2024 HYSS Prelim Sec 4G2 Math QP P1

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAM 2024 4-G2 NAME CLASS INDEX NUMBER MATHEMATICS 4045/01 PAPER 1 (XX) 31 July 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. 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 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 13 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 1 [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 1 [Turn Over 1 Solve 5( 2) 8xx+ = − . Answer x = ...……….……………… [2] _____________________________________________________________________________ 2 5  0.6 5 8 0.60 Write these numbers in order of size, starting with the smallest. Answer …..…… , …..…… , …..…… , …..…… smallest [1] _____________________________________________________________________________ 3 (a) Write 0.000845 in standard form. Answer …………………..…….…… [1] (b) ( ) ( )2.5 10 4.9 10 10m n b a   =  where 1 10a . (i) Find the value of a. Answer a = ...……….……………… [1] (ii) Write an expression for b in terms of m and n. Answer b = ...……….……………… [1]

4 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 4 By writing each number correct to 1 significant figure, estimate the value of 5.9 24.2 0.333  . Answer …...……………….....…...… [2] _____________________________________________________________________________ 5 The diagram below shows an incomplete figure made up of a regular pentagon Y and another regular polygon X of n sides. (a) Complete pentagon Y. Answer shown in diagram above [2] (b) Find the value of n. Show your working clearly. Answer …...……………….....…...… [4] 108  Y X

5 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 6 (a) Write 2 11 5 25xx +−− as a single fraction in its simplest form. Answer …...……………….....…...... [2] (b) Rearrange this formula to make h the subject. 1 ()3a h k b=+ Answer …...……………….....…...... [2] _____________________________________________________________________________ 7 Mary scored 65 marks in her English test, 60 marks in her Science test and x marks in her Mathematics test, where x is an integer. The full mark for each test is 100 and she only takes these three subjects. Mary claims that her mean test score can be at least 80 marks. (a) Form an inequality involving x and that represents Mary’s claim. Answer …...……………….....…..... [1] (b) Determine whether Mary is correct in her claim. Show your working. Answer [1]

6 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 8 (a) ABC is a triangle with BC = 7 cm and 50CAB =  . Construct triangle ABC. AB has been drawn for you. [2] (b) Construct the angle bisector of CAB . [1] (c) Construct the perpendicular bisector of AB. [1] (d) X is the point where the angle bisector of CAB meets the perpendicular bisector of AB. Measure CX. Answer ………………………... cm [1] A B

7 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 9 The graph below shows a line segment PQ which cuts the y-axis at R. (a) Find the gradient of PQ. Answer …………………….……… [2] (b) Hence find the equation of the line PQ. Answer …………………….……… [2] (c) Write down the coordinates of R. Answer ( .…………… , ……….…. ) [1] (d) A line, l, is parallel to PQ and passes through the point )5 ,4( −S . Find the equation of l. Answer …………………….……… [2]

8 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 10 Simplify the following expressions. (a) 2( 3) 45 xx −− , Answer …………………….……… [2] (b) 210 8 3 15 x y x y  . Answer …………………….……… [2] _____________________________________________________________________________ 11 A building can be completed in 120 days with 50 workers. Assuming that all the workers work at the same rate, find (a) the number of days it takes to complete the building with 20 workers, Answer ……………………….. days [1] (b) how many more workers are required to complete the building in 100 days. Answer …………………….……… [2]

9 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 12 (a) An expression for the nth term of a sequence is 10 3 n− . Find the 20th term of the sequence. Answer …………………….……… [1] (b) The first four terms of a sequence are 1, 3, 7, 11.− (i) Find an expression for the nth term in this sequence. Answer …………………….……… [1] (ii) Is 121 a term in this sequence? Explain your answer. Answer [2] _____________________________________________________________________________ 13 Ten years ago, item A cost $8. It was then increased by 200% from its original price. Two months ago, there was a discount of 8% for item A. Today there is a further reduction of price by 2%. How much does item A cost today? Answer $ .………………….……… [3]

10 2024_4-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn Over 14 There are two numbers , x and y. When the second number is subtracted from twice the first number, the result is 18. When 9 is added to the first number, the result is equal to twice the second number. (a) Write down a pair of simultaneous equations to represent the information above. Answer …………………….………