CCHM 2024 S4 Math Prelim P2

2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2024 SECONDARY 4 MATHEMATICS 4052/02 Paper 2 Tuesday 20 August 2024 Candidates answer on the Question Paper 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. 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 with the answer. Omission of essential working will result in loss of marks. The total number of 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 π , use either your calculator value or 3.142. This document consists of 23 printed pages and 1 blank page. For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 Total Marks

2 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radian Sector area = , where is in radian Trigonometry Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx nrP      + 1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin == Acbcba cos 2 222 −+=

3 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over TURN OVER FOR QUESTION 1

4 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 1 (a) The table shows the total electricity consumption in Singapore over three years. (i) In 2021, the electricity consumed by households t ook up 15.5% of the total electricity consumption. Calculate the amount of electricity consumed by households in 2021, correct to two significant figures. Answer ………………………… GWh [1] (ii) Calculate the percentage increase in the total electricity consumption from 2020 to 2022. Answer ……………………………% [2] (iii) Express the 2020 electricity consumption in kilowatt hours (kWh), leaving your answer in standard form, correct to two significant figures. Answer ………………………… kWh [1] Year 2020 2021 2022 Total Electricity Consumption in Gigawatt Hours (GWh) 50 779 53 483 54 884

5 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over (b) A microprocessor is in the shape of a cube where the sides are 5 mm in length. (i) Find the maximum number of microprocessors that can be placed into a container with dimensions 10 cm by 2 cm by 8 cm. Answer ……………………………… [2] (ii) A model of the microprocessor was made to a scale of 10 : 1. Given that the surface area of microprocessor is 150 mm 2, find the surface area of the model microprocessor in square centimetres. Answer …………………………… cm2 [2]

6 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 2 (a) Solve ( )2 7 3 1 3xx− = − . Answer x = …………………………… [2] (b) Solve the inequalities 7 1 13x− and ( )1 222 x x+ − − . Answer ………………………………… [3] (c) Rearrange the formula 2 2 5 7 xy x += to make x the subject. Answer x = …………………………… [3]

7 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over (d) Solve the equation 21 31 2 3 x xx−=−− . Give your solutions correct to two decimal places. Answer x = ……………. or …………… [5]

8 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 3 The diagram show s two open containers , a right cylinder and a n inverted frustum. The right cylinder has a base radius of 10 cm and a height of 20 cm. The frustum is formed by cutting a smaller cone off the bottom of a larger cone. The smaller cone that was cut off has a height of 4 cm. The larger cone has a base radius of 15 cm and a height of 12 cm. Three identical spherical marbles, each of radius 3 cm, are placed into the cylindrical container and water is poured in to a depth of h cm. (a) Find the volume of each marble, leaving your answer in terms of π . Answer …………………………… cm3 [1] (b) Find the volume of the frustum, leaving your answer in terms of π . Answer …………………………… cm3 [3] h cm 20 cm 10 cm 15 cm 12 cm 4 cm

9 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over (c) All the water from the cylinder , without the marbles, is then poured into the empty frustum, filling it completely without any overflow. Find the value of h, correct to two decimal places. Answer h = …………………………… [3] (d) The exterior surface area of each container is painted. Find the total area painted. Answer …………………………… cm2 [6]

10 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 4 (a) 12 students from class A took a Mathematics test. The table below shows the test marks of the students. However, two of the students’ marks are covered with ink. (i) Given that the box-and-whisker plot below shows the distribution of the results, explain why the information may not be sufficient to find the missing marks of the two students. Answer …………………………………………………………………………………… …………………………………………………………………………………… ………………………………………………………………………………… [1] (ii) Given further that the modal mark is 63, find the two missing marks. Answer …………… and …………… [2] 40 95 84 47 63 52 63 55 52 61 40 50 60 70 80 90 100 Mathematics Test Marks