ACSBR 2024 4E5N Prelim Math P1 QP

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMINARY EXAMINATION 2024 SECONDARY FOUR EXPRESS / FIVE NORMAL (ACADEMIC) MATHEMATICS 4052 PAPER 1 2 HOURS 15 MINUTES Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. This document consists of 21 printed pages and 1 blank page. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 Mathematical Formulae Compound interest Total amount 1 100 n rP=+  Mensuration Curved surface area of a cone rl= Surface area of a sphere 24 r= Volume of a cone 21 3 rh= Volume of a sphere 34 3 r= Area of triangle ABC 1 sin2 ab C= Arc length r= , where  is in radians Sector area 21 2 r = , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean fx f=  Standard deviation 22fx fx ff  =−   

Anglo-Chinese School (Barker Road) 3 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 1 Write the following numbers in order of size, starting with the smallest. 81.0 , 0.902, 441 399 , 3 2 86.0 Answer ___________ , ___________ , ___________ , ___________ [1] 2 Write as a single fraction in its simplest form xx x −+− 5 1 )5( 7 2 . Answer __________________________ [2] 3 The capacity of a SD card is 250 gigabytes correct to 2 significant figures. The size of a picture file is 2.5 megabytes correct to 1 decimal place. Calculate the largest number of files that can be stored in this SD card. Give your answer in standard form, correct to 3 significant figures. (1 gigabyte = 109 bytes, 1 megabyte = 106 bytes) Answer __________________________ [2]

Anglo-Chinese School (Barker Road) 4 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 4 Simplify 25 20 2 cc d . Answer __________________________ [2] 5 y is directly proportional to x2. If x is increased by 200%, find the percentage increase in y. Answer _________________________ % [2] 6 A sum of money was divided between Amelia, Brandon and Claire in the ratio 2 : 3 : 4. If instead, this money had been divided equally between them, Amelia would have received an extra $20. What was the total sum of money? Answer $ _________________________ [2]

Anglo-Chinese School (Barker Road) 5 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 7 (a) Solve the inequalities 18 2 3 7 2xx−  −  − . Answer __________________________ [2] (b) Write down all the integers that satisfy 18 2 3 7 2xx−  −  − . Answer ___________________________________ [1] 8 (a) On the Venn diagram, shade the region which represents 'AB . [1] (b)  = {integers x : 1 ≤ x ≤ 12} A = {2, 3, 5, 7, 11} B = {3, 6, 9, 12} This information is shown on the Venn diagram. Use one of the symbols below to complete each statement.      (i) 7 ___________ B [1] (ii)  3,7 _________ A [1]

Anglo-Chinese School (Barker Road) 6 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 9 The diagram represents a plot of land, ABCD, which is to be used for a park. (a) Construct the bisector of angle ABC. [1] (b) Construct the perpendicular bisector of AD. [1] (c) A toilet is to be built in the park, nearer to A than to D and nearer to BC than to AB. Shade the region where the toilet is to be built. [1] 10 Using factorisation, solve 2 6 9 6 0pp− − = . Answer p = _________ or _________ [3]

Anglo-Chinese School (Barker Road) 7 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 11 A supplier sells watches at $210 each. Jimmy buys the watches from the supplier at a discount of 20%. Jimmy intends to then sell the watches at a profit of 20%. As a marketing strategy, Jimmy plans to offer a 10% discount on the marked price without affecting his intended 20% profit. Calculate the marked price that Jimmy should sell each watch at. Answer $_________________________ [3] 12 Jim sets off at 08 50 to walk 1000 metres at an average speed of 4 km/h. He takes a 5 minutes break and then runs 1.3 km in 5 minutes. (a) He aims to complete the entire exercise by 09 30. Will he achieve his target? Show your working clearly. Answer ______________________________________________________ [2] ______________________________________________________________ (b) Calculate his average speed for the entire exercise. Give your answer in metres per minute. Answer ____________________ m/min [1]

Anglo-Chinese School (Barker Road) 8 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 13 (a) Two bottles of Brand A coffee are geometrically similar. The larger bottle contains 200 g of coffee granules. The larger bottle is approximately 49% taller than the smaller bottle. Find, in grams, the amount of coffee granules in the smaller bottle. Give your answer to the nearest gram. Answer ____________________ g [2] (b) Brand Y claims that its sales of 200 g bottles of coffee are better than that of Brand X in the past 5 years. State one aspect of the charts that makes this claim wrong. Answer ________________________________________________________ _______________________________________________________________ [1]

Anglo-Chinese School (Barker Road) 9 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 14 (a) Express 1260 as a product of its prime factors. Answer __________________________ [1] (b) The highest common factor of two numbers is 12 while the lowest common multiple is 1260. Both numbers are less than 200. Find the two numbers. Answer ______________ and ______________ [2] (c) 5486 2 3= . m and n are both prime numbers. Find the values of m and n so that 486 m n is both a perfect square and a perfect cube. Answer m = ___________ and n = __________ [1]

Anglo-Chinese School (Barker Road) 10 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 1 15 (a) Express 2 1 12xx++ in the form 2()x a b++ . Answer __________________________ [2] (b) Sketch the graph of 2 1 12y x x=