YCSS 2024 4NA Maths Prelim P2(Marking Scheme)

1 YUAN CHING SECONDARY SCHOOL Secondary Four Normal (Academic) Course Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Candidates answer on the question paper. 4045/02 1 August 2024 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 staple, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer one question. 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 70. 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. MARKS Total / 70 This paper consists of 18 printed pages. [Turn Over

2 Mathematical Formulae Compound Interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = lr Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin  Abccba cos2222  Statistics Mean =   f fx Standard deviation = 22            f fx f fx

3 Section A (62 marks) Answer all the questions in this section. 1 (a) Work out 45.3 0.0568 16.5 . Answer ………………………………. [1] (b) y is directly proportional to the square of x. Given that y = 10 when x = 2, find y when x = 6. Answer y = …………………………... [2] 2 (a) Write 0.006 013 74 in standard form, correct to 3 significant figures. Answer ………………………………. [1] (b) Simplify 2 6 3 64 x    . Answer ………………………………. [2]

4 3 (a) The interior angle of a regular polygon is 165 . Find the number of sides of the polygon. Answer ………………………… sides [2] (b) The diagram below shows triangle PQR. Determine if triangle PQR is a right-angled triangle. Show your working clearly. Answer …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. [2] 8.9 cm 5.9 cm 6.7 cm P Q R

5 4 Mr Wong travels from Singapore to Japan. He exchanges Singapore dollars ($) $1500 into Japanese Yen (¥) when the exchange rate is $1 = ¥115.98. (a) How much Japanese Yen (JPY) does he have? Answer JPY ¥………………………. [1] (b) In Japan, Mr Wong spends ¥23 370. On his return, he exchanges the remaining Japanese Yen (¥) into Singapore dollars ($) when the exchange rate is $1 = ¥116.25. How many Singapore dollars does he receive? Answer SGD $ ……………………… [2]

6 5 (a) Solve the simultaneous equations. 6 2 2 4 3 29 xy xy    Answer x = …………………………... y = …………………………... [3]

7 (b) Two car rental companies charge the following values of y for 𝑥 km driven. Company A: 3 150yx Company B: 4 100yx (i) Which rental company has a higher initial fee? Answer Company …………………… [1] (ii) Calculate the driven distance for the cost of the two companies to be the same. Answer …………………………... km [2] (c) A water balloon is launched into the air so that the height, h metres, after t seconds is 24 27 2h t t   . Calculate the time taken for the water balloon to burst as it hits the ground. Answer …………………………….. s [3]

8 6 The table gives information about the time spent, in minutes, by 50 students revising Mathematics on Sunday. Time spent (𝑥 minutes) Frequency 0 < 𝑥 ≤ 15 12 15 < 𝑥 ≤ 30 25 30 < 𝑥 ≤ 45 8 45 < 𝑥 ≤ 60 5 (a) On the grid, draw a histogram to represent this information. [2] (b) State the modal time interval. Answer ………………………………. [1] Frequency Time (seconds)

9 Calculate an estimate of the (c) (i) mean time, Answer ………………………….. min [2] (ii) standard deviation time. Answer ………………………….. min [1] (d) Find the percentage of students who spent more than 30 minutes revising Mathematics on Sunday. Answer …………………………… % [1]

10 7 This table of values is for 3 61y x x   . x 3 2 1 0 1 2 3 y 8 a 6 1 4 b 10 (a) Calculate the value of a and the value of b. Answer a = …………………………... b = …………………………... [2] (b) Draw the graph of 3 61y x x   for 33 x   . [3]