Serangoon Garden 4E5NA E Maths Prelim P1 2021 QP

SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP [Turn over CANDIDATE NAME CLASS REGISTER NUMBER ____________________________________________________________________ _ MATHEMATICS 4048/01 Paper 1 20 August 2021 Secondary 4 Express/ 5 Normal Academic 2 hours 1030 - 1230 Candidates answer on the Question Paper. ____________________________________________________________________ _ READ THESE INSTRUCTIONS FIRST Write your name, class and class register number on all 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 staples, paper clips, highlighters, 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. 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, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80. This question paper consists of 19 printed pages and 1 blank page. Setter: Ms Tay HY Vetter: Mr Poh Wei Ren SERANGOON GARDEN SECONDARY SCHOOL Vision: Learners with Grit, Leaders with Heart Mission: Nurturing and empowering individuals to lead purposeful lives PRELIMINARY EXAMINATION 2021 FOR MARKER’S USE 80 __________________________ _______________ Name/Signature of Parent/Guardian Date

2 SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP Mathematical Formulae Compound interest Mensuration Trigonometry Statistics

3 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP

4 SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP Answer all the questions. 1 (a) Calculate . Write down the first five digits of your answer. Answer …………………………..…………. [1] (b) Correct your answer in part (a) to 3 significant figures. Answer …………………………..…………. [1] 2 In Singapore, Leon pays S$1.98 for one litre of petrol. On a self-drive holiday to Los Angeles, he paid US$5.40 for a gallon of petrol. The information is given below. 1 US dollar = 1.33 Singapore dollars. 1 gallon = 3.79 litres. Determine if petrol was cheaper in Singapore or Los Angeles? Show your calculations clearly. Answer …………………………………………………………………………………………. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. [2]

5 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP 3 The diagram shows a ladder, , leaning against a vertical wall, . Given that , express as a fraction, the value of (a) , Answer ………..………………. [1] (b) . Answer ……………..…………. [1] 4 At full capacity, a power plant can produce 510 gigawatts of energy annually. In 2020, it did not operate at full capacity and produced only 85% of its annual output. Find the amount of energy produced in 2020 by the power plant, given that 1 gigawatt watts, expressing your answer in standard form. Answer ……………….…………. watts [2]

6 SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP 5 AB is a chord of a circle whose centre is O. The bisector of the angle OAB meets the circumference of the circle at P. Prove that OP is parallel to AB. Answer …………………………………………………………………………………………. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. [2] 6 The length of two sides of a triangle is 2.5 and 3 times of the length of the shortest side respectively. Find the size of the largest angle in the triangle.

7 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP Answer ………………………… º [3] 7 A map is drawn to a scale of 1: 50 000. (a) Two towns are 12 cm apart on the map. Find the actual distance between the towns. Answer ……………….…………. km [1] (b) A theme park on the map has an actual area of 18 km2. Calculate its area represented on the map. Answer ……………….…………. cm2 [2] 8 A submarine is 380 m below sea level and a helicopter hovering 240 m above sea level is directly above it. (a) Find the vertical distance between the submarine and the helicopter. Answer…………………..……… m [1] (b) A diver swimming in the sea is exactly midway between the helicopter and the submarine. Given that the sea bed is 565m deep, find the distance between the diver and the sea bed.

8 SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP Answer…………………..……… m [1] 9 (a) Written as a product of its prime factors, . Find the smallest positive integer such that is a cube number. Answer = ………………..…… [1] (b) It is given that and where is a positive integer. (i) Find, as product of prime factors and in terms of , the lowest common multiple of and . Answer ………..………….………..…………. [1] (ii) Justify whether is a perfect square. Answer ……………………….……..…………………………………………………….. ………………….…………………………………………………………………………. …………………………………………………………………………………………….. [1] 10 (a) Express in the form . Answer …………………………..…………. [2] (b) Write down the coordinates of the minimum point of the graph of Answer (…………… , ……..……) [1] (c) Explain why the graph will not cut the -axis.

9 [Turn over SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP Answer ………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. [1] 11 Water is being pumped into a cylindrical tank at a constant rate. The graph below shows how the volume of water in the tank changes as a further 15 litres of water is pumped for 50 seconds. (a) State the initial amount of water in the cylindrical tank. Answer ……………………… litres [1] (b) Find the equation of the straight line in terms of V and t . Answer V = ………………………….. [2] 12 Mr Tan is the owner of an electronic shop and he offered a 30% discount on all items in his shop during Black Friday. Three days later, on Cyber Monday, Mr Tan offered a further V (Volume in litres) 25 20 15 10 5 t (time in seconds) 0 10 20 30 40 50

10 SGS/Mathematics/4E5N/2021/Prelim/4048/P1/QP 30% discount on the sale price of a washing machine on Black Friday. (a) Jamie paid $1274 for the washing machine on Cyber Monday. Find the original price of the washing machine before the two sales. Answer $ ……………………..…………. [2] (b) Jamie told his father that he was given a 60% discount f