NBSS EM 2024 Prelim P2 QP

1 [Turn over NAVAL BASE SECONDARY SCHOOL PRELIMINARY EXAMINATION, 2024 O Name ( ) Class MATHEMATICS 4052/02 Paper 2 22 August 2024 Candidates answer on the Question Paper. 2 hour 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. 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 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 π , use either your calculator value or 3.142. Item For examiner’s use Presentation Accuracy Units Total Parent’s Signature This paper consists of 25 printed pages and 3 blank pages. [Turn over

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

3 [Turn over Answer all the questions. 1 (a) Solve 23 654 xx −+ = − . Answer x = …………………………………… [2] (b) Simplify ( ) ( ) 2 2 3 3 10 p q q p rr −−  . Answer ………………………………………. [2]

4 [Turn over (c) Solve the inequality 7 2 5 191 45 xxx −++   . Answer ………………………………………. [3] (d) Simplify 2 2 2 7 9 4 81 yy y +− − . Answer ………………………………………. [3]

5 [Turn over 2 (a) Cheryl wants to open a fixed deposit account with either Bank H or Bank L for a period of 4 years. The following are the promotions offered by the two banks. Bank H Bank L Fixed Deposit Account • Minimum deposit of $10 000. • For the first $10 000, earn 0.05% simple interest per annum. • For the subsequent amount, earn 0.95% simple interest per annum. Fixed Deposit Account • No minimum amount required. • Compound interest at the rate of 0.8% per annum. (i) Cheryl deposited $30 000 into Bank H. Calculate the total amount in her account after 4 years. Answer $…………………………………….. [3]

6 [Turn over (ii) Cheryl claimed that Bank H offers a better deal than Bank L. Do you agree with Cheryl’s claim? Justify your conclusion with clear calculations. Answer ……………………………………..……………………………………………. ……………………………………..……………………………………………. ……………………………………..……………………………………………. [3] (b) (i) The exchange rate between Singapore Dollars (S$) and Chinese Yuan (CNY) is S$1 = CNY5.33. The exchange rate between Hong Kong dollars (HK$) and Singapore Dollars is HK$1 = S$0.17. Tan is planning a trip to Hong Kong and Guangzhou. He finds these hotel prices on a website. Guangzhou Hotel CNY825 Hong Kong Hotel HK$825 By comparing the exchange rates, explain which hotel charges a cheaper rate per night. Show your working clearly. Answer The ……………………………… hotel charges a cheaper rate per night. [2]

7 [Turn over (b) (ii) Tan books 4 nights in the Hong Kong hotel and 2 nights in the Guangzhou hotel. He pays using his credit card. The credit card company converts the prices to Singapore dollars and charges a fee of k% for the currency conversion. Given that the total amount Tan pays for the two hotels, including the credit card fee, is $890, find the value of k. Answer k = ………………………………….. [4]

8 [Turn over 3 (a) In February 2021, a survey was carried out to find the number of days 500 patients stayed at a hospital. The graph shows the cumulative frequency curve for the data collected. Use the curve to estimate (i) the median number of days, Answer …………………………………. days [1] (ii) the interquartile range of the number of days, Answer …………………………………. days [2] (iii) the percentage of patients who stayed more than 20 days in the hospital. Answer ………………………………….. % [2] Number of days Cumulative Frequency

9 [Turn over (b) In February 2022, the same survey was carried out again on another 500 patients with the following result shown in the box-and-whisker plot below. Make two comments comparing the number of days stayed in the hospital in February 2021 and February 2022. Use figures to support your answer. Answer 1. ……………………………………..……………………………………………. ……………………………………..…………………………………………………… 2. ……………………………………..……………………………………………. ……………………………………..…………………………………………………… [3] (c) One patient in February 2021 was selected at random. Find the probability that the patient stayed for at most 20 days. Answer ………………………………………. [1] (d) Two patients in February 2022 were selected at random. Find the probability that one of the patients stayed for at most 8 days while the other stayed for more than 8 days. Answer ………………………………………. [2] No. of days

10 [Turn over 4 (a) Complete the table of values for 3 2 25 xyx= − +  x – 1 0 1 2 3 4 5 y – 3.6 2 1.2 – 0.4 – 1.6 – 1.2 [2] (b) On the grid in the next page, draw the graph of 3 2 25 xyx= − + for 25 x−    [3] – 2