Zhonghua 2024 4E4N5N EM Prelim P1 QP w Answer Key

[Turn over] ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 4 NORMAL (ACADEMIC) SBB / 5 NORMAL (ACADEMIC) Candidate’s Name Class Register Number MATHEMATICS 4052/01 PAPER 1 21 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the 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. 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. Setter: Ms Estee Teo Vetter: Mr Francis Tan This question paper consists of 18 printed pages (including this cover page) 90

2 [Turn over] 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 = n rP      + 1001 rl 24 r hr 2 3 1  3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == Acbcba cos))((2222 −+=   f fx 22       −     f fx f fx

3 [Turn over] Answer all the questions. 1 (a) Expand and simplify ( )2 3 5a a b−+ . Answer [1] (b) Factorise completely 223 12xy−+ . Answer [2] 2 (a) Calculate 25048.9 30140 14.69 9.656 − + . Write your answer correct to 5 significant figures. Answer [1] (b) Write your answer to part (a) in standard form. Answer [1] 3 Given that sin 0.4 = , find the two possible values for angle , where 0 180    . Answer  = or [2]

4 [Turn over] 4 (i) A stack of coloured paper contains green, purple and blue sheets of paper. A piece of paper is selected at random from the stack. The probability that the paper is green is 10%. The probability that the paper is purple is 7 20 . Find the probability that the paper is blue. Answer [1] (ii) A few pieces of green paper were added to the stack. The probability of picking a piece of purple pape