ANDSS 4E2024EM Prelim P2 QP

This document consists of 22 printed pages. Setter: Mr Colin Chen O ANDERSON SECONDARY SCHOOL Preliminary Examination 2024 Secondary Four Express and Five Normal CANDIDATE NAME: CLASS: / INDEX NUMBER: MATHEMATICS 4052/02 Paper 2 15 August 2024 2 hours 15 minutes 1100 – 1315h Candidates answer on the Question Paper. Additional Materials: Nil 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, highlighters, glue, correction fluid or tape. Answer all questions on the answer spaces provided. 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 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, unless the question requires the answer in terms of . At the end of the examination, fasten all your work securely together. 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.

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where  is in radians Sector area = , where  is in radians Trigonometry Statistics Mean = Standard deviation = n rP ÷ ø öç è æ + 1001 rlp 24 rp hr 2 3 1 p 3 3 4 rp Cab sin2 1 r 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+= f fx   22        −  f fx f fx

3 Prelim 4E MATH 2024 4052/2 1 A cone has a radius of 24 cm and a total surface area of 1536  cm2. (a) Show that the volume of the cone is 6144  cm3. [3] (b) The cone is recasted into a solid sphere. Find (i) the radius of the sphere, Answer .................................... cm [2] (ii) the total surface area of the sphere. Answer .................................... cm2 [2]

4 Prelim 4E MATH 2024 4052/2 2 (a) Matthew invests $20 000 into a fixed deposit at r % per month, compounded monthly. After 24 months he will be able to receive $21 337.05. Find the value of r . Answer r = ...................................... [2] (b) Matthew buys a car on hire purchase. He made a 30% downpayment and takes up a 7 year loan which charges simple interest at 2.78% per annum. Given that he pays $1774.40 monthly instalment for the car, calculate the price of the car . Give your answer correct to the nearest dollar. Answer $ .................................... [3]

5 Prelim 4E MATH 2024 4052/2 (c) Matthew wants to invest in Japanese Yen (JPY) to make a profit. In April, he bought JPY with SGD 980. In June, he sold the JPY to get his money back in Singapore dollars. The exchange rates were: • April: SGD 1 = JPY 114.5 • June: SGD 1 = JPY 118.2 Calculate the percentage profit or loss that Matthew made. Answer Matthew made a profit/loss of ......................... % [3] (circle the correct option) 3 A chess club currently has 37 male members and 16 female members. The club hosted a Valentine's Day event to attract married couples to join the club as new members. (Both husband and wife must be totally new to the club.) After this event, the percentage of female members became 40%. Find the number of married couples who joined the club after the event. Answer ................................ couples [3]

6 Prelim 4E MATH 2024 4052/2 4 The marks of a group of 19 students in a test were recorded, as the marks are shown in the stem and leaf diagram. The mode is 42 marks. Stem Leaf 3 a 0 1 2 6 4 1 2 2 2 6 7 5 0 2 4 4 b 5 8 9 Key: 4 1 means 41 marks (i) Find the value of a and b . Answer a= ................................. [1] b= ................................. [1] (ii) Find the median mark. Answer ........................................ [1] (iii) Calculate the mean and standard deviation of the marks. Answer mean= ........................................................ [1] Standard Deviation= .................................. [1] (iv) Marks for another group of 20 students was also recorded. The results are summarized in the table below. Mean 48.2 Standard Deviation 7.22 Make two comparisons between the marks obtain by the group of 19 students and by the group of 20 students. Answer .................................................................................................................. ................................................................................................................................. ............................................................................................................................ [2]

7 Prelim 4E MATH 2024 4052/2 5 (a) Adam has some 50-cent and 20-cent coins in his wallet. Given that he has a total of 73 coins adding up to a value of $28.10, form 2 simultaneous equations to find the number of 50-cent and 20-cent coins he has. Answer He has ................. 50-cent coins and ................... 20-cent coins [5]

8 Prelim 4E MATH 2024 4052/2 (b) Express 2 41 4 25 5 2 x xx +−− as a single fraction in its simplest form. Answer ........................................ [3] 6 The position vectors of points A and B are 9 3 −  and 1 12  − respectively. (a) Find the column vector BA . Answer   [1] (b) Find BA . Answer .................................. units [2]

9 Prelim 4E MATH 2024 4052/2 7 The diagram shows the cross section of a plastic pipe. The arc AB is part of the circle with centre O and radius 45 mm. The pipe has an uniform thickness of x mm. The shaded area represents the cross-sectional area that is filled with water. 65.32AB= mm. (i) Show that 1.6243AOB= radians. [2] (ii) Given that the cross-sectional area of the pipe is 1398.29 mm2, find x . Answer x= ........................... mm [2] 45 A B O x 65.32

10 Prelim 4E MATH 2024 4052/2 8 The diagram shows the positions of 3 points A, B, and C, at sea level. AB = 4.83 km and BC = 7.24 km. The bearing of B from A is 064° and the bearing of C from B is 127°. (i) Show that AC 10.368= km. [3] (ii) Hence find the bearing of A from C. Answer ....................................  [3] A B C North North 127 64 7.24 4.83