[FMS] [2023] 4E EM 4052 Prelims P2 QP

NAME: ____________________________ ( ) CLASS: _______ MATHEMATICS 4052/02 Paper 2 Date: 23 August 2023 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 number of 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 que stion, 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 90 Presentation  1  2 Rounding Off  1 Parent’s/Guardian’s Signature Setter: Mr James Quek This question paper consists of 23 printed pages. FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 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 = 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

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 3 Mathematics Paper 2 Answer all the questions. 1 (a) (i) Find p when . Answer p = …………...….…………….. [1] (ii) Rearrange the formula to make f the subject. Answer f = …………...….…………….. [2] (b) Write as a single fraction in its simplest form . Answer …………...….………………… [2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 4 Mathematics Paper 2 1 (c) Solve these simultaneous equations. You must show your working. Answer x = …….....….…………………….. y = ..……...….………………… [3]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 5 Mathematics Paper 2 1 (d) Solve the equation . Answer y = …………...… or y = .…………….. [3]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 6 Mathematics Paper 2 2 (a) Jeremy earns $7500 each month. Jeremy contributes 20% of his first $6000 into his CPF funds. 21% of his CPF funds are distributed to Medi-Save account. 16% of his CPF funds are distributed to Special account. The remaining of his CPF funds are distributed to Ordinary account. Calculate the amount of Jeremy’s CPF that is distributed to Ordinary account. Answer $ …………...….…………….. [2] (b) Jeremy drives a car that consumes 12.5 litres of petrol for every 100 km. The cost of petrol is $2.50 per litre and there is an additional petrol levy of 20 cents for every litre. Jeremy drives 440 km to a town in Malaysia. Calculate the cost of the petrol used for this journey. Answer $ …………...….…………….. [2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 7 Mathematics Paper 2 2 (c) Jeremy invested $10 000 of his savings for 2 years. The interest from his investment is deposited back to his investment account at the end of each year. The rate of interest for the first year is 2.5%. At the end of the second year, the overall percentage increase of his investment is 8.65%. Find the rate of interest for the second year. Answer …………...….…………… % [2] (d) Jeremy is in Japan and decides to buy a jacket for ¥50 000 using a credit card. The cashier offers him 2 options to pay for the jacket; • Option A: pay in Singapore dollars ($) $468.16 or • Option B: pay in Japanese yen (¥) ¥50 000. When paying in Japanese yen, the credit card company will convert the amount to Singapore dollars and there is a currency conversion fee of 1.5%. The exchange rate between Singapore dollars and Japane se yen is $1 = ¥108. Which option should Jeremy choose? Show your working clearly. Option …………… because ……………………………………………………….. ……………………………………………………………………………………[3]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 8 Mathematics Paper 2 3 The cumulative frequency graph for the duration of 120 movies on Airline A and Airline B is shown below. (a) Use the graph to find (i) the median duration of movies for Airline B, Answer …………...….…………… mins [1] (ii) the interquartile range of duration of movies for Airline A. Answer …………...….…………… mins [2] 0 20 40 60 80 100 120 80 100 120 140 160 180 200 Cumulative Frequency Duration (mins) Airline A Airline B

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 9 Mathematics Paper 2 3 (b) Ali flies with Airline A and he watched 2 different movies with no break between them. What is the maximum possible duration of the 2 movies? Answer …………...…hours.…………… mins [1] (c) Ali prefers to watch movies with a duration between 140 minutes and 160 minutes. Which airlines would be a better choice for Ali? Justify your answer using appropriate figures. Airline …………… because ……………………………………………………… …………………………………………………………………………………… [2] (d) Meals on Airline A are served 2 hours into the flight. Ali starts to watch a movie as the plane takes off. What is the probability that the movie is still playing when h is meal is served? Leave your answer as a fraction in its simplest form. Answer …………...……………...… [1] (e) There are 50 Action movies, 10 Romance movies and 60 Comedy movies. Ali chose 3 different movies at random to watch on the plane. Find, as a fraction in its simplest form, the probability that he chose at least 2 Comedy movies. Answer …………...……………...… [2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4Exp / 5N(A) Preliminary Examination 2023 10 Mathematics Paper 2 4 The table below shows some values of x and corresponding values of y for . (a) Complete the table of values, giving your answer correct to 1 decimal place. x –4 –3 –2 –1 0 1 2 3 4 y 6.7 2.5 1.3 2.2 4 6.7 5.5 1.3 [1] On the grid below, draw the graph of for . [3] 0 10 20 30 40 50 60 70 80 90 0 1 2 3 4 5 6 7 8 9 y x