Sec 3 Express Peicai 2023 Paper 1

[Turn over PEICAI SECONDARY SCHOOL SECONDARY 3 EXPRESS END-OF-YEAR EXAMINATION 2023 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/01 Paper 1 2 October 2023 2 hour 15 minutes Candidates answer on Question Paper READ THESE INSTRUCTIONS FIRST Write your register number, class and name 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. 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 𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. For Examiner’s Use ANnotations ACcuracy Marks Deducted 1 1 This document consists of 19 printed pages and 1 blank page. Setter: Mr Lim Jit Chong

2 Mathematical Formulae Compound Interest Total Amount 1 100 n rP=+  Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where θ is in radians Sector area = 21 2 r  , where θ is in radians Trigonometry sin sin sin a b c A B C== Abccba cos2222 −+= Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

[Turn over 3 Answer all questions 1 A bag contains 7 red marbles, 5 blue marbles and 3 yellow marbles. (a) A marble is chosen at random and then replaced. What is the probability that it is a red marble? Answer .................................. [1] (b) How many more blue marbles must be placed in the bag so that the probability of choosing a blue marble would be 1 2 ? Answer .................................. [2] __________________________________________________________________________ 2 The graph below shows the total number of pizzas sold by a pizza restaurant between 2018 to 2021. Explain how the graph above may be misleading. Answer: ......................................................................................................................... ....................................................................................................................................... ................................................................................................................................... [2] __________________________________________________________________________ Number of pizzas 2018 2019 2020 2021 Year 10000 12000 8000

4 3 The sine of an angle is 0.7654. Give two possible values for the angle. Answer ............. or ............. [2] __________________________________________________________________________ 4 The speed of a space shuttle is 28 000 km/h. The distance of the Moon from the Earth is approximately 53.84 10 km. Calculate the time taken for the space shuttle to reach the Moon from Earth, giving your answer in hours and minutes. Answer ............ h ........... min [2] __________________________________________________________________________ 5 3x= is a solution to the equation 2 15 0x kx+ − = , where k is a constant. (a) Show that 2k = . [1] Answer: (b) Find the other solution of x. Answer x = ........................... [2] __________________________________________________________________________

[Turn over 5 6 The stem and leaf diagram below shows the math exam scores of students in Class A. Stem Leaf 5 2 2 5 7 8 6 2 3 5 5 6 9 9 7 0 0 0 0 1 4 5 9 8 1 6 7 9 2 5 Key: 9 | 2 means 92 Find (a) the mean score, Answer .................................. [1] (b) the median score, Answer .................................. [1] (c) the modal score. Answer .................................. [1] __________________________________________________________________________

6 7 In Singapore, Mr Lim pays $2.80 for one litre of petrol. On a visit to America, he paid 8.40 US dollars for one gallon of petrol. (a) Given that 0.74 US dollar (USD) = 1 Singapore dollars (SGD), find the amount that Mr Lim paid for the petrol in Singapore dollars on his visit to America. Answer ......................... SGD [1] (b) Given that 1 gallon = 3.785 litres, is petrol cheaper in Singapore or America? Justify your answer with workings clearly. Answer: ......................................................................................................................... ........................................................................................................................................ ................................................................................................................................... [2] __________________________________________________________________________

[Turn over 7 8 (a) Express 540 as a product of its prime factors. Answer .................................. [1] (b) Written as a product of its prime factors, 3168 2 3 7=   . Find the highest common factor of 540 and 168 . Answer .................................. [1] (c) Find the lowest common multiple of 540 and 168 . Leave your answer in index notation. Answer .................................. [1] (d) Find the smallest positive integer value of n such that 168n is a perfect cube. Answer .................................. [1] __________________________________________________________________________

8 9 (a) (i) Calculate 3 4 234 1.3 0.2 − and write down the first 5 digits. Answer .................................. [1] (ii) Correct your answer in part (a)(i) to 3 significant figures. Answer .................................. [1] (b) Arrange the following numbers in order of size, starting with the largest. 4 30.2− , 3, 4 123 , 0.1− Answer ............. , ............. , ............. , ............. [2] __________________________________________________________________________ 10 (a) Simplify 2(2 5) 3( 2)xx+ − − . Answer .................................. [2] (b) Factorise 2 6 3 9ax a bx b− + − Answer .................................. [2] __________________________________________________________________________

[Turn over 9 11 The first five terms of a sequence are 2, 5, 8, 11 and 14. (a) Write down the next two terms in the sequence. Answer ............... , ................ [1] (b) Find an expression for the nth term of the sequence. Answer .................................. [2] (c) Is 61 a term in this sequence? Explain your answer with clear workings. Answer: ......................................................................................................................... ................................................................................................................................... [2] ___________________________