CCHM 4048 01 QP

[Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2022 SECONDARY 4 MATHEMATICS 4048/01 Paper 1 Wednesday 14 September 2022 Candidates answer on the Question Paper. 2 hours 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 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 . 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 number of marks for this paper is 80. For Examiner’s Use Total / 80 This document consists of 17 printed pages and 1 blank page. _________________________ Parent’s Signature

2 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 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 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 [Turn over Answer all the questions. 1 Evaluate 3 9.45 36.03 26.9  − , correct to 3 significant figures. Answer ................................... [1] 2 Simplify 22 16 12 32 18 ab ab − − . Answer ................................... [2] 3 Ken drives at an average speed of 85 km/h on the expressway for the first stage of his journey. After exiting the expressway, he continues to drive at an average speed of 60 km/h on the city roads for the second stage of his journey. If the average speed of his entire journey is 75 km/h, find the ratio of the time taken for the first stage of his journey to the time taken for the second stage of his journey. Answer ................ ................ [2] 4 Factorise completely 22 3 12 8x x y xy+ − − . Answer ................................... [2] :

4 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 5 The mass of an electron is 289.11 10 − g. (a) Write in standard form, the mass of an electron in kg. Answer ................................ kg [1] The mass of a hydrogen atom is 271.66 10 − kg. (b) Find the number of electrons that will have the same mass as 1 hydrogen atom, giving your answer to the nearest whole number. Answer ................................... [1] 6 Teacher: The length of a certain rectangle is decreased by 20%, whereas its breadth is increased by 20%. Student: The area of the rectangle will remain the same as the percentage decrease of the length is equal to the percentage increase of the breadth. Therefore, there is a 0% change in the area. Is the student’s statement correct? Support your answer with mathematical calculations. Answer ……………………………………………………………………………………………….. ……………………………………………………………………………………………..[2] 7 Find the range of values of x which satisfy the inequalities 2 2 5 4 9 15 6 x x x− + + . Answer ................................... [3]

5 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 [Turn over 8 Solve the equation ( 1) 6xx += . Answer x = ............ or .............. [2] 9 Given that 23 2 ayx by −= + , (a) calculate x when 5, 2 and 3a b y= =− = , Answer x = .............................. [1] (b) express y in terms of a, b and x. Answer y = ................................. [3]

6 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 10 A company manufactures two sizes of the same brand of shampoo. The prices of the two sizes are indicated in the table below. Shampoo Size (ml) Price ($) 330 7.95 620 14.35 Which shampoo size is a better value for money? Explain your answer clearly. Answer ……………………………………………………………………………………………….. …………………………………………………………………………………………….. [2] 11 The numbers of hours spent daily online by 10 students are recorded in ascending order. 3, 4, 4, 4, 5, 6, 7, 8, 9, a The data is presented as a box and whisker plot shown below. Find the values of a, b, c and d. Answer a =........ , b =........ , c =........ , d =........ [2] b 4 c d 10

7 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 [Turn over 12  = {integers x: 30 40x } A = {x : 1 7 102 x− } B = {x : x is a multiple of 5} (a) Draw a Venn Diagram to illustrate this information. Answer [2] (b) List the elements in 'AB . Answer ................................................ [1] (c) Given also that C = {prime numbers} and D = {multiples of 20}, complete the following statements. (i) Sets B and C are ………………… sets because BC= ………………… [1] (ii) Set D is a …………………. of B because BD= .….………………… [1] { }

8 2022 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4048/01 13 A map is drawn to scale of 4 cm: 1 km. (a) Write this scale in the form 1 : n. Answer ................................... [1] (b) A park on the map has an area of 8 cm2. Find the actual area of the park. Answer ................................ km2 [2] 14 (a) Express 550 as the product of its prime factors. Answer ................................... [1] (b) x is an odd number. The lowest common multiple of 10, 55 and x is 550. Find the two possible values of x. Answer x = ............ or .............. [2] (c) Find the smallest integer p such that 550p is a perfect square. Answer p = ............................. [1]

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