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