S4 E-Math JURONGVILLE P2 2024 EXAM555

JURONGVILLE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 Secondary 4 Express STUDENT NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 Paper 2 02 AUGUST 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. Answer ALL the 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 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  , use either your calculator value or 3.142. DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO This document consists of 25 printed pages. [Turn Over For Examiner’s Use 90 O

2 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved Surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , 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

3 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over 1 (a) Simplify 32 3 28 7 5 30 xy x y hk  . Answer ……………………….….… [2] (b) Given that 1011 1011 1011 10112 4 4 4 4y = + + + , find the value of y. Answer y = …………………….….… [3]

4 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over (c) It is given that 2 2 xac xb −= + . (i) Find the value of c when a = –1, b = 5 and x = –3. Answer c = …………………….….… [1] (ii) Rearrange the formula to make x the subject. Answer ……………………….….… [2]

5 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over (d) (i) Solve the equation 31 211 zz−=−− . Answer z =…………….….… [2] (ii) Hence, find the value of a when 31 21 2 2 1aa−=−− . Answer a = …………….….… [1]

6 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over 2 (a) Elly played a computer game 500 times and won 370 of these games. She then won the next x games and lost none. She has now won 75% of the games that she has played. Find the value x. Answer x = ……………….….… [2] (b) Grade A coffee costs $48 per kilogram. Grade B coffee costs $32 per kilogram. Alen mixes Grade A coffee with Grade B coffee in the ratio 3 : 2 to obtain a mixture. He then sells the mixture at $45 per kilogram. Calculate the percentage gain on the cost price. Answer ……………………….… % [3]

7 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over (c) Raju has a hard disk with a memory space of 2.4 terabytes. (1 terabyte = 1012 bytes) (i) 122.4 10 can be written as k billion. Find the value of k. Answer k = ……………….….… [1] (ii) If the size of a one-minute video is 50 megabytes, how many 2-hour full length movie videos can be stored in Raju’s hard disk? (1 megabyte = 106 bytes) Answer …………… movies [1] (d) A car is selling at $13 500. Ms Tan bought it at a hire purchase price, with a deposit of $500 and monthly instalment of $243.75 for 5 years at a flat rate of r% per year. Calculate the interest rate, r. Answer ……………….….… [3]

8 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over 3 The diagrams show two ways of packing four identical spherical balls. The radius of each ball is 3 cm. Package A is a closed cuboid with a square base. Each ball touches the top, bottom and the two sides of the cuboid. Each ball also touches two other balls. Package B is a closed cylinder. Each ball touches the side of the cylinder. Two balls touch the ends of cylinder while the two inner balls touch two other balls. For both packages, the material used is of negligible thickness. (a) Write down the dimensions of the cuboid. Answer Length = ……………….…. cm Breadth = ……………….…. cm Height = ……………….…. cm [1] (b) Calculate the total volume of the four balls. Answer ……………………….… cm3 [2] Package A Package B

9 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over (c) Jasmine claims that the volume of empty space in package A is more than that in package B. Do you agree with her? Show your working clearly. Answer [3] (d) Jasmine intends to wrap Package B with wrapping paper. She estimates that the amount of wrapping paper she needs will be at least 20% more than the total external surface area of the package. Calculate the minimum amount of wrapping paper required. Give your answer to the nearest square centimetres. Answer ……………………….… cm2 [3]

10 Jurongville Secondary School 4E5N PRELIM / 4052_02 / 2024 [Turn Over 4 In the diagram, ACDB is a semicircle with diameter 15 cm and centre O. ABE is a sector with centre A. BD is 9 cm. (a) Prove that angle BAD = 0.6435 radians, correct to 4 decimal places. Give a reason for each statement you make. Answer [2] (b) Calculate arc length BE. Answer ……………………….… cm [1] D C 15 cm 9 cm A B E O