2024 ACSI Prelim P1

Anglo-Chinese School (Independent) PRELIMINARY EXAMINATION 2024 YEAR FOUR EXPRESS MATHEMATICS PAPER 1 4052/01 Thursday 1 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces on top of this 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 . 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. This document consists of 23 printed pages. [Turn over 90 INDEX NUMBER CANDIDATE NAME CLASS

2 ACS(Independent)MathDept/EM1/y4/2024/Prelim Mathematical Formulae Compound Interest Total amount = 100 r 1      + n P Mensuration Curved surface area of a cone = rl 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 = 2 1 absin C Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sin sin sin == a 2 = b 2 + c 2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22         −     f fx f fx

3 ACS(Independent)Math Dept/EM1/y4/2024/ PrelimEdited [Turn over Answer all the questions. 1 The point C lies on the line AB such 𝐴𝐶: 𝐴𝐵 = 2: 7. (a) Write AC as a fraction of BC. Answer …………..….…….……… [1] (b) Given that AC is 24 cm, calculate the length of BC. Answer …………...….…….… cm [1] 2 (a) sin 0.66913x= Given that x is an obtuse angle, find x. Answer x =………..….…….…… [1] (b) cos cos121y=−  Given that y is an acute angle, find the value of y. Answer y =………..….…….…… [1]

ACS(Independent)MathDept/EM1/y4/2024/Prelim 4 3 During a game, Lee rolled two fair six-sided die. To obtain the score, he subtracted the lower number from the higher number. If the numbers shown on the dice were the same, his score is zero. (a) Construct a possibility diagram to show all possible outcomes. [1] Answer (b) Find the probability that Lee’s score is 5. Answer ………..……….……….. [1] 4 A shopkeeper bought a pair of shorts for $24. He made a percentage profit of 45% despite selling it at a discount of 20% off the listed price. Calculate the listed price for this pair of shorts. Answer $………..….…….…… [2]

5 ACS(Independent)Math Dept/EM1/y4/2024/ PrelimEdited [Turn over 5 Part of the graph of a quadratic function is shown below. The graph passes through the point A (1, 15) and it cuts the x-axis at the points B and C. Given that C is (6, 0) and x = 2 is the line of symmetry of the graph, (a) write down the equation of the quadratic curve in the form 2()y a x h k= − + . Answer ………..……….……………….. [2] (b) find the positive value of x when y = 4, leaving your answer in exact form. Answer x = ………….…… [1] O B C (6, 0) A (1, 15) y x x = 2

ACS(Independent)MathDept/EM1/y4/2024/Prelim 6 6 Justin drew this graph to show his mobile data usage for each of the following four months. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. Answer …………………………………………………………………………………………….……. ……………………………………………………………………………………………………..…..... ……………………………………………………………………………………………………….….. …………………………………………………………………………………………………….…. [2] 7 Simplify ( ) 3 3251 42 xx  giving your answer in the form of nax , where a and n are rational numbers. Answer ………..……….……….. [2] Mobile Data Usage (Gigabytes) Jan Feb Mar Apr Month

7 ACS(Independent)Math Dept/EM1/y4/2024/ PrelimEdited [Turn over 8 (a) Express 13 824 as a product of its prime factors. Answer ……….……………………………..……….. [1] (b) Explain why 13 824 is a perfect cube. Answer ……………………………………………………………………………………………. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………. [1] (c) Given that a is a prime number, find the value of a such that 1 138248a is a perfect square. Answer a = .…………..………[1]

ACS(Independent)MathDept/EM1/y4/2024/Prelim 8 9 In the diagram, ABCD is a rectangle and E and F are points on AD and BC respectively. The ratio of the area of triangle ABF to the area of rectangle ABCD is 1: 9. The ratio of the area of triangle AFE to the area of rectangle ABCD is 1: 6. Explain with clear workings, if the following statements are true/ false. A: The ratio of the area of triangle ABF to that of triangle AFE is 2: 3. B: The ratio of the area of triangle DFC to that of rectangle ABCD is 2: 5. C: The sum of the area of triangles ABF and triangle DFC is equal to the sum of the area of triangles AFE and EFD. Answer ……………………………………………………………………………………………. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………….. …………………………………………………………………………………………………. [6] A B C D E F

9 ACS(Independent)Math Dept/EM1/y4/2024/ PrelimEdited [Turn over 10 The ratio of the number of soccer balls and volleyballs in a sports shop was 11: 7. After 126 soccer balls were added and 233 volleyballs were sold, the ratio became 14: 3. How many volleyballs were there in the shop at first? Answer ………..……volleyballs [3] 11 Explain why ( ) ( ) 22 5 2 5 2nn+ − − is a multiple of 8 for all integer values of n. Answer ……………………………………………………………………………………………………….….. …………………………………………………………………………………………………….…. [2]

ACS(Independent)MathDept/EM1/y4/2024/Prelim 10 12 Factorise the following completely. (a) 245 18 2 5b ab a a− − + , Answer ………..….…….….………… [2] (b) 6 1 3 22 2 −− pp . Answer ……..…….…….….………… [2] 13 Simplify 22 22 9 3 7 6 xy x xy y − +− . Answer …….…….…….…………… [3]