Kranji 4048 01 QP

Name: ___________________________ ( ) Class: ______ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Express / 5 Normal Academic MATHEMATICS 4048/01 Paper 1 Tuesday 23 August 2022 2 hours KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI READ THESE INSTRUCTIONS FIRST: Do not open this question paper until you are told to do so. Write your class, index number and name on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, 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 your answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of . 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. Setter : Ms Madeleine Chew This question paper consists of 21 printed pages, including the cover page. [Turn over For Examiner’s Use Total 80 4E5N Session 2

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = r , where  is in radians Sector area = , where  is in radians Trigonometry Statistics Mean = Standard deviation = n rP      + 1001 hr 2 3 1 3 3 4 r Cabsin2 1 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22       −     f fx f fx

3 Answer all the questions. 1 A solid block has a mass of 70 grams when corrected to the nearest gram. Write down the smallest possible mass of the block. Answer ………..…………………….. g [1] 2 The graph below shows the crude birth rate, live births per thousand population, estimated at mid year in a Country G from the year 2017 to 2020. Explain how the graph above may be misleading. Answer ………..……………………………………………………..…………..…… ………..……………………………………………………..………………………… ………..……………………………………………………..………………………… [1] 3 The radius of a circular face is 0.000 905 74 mm. Express the exact value of the diameter in metres, giving your answer in standard form. Answer ………..…………………… m [2] 2019 2017 2018 2020 Year Crude birth rate per thousand population 20 10 30 40

4 4 A windscreen wiper of a car is of length 48 cm and sweeps through an angle of 120º each time it moves from one end to another. On a rainy day, Oliver observed that the tip of the wiper moved from one end to another in 0.8 seconds. Find the speed at which the tip of the wiper moves. Answer ………..…………………… cm/s [2] 5 The length of a blade, L, is directly proportional to the square of its flat surface area, A. Given that the length of a particular blade is 15 cm for a flat surface area of 3 cm 2, form an equation connecting L and A, expressing L in terms of A. Answer ………..………………………… [2] 48 cm

5 6 The equation of a curve is y = (x – p)2 + q, where p < 0 and q > 0. Sketch a possible curve of y = (x – p)2 + q in the axes below. Answer [2] 7 A class took a science test and a history test. The box-and-whisker plots below show their results. Science: History: Oliver scored 78 marks for both the science test and history test. Explain whether Oliver did better for the history test or the science test. Answer ……….…………………………………………....………………………… …………….……………………………………....…………………………………. …………….……………………………………....…………………………………. [2] 10 20 30 50 55 70 80 85 100 Marks x y 0

6 8 The table below shows information collected by Maggie about her driving in 2021. Total distance driven in 2021 18 723 km Average price paid for petrol USD 1.21 per litre Average petrol consumption of her car 1.79 gallons per 100 km [1 gallon = 3.785 litres] Calculate the total amount Maggie paid for petrol in 2021. Correct your answer to the nearest dollar. Answer USD ……..………………………… [3] 9 (a) The enrolment for a school in 2019 and 2020 are 108 1 and 1115 respectively. Find the percentage increase in the enrolment, giving your answer to 3 decimal places. Answer ..……..……………………… % [1] (b) In a class of 50 students, the ratio of the number of boys to the number of girls is 9 : 16. After some girls join the class, the ratio of the number of boys to the number of girls become 6 : 13. What is the total number of students in the class now? Answer ………..……………… students [2]

7 10 A model of a space shuttle is made using a scale of 1 : 20. (a) The actual length of the space shuttle is 38.2 m long. Find the length, in centimetres, of the model. Answer ………..…………………… cm [1] (b) On the model, the area of the tail section painted blue is 80 cm2. Find the actual area of the tail section that is painted in blue, giving your answer in square metres. Answer ………..……………………… m2 [2] 11 (a) Express 5832 as a product of its prime factors. Answer ………..………………………… [1] (b) Using your answer to part (a), explain why 5832 is a perfect cube. Answer ………..……………………………………………………………….. ………..………..…………………………………………...………………….. [1] (c) Find the smallest positive integer k such that 5832k is a perfect square. Answer k = ……..………………………… [1]

8 12 The nth term of a sequence is given by 6n + 3. (a) List the first 4 terms in the sequence. Answer …………..…… , ……..………… , …..…………… , ….…………… [2] (b) Explain why the terms of this sequence are all multiples of 3. Answer ……………………………………………....………………………… ……………………………………………....…………………………………. [1] 13 (a) Solve the inequalities 7335 2 xx −−   . Answer ………..………………………… [2] (b) Write down all the integers that satisfies 7335 2 xx −−   . Answer ………..………………………… [1]

9 14 The diagram shows one interior angle of three polygons, A, B and C. The polygons fit together at the point O. A is a square. The interior angle of the polygon C at the point O is 115°. Explain why polygon B cannot be a regular po