Manjusri 4045 01 PRELIM 2024 QP

This document consists of 18 printed pages and 2 blank pages [Turn over MANJUSRI SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION Name Class Index Number MATHEMATICS Secondary Four Normal (Academic) / NT SBB Paper 1 Candidates answer on the Question Paper. 4045/01 1 August 2024 2 hours READ THESE INSTRUCTIONS FIRST Write your Name, index number and class on all the work you hand in. 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. 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 answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 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 70. Parent’s / Guardian’s Signature: …………………….. For Examiner’s Use Total / 70

2 4045/01/PRELIM/2024 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr 2 Volume of a cone = 3 1πr2h Volume of a sphere = 3 4πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sin sin sin= = a2 = b2 + c2 – 2bc cos A Statistics Mean = ∑ ∑ f fx Standard deviation = 22       − ∑ ∑ ∑ ∑ f fx f fx

3 4045/01/PRELIM/2024 [Turn over Answer all the questions. 1 Write the following numbers in order of length, starting with the largest. 48 1000 , 48, 4 48 10 , 48 × 104 Answer ………………….… , ………..…...…..…… , ………….......…… , ….…….…….…… [2] largest 2 By rounding each number to 1 significant figure, estimate the value of 0.87 547 0.498 × Show your working. Answer …………………………... [2] 3 Find the largest integer x satisfying the inequality 5 36x−> . Answer x =…………………… [2]

4 4045/01/PRELIM/2024 4 Draw an enlargement of this trapezium using a scale factor of 1.5 . [2] 5 The first five terms of a sequence are 9, 16, 23 and 30. (a) Write down the next two terms in the sequence. Answer ………… , ………… [1] (b) Find an expression for the nth term of the sequence. Answer ……………………… [1]

5 4045/01/PRELIM/2024 [Turn over 6 Majority of the Customers like Brand X shampoos Bryan went to a supermarket to buy shampoo. He saw the above poster on a noticeboard and decided to buy Brand X shampoo as he saw that Brand X shampoo is twice as popular as the other brands. Explain with calculations why Bryan was misled by the poster. Answer ……………………………………………………………………………………, …………………………………………………………………………………………….,. ………………………………………………………………………………………… [2] 7 Given that 21ba bc −= , make b the subject of the formula. Answer b = ………………………. [3] 260 − 240 − 220 − 200 − Brand X Shampoo Shampoos of the other brands Number of customers

6 4045/01/PRELIM/2024 8 (a) Construct the angle bisector of angle BCD. [1] (b) Construct the perpendicular bisector of AD. [1] (c) E is the point of intersection of the bisector of angle B CD and the perpendicular bisector of AD. Measure the angle AEB. Answer ………………………° [1] A B D C

7 4045/01/PRELIM/2024 [Turn over 9 Rope A is 1.26 m and rope B is 84 cm. (a) Find the ratio of the length of rope A to the length of rope B. Answer ……….…… : ……….....… [1] (b) Rope B is cut into three pieces in the ratio 2 : 3 : 5. Find the difference in cm, between the lengths of the shortest and the longest piece. Answer ………………………..…cm [2] 10 Solve the following equation, giving your anwers correct to 2 decimal places. (5 ) (6 ) 9xx+ −= Answer x =………………………...….. [3]

8 4045/01/PRELIM/2024 11 Solve the following equations (a) 5 39x−= , Answer x=…………….…. [1] (b) 3 41 4 25 x x + =− . Answer x=…………............ [2] 12 Factorise the following algebraic expressions completely (a) 5 7 15 21wx wy xz yz+−− , Answer ………………….….. [2] (b) 25 17 6yy−+ . Answer ………………......... [2]

9 4045/01/PRELIM/2024 [Turn over 13 The table below shows the tax rates on chargeable income for the year of assessment 2024. Chargeable Income Income Tax Rate (%) Gross Tax Payable ($) First $20,000 Next $10,000 0 2 0 200 First $30,000 Next $10,000 - 3.50 200 350 First $40,000 Next $40,000 - 7 550 2,800 First $80,000 Next $40,000 - 11.5 3,350 4,600 First $120,000 Next $40,000 - 15 7,950 6,000 Mr Fong’s annual income was $113 400. He donated $100 to Community Chest and he was entitled to the personal relief of $16,000. Chargeable income = annual income – donation – total personal relief. Calculate (a) Mr Fong’s chargeable income. Answer $…………………… [1] (b) the amount of personal income tax that he needed to pay. Answer $…………………… [2]

10 4045/01/PRELIM/2024 14 The diagram shows the position of 3 towns A , B and C. The bearing of B from A is 110° and the bearing of C from A is 070°. AC = 26.3 km and BC = 19.8 km. Find (a) angle ABC. Answer …………………..…° [2] (b) the bearing of C from B. Answer …………………..…° [2] A B C N 70° N 110°