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 paper from this stack at random is now 1 3 . If there were 120 sheets of paper initially, find the new probability of picking a blue piece of paper. Answer [3] 5 5.4 4.8 7.8 6.4 1.9 9.3 6.3 8.7 (a) Find the median of the set of numbers. Answer [1] (b) Find the range of the set of numbers. Answer [1]

5 [Turn over] 6 A picture taken on a particular handphone has dimensions in the ratio width : height = 3 : 4. On a sharing platform, the recommended dimensions for the picture are in the ratio width : height = 9 : 16. When uploaded, the picture only fills the height of the sharing platform and not the width, as shown in the diagram, with the grey areas representing the portions of the image that will not be seen on the sharing platform. Find the fraction of the image that will not be seen on the sharing platform. Give your answer in its lowest terms. Answer [3] Image Sharing platform

6 [Turn over] 7 Simplify ( ) 4 5 2 3 6 q p qp −  − . Leave your answer in positive index notation. Answer [3] 8 The cost of a pen is $a. The cost of a marker is $b. Amelia buys 5 pens and 3 markers for $11.90. Benny buys 8 pens and 2 markers for $14. Form and solve two simultaneous equations to find the cost of a pen and the cost of a marker. Answer Pen $ Marker $ [3]

7 [Turn over] 9 In this scale drawing, A is a house on a piece of land. An object is buried 100m from house A at a bearing of 200°. (a) Mark and label on the drawing the position, T, of the object. [2] (b) A house B is located equidistant between house A and the object T, and is on a bearing of between 90° and 180° from house A. Mark and label on the drawing a possible location of house B. [2] Scale : 1 cm to 10 m A North

8 [Turn over] 10 The first four diagrams in a sequence are shown below. Diagram 1 Diagram 2 Diagram 3 (a) Find the number of grey squares in Diagram 5. Answer [1] (b) Find an expression, in terms of n, for the number of grey squares in Diagram n. Answer [2] (c) Diagram n has 400 white squares. Find n. Answer Diagram [3]

9 [Turn over] 11 264 1-cm cubes are to be arranged to form a cuboid. Only one length of the cuboid is a prime number. Find a possible set of dimensions of the cuboid. Answer cm by cm by cm [2] 12 A model of a school is made. The actual floor area of the school field is 4050 square metres. (a) On the model, the area of the school field is 20 cm2. Find the scale of the model in the form 1 : n, where n is correct to two significant figures. Answer 1 : [2] (b) The scale on another model is 1 : 4000. Find the area of the school field on this model. Answer cm2 [2]

10 [Turn over] 13 The table shows the heights of 50 students, measured in January 2023. Heights, h cm Frequency 130 ≤ h < 140 1 140 ≤ h < 150 4 150 ≤ h < 160 16 160 ≤ h < 170 27 170 ≤ h < 180 2 (a) Calculate an estimate for (i) the mean height of the students, Answer cm [1] (ii) the standard deviation of the heights. Answer cm [1] (b) The heights of the same group of students were measured again in January 2024. The shortest height measured was 146 cm. The tallest height measured was 180 cm. State how the mean and standard deviation will change in January 2024. [1] 14 Given that 29 243 3xx= , find x. Answer [2]