Zhonghua 2024 4E4N5N EM Prelim P2 QP w Answer Key

1 [Turn over ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 4 NORMAL (ACADEMIC) SBB SECONDARY 5 NORMAL (ACADEMIC) Candidate’s Name Class Register Number MATHEMATICS 4052/02 PAPER 2 27 August 2024 2 hours and 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and register number in the spaces at the 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 paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degree, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. 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 Lee Jie Li Vetted by: Mr Francis Tan This document consists of 24 printed pages. 90

2 [Turn over Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r V olume of a cone = hr 2 3 1 V olume of a sphere = 3 3 4 r Area of 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 [Turn over 1 Write down the following numbers in ascending order. 25 37− , ( ) 2 30.51− , 0.36 , 0.6 • , 6 − Answer .............., ............., .............., .............., .............. 2 The diagram shows two geometrically similar pails. The area of the base of the smaller pail is 54 cm2. The area of the base of the larger pail is 150 cm2. The height of the larger pail is 26 cm. Calculate the height of the smaller pail. . Answer cm [2] [1]

4 [Turn over 3 (a) Solve 2 3 1125 15 xx −=+ . Answer x = [2] (b) Simplify 2 2 5 33 12 3 7 14 p q p r rq  , giving your answer in positive index notation. Answer [2]

5 [Turn over The diagram shows the cross-section of a pipe filled with water. The cross-section is a circle with centre O and radius