2024 HYSS Prelim Sec 4G2 Math QP P2

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAM 2024 4-G2 NAME CLASS INDEX NUMBER MATHEMATICS 4045/02 PAPER 2 (XX) 05 August 2024 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Name, Class and Index Number in the spaces provided 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 staples, paper clips, glue or correction fluid. Section A Answer all questions. Section B Answer one question. 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 70. 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. For Examiner’s Use This document consists of 19 printed pages and 1 blank page. © HYSS 2024 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior permission of Hua Yi Secondary School. Setter: Ms Shirlynn Khoo 70

2 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = lr Surface area of a sphere = 24 r Volume of a cone = Volume of a sphere = Area of triangle = ABC Arc length = , where is in radians Sector area = , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r

3 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over Section A (62 marks) Answer all the questions in this section. 1 Written as the product of its prime factors, 22396 2 3 11=   . (a) (i) Explain why 396 is not a perfect square. ………………………………………………………………………….. ………………………………………………………………………….. [1] (ii) Find the smallest positive integer value of k such that 396k is a perfect cube. Answer k = …….…………………… [1] (b) (i) Express 2100 as the product of its prime factors. Answer …….……………………….. [2] (ii) Hence find the highest common factor of 396 and 2100. Answer …….……………………….. [1]

4 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 2 A train travels with a speed of 70 km/h for 2.5 hours. It then travels for 2 hours at x km/h. Given that the average speed of the train for the whole journey is 80 km/h, find the value of x. Answer x = …….…………………… [3] _____________________________________________________________________________ 3 $10 000 is placed in an account, earning compound interest of p % per annum. At the end of 2 years, the total amount in the account is $10506.25. Calculate p. Answer p = …….…………………… [3]

5 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 4 Factorise the following expressions completely (a) 22 9 5xx−− , Answer …….……………………….. [2] (b) 222 18xy− . Answer …….……………………….. [2] _____________________________________________________________________________ 5 On a map, a length of 5 cm represents an actual distance of 1 km. Find (a) the scale of the map, in the form of 1 : n, Answer ………..…………………... [1] (b) the area on the map, in cm2, which represents an actual area of 8 km2. Answer ……………………….. cm2 [2]

6 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 6 XYZ is a triangle where 20XZ cm= , 99XY cm= and 101YZ cm= . (a) Is XYZ a right-angled triangle? Explain, showing your working clearly. Answer [2] (b) Find the shortest distance from X to YZ. Answer ………………………… cm [3] X Y Z 20 99 101

7 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 7 Leticia throws a fair 6-sided die and a fair coin together. (a) Draw a tree diagram in the space below to display all the possible outcomes. [2] Answer (b) Find the probability of obtaining (i) a prime number and a tail, Answer ………..…………………... [1] (ii) a ‘7’ and a tail. Answer ………..…………………... [1]

8 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 8 The variables of x and y are connected by the equation 22 5 4y x x= − − . Some corresponding values of x and y are given in the following table. x 3− 2− 1− 0 0.5 1 2 3 4 5 y 29 14 p 4− 6− 7− 6− 1− 8 21 (a) Calculate the value of p. Answer p = …….…………………… [1] (b) Draw the graph of 22 5 4y x x= − − for 35 x−   on the grid provided on the next page. [2] (c) Use your graph to find the values of x when 15y= . Answer x = …….…… , …………… [2] (d) Explain why it is not possible to find a value of x when 15y=− . Answer …………………………………………………………………………………. …………………………………………………………………………………. [1] (e) By drawing a suitable tangent, find the gradient of the curve when 2x= . Answer ………..…………………... [2]

9 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over y x 5 10 15 20 25 30 0 5− 10− 5 1 2 3 4 1− 2− 3−

10 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 2 [Turn Over 9 At the Great Singapore Sale, Caleb paid $300 for x number of T-shirts. He plans to sell the T-shirts, at which he will make a profit of $1.50 on each T-shirt. (a) Write down, in terms of x, expressions for the (i) amount of money that Caleb paid for each T-shirt, Answer $ .…………..……………… [1] (ii) price at which he plans to sell each T-shirt. Answer $ .…………..……………… [1] (b) However, Caleb later discovered that 30 of the T -shirts either had holes or stains on them so he kept them for other use. He sold the remaining T-shirts. After selling all the T-shirts, he found that his sale amounted to $360. Form an equation in x and simplify it to 2 70 6000 0xx− − = . [3] Answer (c) Solve 2 70 6000 0xx− − = . Answer x = …….…… , …………… [3] (d) Explain why one of the answers in (c) has to be rejected. Answer …………………………………………………………………………………. [1]