2024 FMSS EMATH P2 PRELIM QP

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) MATHEMATICS 4052/02 Paper 2 Date: 20 August 2024 Duration: 2 hours 15 minutes Candidates answer on the Question Paper. 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 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 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 , use either your calculator value or 3.142. For Examiner’s Use Table of Penalties Question Number Presentation  1  2 Rounding off  1 Parent’s/Guardian’s Signature Setter: Mr James Quek This question paper consists of 26 printed pages  90

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 2 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = P n r       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 a triangle ABC = Cab sin2 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

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 3 Mathematics Paper 2 Answer all the questions. 1 (a) (i) Find g when and . Answer g = …………...….…………….. [1] (ii) Rearrange the formula to make p the subject. Answer p = …………...….…………….. [2] (b) Solve the inequality . Answer ..……………...….…………….. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 4 Mathematics Paper 2 1 (c) Solve the equation . Answer x = …………...….…………….. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 5 Mathematics Paper 2 1 (d) Solve the equation . Give your solutions correct to two decimal places. Answer x = ……...… …… or x = ………… …… [5]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 6 Mathematics Paper 2 2 (a) Susan owns an online shop that sells power banks. She buys a box of 120 power banks from an overseas warehouse at $1800. It cost her $150 to ship the power banks. She plans to sell each power bank at $45. Calculate the percentage profit Susan makes on each power bank she sells for $45. Answer …………...….……………..% [2] (b) Susan borrows $5000 from a bank to import more products for her online shop. She is charged with a compound interest of 2.55% per year. She pays the money back after 2 years. Calculate the total amount of interest she needs to pay to the bank. Give your answer correct to the nearest cent. Answer $ …………...….……………. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 7 Mathematics Paper 2 2 (c) In the year 2022, Singaporeans spent $12 163 million on e-commerce. The population of Singapore in 2022 was . (i) Write $12 163 million in standard form correct to 3 significant figures. Answer $ …………...….……………. [ 1] (ii) Calculate the mean amount of money spent per Singaporean per month in 2022. Give your answer correct to the nearest dollar. Answer $ …………...….……………. [ 2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 8 Mathematics Paper 2 2 (d) The exchange rate between Singapore dollars (SGD) and Hong Kong dollars (HKD) is SGD 1 = HKD 5.75. The exchange rate between Chinese Yuan Renminbi (CNY) and Singapore dollars is CNY 100 = SGD18.64. Susan is planning for a business trip to Shenzhen (China) and Hong Kong. She finds these hotel prices from a tour agency. Susan books 3 nights in Shenzhen and 2 nights in Hong Kong. (i) Calculate the total amount Susan pays for three nights in Shenzhen. Answer CNY …………...….……………. [ 1] She uses her credit card for stay in Hong Kong and Alipay to pay for her stay in Shenzhen. The credit card company will convert the overseas amount to Singapore dollars and there is a currency conversion fee of 1.5%. There is no conversion fee when using Alipay. (ii) Calculate the total amount Susan pays for the two hotels in Singapore dollars. Give your answer correct to the nearest dollar. Answer SGD …………...….…………… [ 3] Shenzhen Hotel CNY 2550 per night plus 10% service charge. Hong Kong Hotel HKD 2550 per night.

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 9 Mathematics Paper 2 3 The cumulative frequency graph shows the height distribution of 120 girls in Secondary One of Casa Secondary School. (a) Use the graph to estimate (i) the median height, Answer …………...….…………… cm [1] (ii) the interquartile range of the heights. Answer …………...….…………… cm [2] 0 20 40 60 80 100 120 100 110 120 130 140 150 160 170 Cumulative Frequency Height (cm)

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2024 10 Mathematics Paper 2 3 (b) For a girl to be selected to join the school’s volleyball team, she must be of at least 160 cm in height. Estimate the percentage of the girls who meets the above criteria. Answer …………...….…………… % [2] (c) The heights of 120 girls in Secondary One from Landmark Secondary School were recorded. The median height is 140 cm and the interquartile range of the height is 13 cm. Make two comparisons between the height distribution in Casa Secondary School and Landmark Secondary School. 1 ………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… 2 ………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… …