CCHM 2024 S4 Math Prelim P1

2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2024 SECONDARY 4 MATHEMATICS 4052/01 Paper 1 Friday 23 August 2024 Candidates answer on the Question Paper. 2 hours 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 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 Total / 90 This document consists of 20 printed pages.

2 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 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 = nrP      + 1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin == Acbcba cos 2 222 −+=   f xf 22      −     f xf f xf

3 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Answer all the questions. 1 The length of a court is 0.028 km and the width of the court is 16 m. Express the ratio of the length to the width of the court in its simplest form. Answer ………… : ………… [1] ________________________________________________________________________________ 2 Given that 0 180x , find the possible values of x for sin 0.985x= . Give your answers correct to 1 decimal place. Answer x = ………..…or…………… [2] ________________________________________________________________________________ 3 (a) Simplify ( ) 34 37 4 10 ab ab , leaving your answer in positive index form. Answer ………………………………... [2] (b) Given that 23x = , 27y = and 92 49 z = , use the laws of indices to find the value of 13 22. x y z−+ Answer ………………………………... [2]

4 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 4 A group of students won $ 226 in a competition and shared the amount equally, leaving $ 4 leftover. Competing for a second time , the same group of students won $ 296. They shared the $296 along with the $4 left over from the first competition equally, with no amount remaining. Assuming that each student received a whole number of dollars in both distributions, find the greatest possible number of students in the group. Answer ………………………students [2] ________________________________________________________________________________ 5 (a) On 6 June 2020, Elijah invested some money in a bank which pays a simple interest at a rate of 3.5% per annum. He received a total interest of $680.40 on 6 June 2023. Find the amount of money Elijah invested in the bank. Answer $……………………………... [2] (b) Freddy invested $8000 in another bank that paid compound interest at a rate of 1.75% per annum, compounded quarterly. Find the total amount Freddy received at the end of 5 years. Give your answer correct to the nearest cent. Answer $……………………………... [2]

5 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over 6 From the diagrams above, select one of them which best illustrates each of the following statements. (a) 34πyx= . (b) The cost of a project $y is a linear function of x, where x is the number of man-hours required to complete the project. The project has a fixed cost of $100. (c) An object is travelling at a constant speed towards a fixed point O. The distance y (in metres) represents how far the object is from point O at time x (in minutes). Answer (a) Diagram ………………………… [1] (b) Diagram ………………………… [1] (c) Diagram ………………………… [1] 7 Write as a single fraction in its simplest form 42 23 x xx − −+− . Answer ……………………………........... [2] y x y x y x y x y x Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 O O O O O

6 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 8 The table shows the distribution of the weights of 40 students. Weight (W kg) 40 50W 50 60W 60 70W 70 80W 80 90W Frequency 6 8 a 11 3 (a) Find the value of a. Answer a = ………………………….[1] (b) Calculate an estimate for (i) the mean weight of the students, Answer ……………………………kg [1] (ii) the standard deviation of the weights. Answer ……………………………kg [1] (c) An error in the weighing machine caused the students’ weights to be recorded 2 kg more than their actual values. Explain how the mean and standard deviation will change after the error is rectified. Answer …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………………[1]

7 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over 9 Andy bought a limited-edition watch from an online website based in Thailand for 10 460 baht. Andy also paid $15 in Singapore dollars for shipping and GST of 9% on the cost of the watch. The exchange rate between Thai baht (฿) and Singapore dollars (S$) was ฿100=S$P. Andy spent a total of $436 in Singapore dollars. Find the value of P, giving your answer correct to 3 significant figures. Answer P =………………………………. [3] 10 The gradient of the line joining the points ( )3 2 ,7a−+ and ( )1, 2a+ is 2 3− . Find the value of a. Answer a = …………………………........... [2] 11 Given that 2 2 69 0aa bb− + = , find the value of ab . Answer ab =………………………........... [2]

8 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 12 Factorise completely 2 2 34 16 4 64mn n m n n− − + . Answer ……………………………........... [3] 13 A bag contains 4 black coins, 7 red coins and 11 white coins. Two coins are drawn from the bag at random, one after another without replacement. (a) Find the probability that a white coin will be chosen on the second draw. Answer ……………………………........... [1] (b) x yellow coins are added to the bag. The probability of picking a black coin in both draws is 1 50 . Find the value of x. Answer x = ………………………........... [3]

9 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over 14 A number of regular n-sided polygons are placed together in a ring to form a regular N-sided polygon as shown in the diagram below. (a) Show that 2 4 nN n= − . Answer [3] (b) Hence, explain why a regular octagon cannot be formed by placing smaller n-sided regular polygons in a ring. Answer