CCHM 2024 P2 Worked Solution

2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 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 MARKS SCHEME This document consists of 23 printed pages and 1 blank page.

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. Electricity consumed by household =15.5% 53483 8289.865 8300 GWh (2 s.f.)  = = Answer ………………………… GWh [1] (ii) Calculate the percentage increase in the total electricity consumption from 2020 to 2022. 54884 50779Percentage increase = 100%50779 8.08% −  = Answer ……………………………% [2] (iii) Express the 2020 electricity consumption in kilowatt hours (kWh), leaving your answer in standard form, correct to two significant figures. 9 3 10 10 50779 10 10 5.0779 10 5.1 10 kWh (2 s.f.)   =  = 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 microprocessor s that can be placed into a container with dimensions 10 cm by 2 cm by 8 cm. 10 200.5 2 40.5 8 160.5 20 4 16 1280 = = =    = 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. Model : Actual (Linear Scale) 10 :1 (Area Scale) 100 :1 The surface area of the model is 100 times of the actual object. 2 2 2 Surface Area of Model 100 150 15000 mm 15000 cm100 150 cm = = = =