BVSS 2024 Prelim EM Paper 1

BUKIT VIEW SECONDARY SCHOOL Secondary Four Express/Five Normal (Academic) Preliminary Examination 2024 CANDIDATE NAME CLASS REGISTER NUMBER Mathematics 4052/01 Paper 1 19 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class in the spaces provided on top of this cover page. 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 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  , 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. Marks 90 Setter: Mrs Irni Prasad Parents’ Signature: This question paper consists of 20 printed pages. BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL

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  is in radians Sector area = 2 2 1r , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 Answer all the questions. 1. Evaluate 34.5 23.4 8.17 , leaving your answer correct to 4 significant figures. Answer ……………….………….. [1] ---------------------------------------------------------------------------------------------------------------- 2. Express the ratio 21 3 kg : 450 g : 300 g in its simplest form. Answer ……… : ..……. : ……… [2] ---------------------------------------------------------------------------------------------------------------- 3. The Mathematics grades of students in Class A and Class B are summarised on accurate pie charts shown below. For each statement, state whether you agree or disagree and explain your reason. Statement Agree / Disagree Reason (a) More students in Class A failed Mathematics compared to Class B. (b) The percentage of students who achieved A1-A2 are the same for both classes. [2] A1-A2 B3-C6 D7-F9 Class B A1-A2 B3-C6 D7-F9 Class A

4 4. A regular polygon has n sides. The size of each interior angle is 5 times the size of each exterior angle. (a) Calculate the value of each exterior angle. Answer ………….………….. [1] (b) State the value of n. Answer n = ……….…………. [1] ---------------------------------------------------------------------------------------------------------------- 5. The radius, r, of an object is directly proportional to the square root of its surface area, A. (i) Sketch the relationship between r and A on the space below. r A [1] (ii) The surface area of the object is 1.21 cm2 when the radius is 0.44 cm. Find the surface area of the object when the radius is 1.2 cm. Answer ………….……….. cm2 [2] ----------------------------------------------------------------------------------------------------------------

5 6. (a) Expand and simplify 2(4 1) 2x−+ . Answer ………….………….. [1] (b) Hence, or otherwise, explain if 2(4 1) 2x−+ is always odd, given that x is an integer. Answer : ……………………………………………………………………………… ………………………………………………………………………………………... ……………………………………………………………………………….…… [2] ---------------------------------------------------------------------------------------------------------------- 7. (a) Write down the set represented by the shaded region. Answer ……………………..…………. [1] (b) It is given that 𝜉 = { x : x is an integer}, A = {x : 9x } and B ={2, 4, 6, 8}. State and explain whether the following mathematical statements are true or false. (i) 𝐵 ⊂ 𝐴. This is …………….. because …………………………………………………. ……………………………………………………..……………………….. [1] (ii) 𝐵 ∈ 𝐴. This is …………….. because …………………………………………………. ……………………………………………………..……………………….. [1]

6 8. Express 22 2 15 39 de d e d e −−+− as a single fraction in its simplest form. Answer ……………….………….. [3] ---------------------------------------------------------------------------------------------------------------- 9. A plan of a garden is drawn to a scale 1 : 20. (a) Calculate the length of the line on the plan, in cm, which represents 13 m long. Answer ………….………….. cm [1] (b) The actual area of a pond in the garden is p m2. Show, with clear working, that the area of the pond represented on the map is 25p cm2. [2] ----------------------------------------------------------------------------------------------------------------

7 10. x is 35% of y. 2 45xy+= . Find the value of x and of y. Answer x = ………… , y = .………… [3] ---------------------------------------------------------------------------------------------------------------- 11. The difference between simple interest and compound interest for a period of 3 years at 5% per annum is $366. Find the principal amount. Answer $………….………….. [3] ----------------------------------------------------------------------------------------------------------------

8 12. The following data shows the masses of 11 parcels in kg. 1.8 2.1 2.4 2.5 2.6 3.2 3.3 3.5 3.8 4.0 4.9 (a) Calculate the mean mass. Answer ……………….………… kg [1] (b) Find the median mass. Answer ……………….……… kg [1] (c) Two parcels (the 2.4 kg and the 4.9kg) were removed from the delivery van. Explain why the median mass remains unchanged. Answer …………………………………………………………...……………………. …………………………………………………………………………………………. ……………………………………………………………………………………… [1]

9 13. (a) By completing the square, find the coordinates of the turning point of the curve y = x2 + 4x + 7. Answer (……… , .…..…) [2] (b) Hence, sketch the graph of y = x2 + 4x + 7 in the space below, showing your y-intercept and turning point clearly.