023 CCHY 4NA Prelim EM P1 QP

* [Turn_over 2023 Preliminary Examination Secondary Four Normal Academic CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS SYLLABUS A 4045/01 Paper 1 27 July 2023 2 hours Candidates answer on the Question Paper. 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 questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown in the space below the question. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. 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 π , use either your calculator value or 3.142. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. Question Number Marks Marks Obtained 1 2 2 3 3 2 4 5 5 4 6 3 7 6 8 5 9 3 10 4 11 3 12 3 13 3 14 3 15 3 16 1 17 3 18 4 19 6 20 4 TOTAL 70 This document consists of 15 printed pages and 1 blank page. CHUNG CHENG HIGH SCHOOL (YISHUN)

2 [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 rθθ= 2 , where is in radians1Sector area 2 r θθ= Trigonometry sin sin sin abc ABC= = 2 22 2 cos Aa c bcb += − Statistics Mean fx f= ∑ ∑ 22 Standard deviation fx fx ff  = −  ∑∑ ∑∑

3 [Turn_over Answer all the questions 1 7 2 330% 2 π 0.325 12 15 Write these numbers in descending order. Answer: ………. , ………. , ………. , ………. , ………. [2] 2 (i) Solve 4 6 21x− − ≤− and represent your answer on a number line. [2] (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. Answer: ………………… : …………………… [1] (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 [Turn_over 4 (a) Write 628 as a product of its prime factors. Answer: ……………………………………… [1] (b) Find the largest perfect square that is a factor of 600. 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. Answer: ……………………………………… [1] (d) Find the smallest positive integer of x such that 600x is a perfect cube. Answer: ……………………………………… [1]

5 [Turn_over 5 (a) Given that 2 2 dva= − , find the value of v when 5a= and 8d =− . Answer: ……………………………………… [2] (b) Make d the subject of the formula 2 2 dva= − . Answer: d = …………………………………… [2] 6 Simplify ( ) 2 3 0 5 62 ad ad x ×÷ . Answer: ……………………………………… [3]

6 [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. 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 a simple interest rate at 6% per annum. Which bank should Sheldon invest in? Explain your answer. Answer: Bank ……………………… This is because …………………………………………………………………...……… …………….……………………………………………………………………..……… …………………………………………………………………………………….…… [3]

7 [Turn_over 8 Expand and simplify (i) ( ) ( )2 74cp p c+ −− + , Answer: ……………………………………… [2] (ii) (5 2)(2 3) 2(5 3)( 1)x x xx− +− − + . Answer: ……………………………………[3] 9 (i) Expand 2 ( )( )p papa−+ − . Answer: ……………………………………… [2] (ii) Hence, write down the value of 2123456 (123459)(123453)− . Answer: ……………………………………… [1]

8 [Turn_over 10 ( ) 22 16 8x x xa b− += − + (a) Find the value of a and of b. Answer: a = .………………………… [2] b = …………………………. [2] (b) Hence, solve 2 16 8 0xx− += , giving your answers correct to 2 decimal places. Answer: x = …………… or x = ……………… [2] 11 Janelle travelled from Singapore to Thailand. She exchanged 400 Singapore dollars ($) into Thai Baht (THB) when the exchange rate was 1 THB = $0.03875. While in Thailand, she spent 6500 THB. On her return, she exchanged her remaining Thai Baht when the exchange rate was 1 THB = $0.03765. How much Singapore dollars did she receive? Answer: $……………………………………… [3]

9 [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 [Turn_over 13 EFG and XYZ are similar triangles with all the lengths given in cm. (a) Find EFG∠ . Answer: …………………………………… [1] (b) Triangle EFG is an enlargement of triangle XYZ. Find the scale factor. Answer: ……………………………………… [1] (c) Hence, find x in terms of e. Answer: ……………………………………… [1] E F e G 2.25 0.25 X Y Z x 44°