Zhonghua 2024 4E4N5N EM Prelim P2 QP w Answer Key

1 [Turn over ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 4 NORMAL (ACADEMIC) SBB SECONDARY 5 NORMAL (ACADEMIC) Candidate’s Name Class Register Number MATHEMATICS 4052/02 PAPER 2 27 August 2024 2 hours and 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and register number in the spaces 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 paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degree, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. 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 90. Setter: Ms Lee Jie Li Vetted by: Mr Francis Tan This document consists of 24 printed pages. 90

2 [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 V olume of a cone = hr 2 3 1 V olume 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 [Turn over 1 Write down the following numbers in ascending order. 25 37− , ( ) 2 30.51− , 0.36 , 0.6 • , 6 − Answer .............., ............., .............., .............., .............. 2 The diagram shows two geometrically similar pails. The area of the base of the smaller pail is 54 cm2. The area of the base of the larger pail is 150 cm2. The height of the larger pail is 26 cm. Calculate the height of the smaller pail. . Answer cm [2] [1]

4 [Turn over 3 (a) Solve 2 3 1125 15 xx −=+ . Answer x = [2] (b) Simplify 2 2 5 33 12 3 7 14 p q p r rq  , giving your answer in positive index notation. Answer [2]

5 [Turn over The diagram shows the cross-section of a pipe filled with water. The cross-section is a circle with centre O and radius r cm. P, X, A and Q are points on the circle. PBQ is a straight line such that PB BQ= and 8 cmBQ= . The ratio of :AB BO is 1: 2 . Show that 10.733 cmr = . [3] (b) Find arc length AXP. Answer cm [3] X Answer 4 (a) O r A

6 [Turn over 5 Tom requires a 7 year loan of $120 000 to purchase a new car. Bank M charges an interest of 4% per annum compounded monthly. Bank N charges a simple interest of 4.3% per annum. Determine which bank loan Tom should take. Justify your answer clearly. Answer 6 (a) The cash price of a furniture set is $10 850. Kate buys the sofa on hire purchase. She pays a deposit of one fifth of the cash price. She then makes 24 monthly payments of $x. Given that the total amount that Kate pays for the furniture set is $11 578, find the value of x. Answer x= [2] [4] He should take loan from Bank because

7 [Turn over (b) The exchange rate between Singapore dollars ($) and US dollars (USD) is $1 = USD 0.74. The exchange rate between British pounds (£) and Singapore dollars ($) is £1= $1.72. Kate wants to buy a handbag. The same handbag costs USD 234 on online shopping platform A and £234 on online shopping platform B. By comparing the exchange rates, explain how you can tell that the handbag costs more on online shopping platform B. [2] Answer

8 [Turn over 7 (a) The cumulative frequency graph shows the distribution of the times of the first 160 students from school A to finish the cross-country run in 2024. Use the curve to estimate (i) the median time, Answer mins [1] (ii) the interquartile range of the times, Answer mins [2] (iii) the value of p , given that %p of the students take more than 26 minutes. Answer p = [2] Cumulative Frequency Time (minutes)

9 [Turn over (b) The box-and-whisker plot represents the distribution of the times of the first 160 students from school B to finish the cross-country run in 2024. Below are three statements comparing these times from the two schools. For each one, write whether you agree or disagree, giving a reason for each answer. Statement Agree/disagree Reason The students in school B are slower on average. Disagree The median time for students in school B is 27 minutes which is shorter than median time for school A (28 minutes), hence students in school B are faster on average. The times of the first 40 students from school A were closer together compared to that of school B. The upper quartile of times from school A is 2.8mins which is shorter than that of school B(4 mins), hence times of the last 40 students from school A were closer together compared to that of school B. The times of students in school A are more consistent compared to that of school B. The interquartile range of times from school B is 7mins which is larger than that of school A(5.8 mins), hence times school B were less consistent compared to that of shool A. [3] Time (minutes)

10 [Turn over 8 (a) Complete the table of values for ( ) 321 432y x x x= + − + . (b) x 4− 3− 2− 1− 0 1 2 3 y 6 9 7 3 0 1 9 On the grid given on page 11, draw the graph of ( ) 321 432y x x x= + − + for 43 x−   . [1] [3] Use your graph to write an inequality in k where ( ) 321 432 x x x k+ − + = has three solutions. Answer [2] (d) Using the graph, find the gradient of the curve at 2.7x=− . Answer [2] (c)