2023 SNGS emath Prelim P1 Solutions

This document consists of 20 printed pages. [Turn Over Name: _________________________ ( ) Class:_____________ PRELIMINARY EXAMINATION GENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL MATHEMATICS Student copy 4052/01 Paper 1 Thursday 17 August 2023 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number, and class on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue, correction fluid or correction tape. 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 with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. 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  , use either your calculator value or 3.142. 90

Mathematical Formulae Compound interest Total amount n rP      += 1001 Mensuration Curved surface area of a cone lr= Surface area of a sphere 24 r= Volume of a cone hr 2 3 1= Volume of a sphere 3 3 4 r= Area of a triangle ABC Cba sin2 1= Arc length r= , where  is in radians Sector area 2 2 1 r= , where  is in radians Trigonometry C c B b A a sinsinsin == Acbcba cos2222 −+= Statistics Mean  = f xf Standard deviation 22       −=     f xf f xf

3 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/01 [Turn Over Simple interest 12000 3.5 4 100 = $1680= Total amount 12000 1680=+ $13680= Store A $120 × 0.9 = $108 Store B $120 × 0.9 = $108 Answer all the questions. 1 Given that 4 2128 a= , find the value of a . Answer a = …………..….…………… [1] 2 Ms Li takes a loan of $12000 from a bank that charges a simple interest rate of 3.5% per annum for 4 years. Calculate the total amount she has to pay the bank at the end of 4 years. Answer $..…………..….…………… [2] 3 Store A sells a spice blender for $124.90 with a 10% discount. Store B sells the same blender for $115.00 with a 12% discount. (a) By rounding the prices to 2 significant figures and the discounts to 1 significant figure, show that the discounted price in Store A and the discounted price in Store B are equal. Show the numbers you use. Answer [1] (b) Without doing any further calculation, explain why the actual discounted price in Store B is lower than the estimated discounted price. Answer ………………………………………………………………………………... ………………………………………………………………………………………… …………………………………………………………………………………….. [1] 541 2128 32 5a −==  =− The actual price ($115) is lower than the estimated price ($12)). The actual discount percent (12%) is more than the estimated discount percent (10%). This gives a lower actual discounted price than the estimated discounted price. A1

4 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/01 2 4(3 ) 1( 3) x x −=− − 4 1( 3)x −=− − 4 ( 3) ( 3) x x − − −= − 11 33 xx xx − − +== −− 4 The times, in minutes, taken by some students to complete an assignment are shown below. 49 53 45 44 53 49 59 y 60 50 (a) If the modal time is 53 minutes, state the value of y. Answer y =………….…..…….…….… [1] (b) Hence, find the median time. Answer ……………….……... minutes [1] 5 Simplify 2 95 3 12 7 27xx yy   . Answer ………….………………………. [3] 6 Write as a single fraction in its simplest form ( ) 2 12 4 1 3 x x − − − . Answer ……………….……………… [3] 44 45 49 49 50 53 53 59 60 53 53 y Mode y = = 44 45 49 49 50 53 53 53 59 60 50 53Middle position Median 2 10 1at 5.5 = 51.5 2 th += + = 2 3 9 5 3 12 7 3 xx yy = 67 85 9xy yx= 9x y= ( )( ) ( )( ) ( ) 2 2 2 2 2 2 2 2 4(3 ) ( 3) ( 3) 12 4 6 9 ( 3) 23 ( 3) 31 ( 3) 31 ( 3) 1 ( 3) xx x x x x x xx x xx x xx x x x −−−= − − − + −= − − + += − −+= − − − += − −+= −

5 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/01 [Turn Over 8.5 3 4x−  − 3 4 11x− 3 4.5x− 3 15x 1.5x− 5x  1.5 5 x−   1,0,1,2,3,4− 7 In a school club, 72 of the members are boys and 48 are girls. Calculate the least number of additional girls that would need to join the club in order to raise the percentage of girls to greater than 45%. Answer ………….………………………. [2] 8 (a) Solve the inequalities 8.5 3 4 11x−  −  . Answer ………….………………………. [2] (b) Write down all the integers that satisfy 8.5 3 4 11x−  −  . Answer ………….………………………. [1] Let x be the number of additional girls needed to join the club. 48 45 48 72 100 x x + ++ or 48 9 48 72 20 x x + ++ 9(120 ) 960 20xx+  + 1080 9 960 20xx+  + 11 120x 10.91x , least number is 11

6 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/01 9 In the triangle ACD, AB = 5 cm, AD = 9 cm, CD = 20 cm and BD is perpendicular to AC. Calculate BC. Answer BC = ……………….……...…… cm [2] 10 State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. Answer ………………………………………………………………………………………... ………………………………………………………………………………………………… ……….………………………………………………………………………………...….. [2] A B C D 9 5 20 ( ) Vertical axis starts from 50 instead of 0. It leads to misinterpretation because it exaggerates the differences between the years.  The title is biased. Or the title uses l oaded words “drastic drop” . It leads to misinterpretation because it does not allow the reader to make own judgement. Covid 19 Causes Drastic Drop in Singapore’s Recycling Rate!!! %

7 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/01 [Turn Over 5 14 1x−= 5 15x= 3x= Prime number 1 (5 3 14)  + 29= ( )( )5 14 5 14xx−+ 22(5 ) 14x=− 225 196x=− 11 (a) Expand and simplify ( )( )5 14 5 14xx−+ . Answer ………….………………………. [2] (b) Given that x is a positive integer and ( )( )5 14 5 14xx−+ is a prime number between 20 and 30, find this prime number. Answer ………….………………………. [1] 12 John, Eric and Kate walk from point A to point B along the same route. Eric takes 10 minutes 30 seconds to complete this journey. John takes 10% less than the time taken by Eric. Kate takes 20% more than the time taken by Eric. (a) Calculate the time taken by Kate in seconds. Answer ………….…..… seconds [1] (b) Express the ratio of the times taken by John, Eric and Kate in the form ::abc , where a, b and c are integers in their lowest terms. or Answer ……….…. : ……….… : …………. [2] Kate’s time 1.