2023 SNGS emath Prelim P2

Name: _________________________ ( ) Class:_____________ PRELIMINARY EXAMINATION GENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL MATHEMATICS 4052/02 Paper 2 Friday 18 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. Paper 1 / 90 Q1 Q4 Q7 Paper 2 /90 Q2 Q5 Q8 Q3 Q6 Q9 Total /100 ________________________________________________________________________________ This document consists of 22 printed pages. [Turn Over

2 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 Mathematical Formulae Compound interest Total amount n rP      += 1001 Mensuration Curved surface area of a cone lr= Surface area of a sphere 24 r= V olume of a cone hr 2 3 1= V olume 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 1

3 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over 1 (a) Solve the inequality 2 1 5 34 xx−+ . Answer …………………..………….. [2] (b) It is given that ( ) 235d b c=+ . (i) Find d when b = −2 and c = − 6.2 . Answer d = ………………..………….. [1] (ii) Express b in terms of c and d. Answer b = ………………..………….. [2]

4 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 (c) Solve the equation 3 221 x xx −=− . Give your solutions correct to 2 decimal places. Answer x = ……………… or …..……….….. [5]

5 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over 2 (a) The speed of light is 83 10 m/s. Find the distance in kilometres travelled by light in 100 nanoseconds, giving your answer in standard form. [ 1 nanosecond 910−= seconds] Answer …………………..………….. km [2] (b) The mass of an ant is 5 milligrams. A cat has a mass of 720 000 times that of the ant. Calculate the mass of the cat in grams in standard form. [I milligram 310−= gram] Answer …………………..………….. g [2] (c) In 2023, the Government increased GST to 8%. At Budget 2023, the Government announced enhancements to the GST Voucher (GSTV) scheme to help Singaporeans with the GST rate increase. Mrs Lee intends to buy an item that has GST of $7. Find the price of the item with GST. Answer $ …………..……..………….. [2]

6 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 (d) June buys an item in Korea costing ₩115000. The exchange rate between Singapore dollars and Korean Won is $1 = ₩967.54 . The same item is on sale in Singapore costing $100. How much would June have saved if she bought the item in Singapore? Answer $ …………..……..………….. [2]

7 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over 3 J is a point )( 2, 7− and K is a point )(10, 1 . (a) Find the length of JK. Answer ………….…..…………… [2] (b) Find the equation of JK. Answer ………….…..………...…… [2] (c) The line with equation 6 7 16yx−= intersects the line JK at point L. Find the coordinates of L. Answer L (……….…. , .………...…) [3] (d) State the ratio JL : JK . Answer ………….….. : ……...…… [1]

8 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 4 Hello Panda is a popular Japanese snack. Its cream-filled biscuits are shaped like panda faces. The biscuits are commonly sold in a hexagonal prism box modelled below. Diagram 1 shows the cross section area of the normal box. It consists of a hexagon formed by two identical trapeziums. PS = 7.5 cm, QR = 4.5 cm and PQ = RS = 2.5 cm. (a) Show that the area of trapezium PQRS is 12 cm2. Answer [2] (b) Given that the height of the box is 14 cm, calculate the total surface area of the box. Answer ……………………….…….. cm2 [3] 4.5 cm 2.5 cm 2.5 cm P Q R S T U Diagram 1 7.5 cm

9 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over Hello Panda has a family box, containing ten individual packets. Given that the two boxes are geometrically similar and the height of the family box is 3 times the height of the normal box. (c) Calculate the total surface area of the family box, correct to 2 significant figures. Answer ……………………….…….. cm2 [2] Jack went to the supermarket to purchase some Hello Panda biscuits. They were sold as Normal boxes and Family boxes. Size Normal Box Family Box Weight Contains 1 packet weighing 50 grams Contains 10 packets, each weighing 26 grams Price Buy 5 boxes for $5.80 Buy 1 box for $6.61 (d) Which packaging is more value for money? Justify your answer with calculations. Answer ………………………………………………………………………………………………… …………………………………………………………………………………………….. [3]

10 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 y 2 4 6 8 10 12 −2 −4 −6 2 1 0 x 3 4 5 6 7 8 5 (a) Complete the table of values for 2 8 56 xy x= + − . [1] (b) On the grid, draw the graph of 2 8 56 xy x= + − for 08 x . [2] x 0.5 1 2 3 4 5 6 7 8 y 3.2 −0.3 −0.8 −0.3 0.8 2.3 4.3 6.7