ACSBR 2023 3EXP Math EYE P1

Full Name Class Index No Class Anglo-Chinese School (Barker Road) END-OF-YEAR EXAMINATION 2023 SECONDARY THREE EXPRESS MATHEMATICS 4052 PAPER 1 1 HOUR 45 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. 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 of the marks for this paper is 70. This question paper consists of 16 printed pages. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 End-of-Year Examination 2023 Secondary 3 Express 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 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 1 Expand and simplify ( ) 2 23xy− . Answer ___________________________ [2] 2 The first 4 terms in a sequence are 6, 10, 14, 18, … . (a) Write down an expression, in terms of n, for the nth term, Tn, of this sequence. Answer ___________________________ [1] (b) Evaluate T11. Answer ___________________________ [1] (c) Explain why Tn is always an even number, for all values of n. Answer ________________________________________________________ ________________________________________________________ ________________________________________________________ [1]

Anglo-Chinese School (Barker Road) 4 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 3 The population of Zimbabwe was 15.99 million with a land area of 390 745 km 2 in 2021. (a) Write 15.99 million in standard form. Answer ___________________________ [1] (b) Calculate the number of people per square kilometre, correct your answer to the nearest whole number. Answer ___________________________ [2] 4 (a) Express 540 as the product of its prime factors. Answer ___________________________ [1] (b) The number 540 p q is a perfect cube. p and q are prime numbers. Find the value of p and the value of q. Answer p = _______________________ q = _______________________ [2]

Anglo-Chinese School (Barker Road) 5 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 5 (a) The time taken to put together a wooden crate is inversely proportional to the number of workers. Four workers take 12.5 hours. Find the time it would have taken 5 workers to put together a wooden crate. Answer ______________________ hours [1] (b) A quantity y is directly proportional to x3. If x is increased by 200%, calculate the percentage change in y. Answer ________________________ % [2] 6 If 2 2 3 12 8 4 16 x x x −+  = , find the value of x. Answer __________________________ [3]

Anglo-Chinese School (Barker Road) 6 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 7 (a) Express 2 64xx−+ in the form ( ) 2 x p q−+ . Answer ___________________________ [2] (b) Write down the coordinates of the minimum point of the graph of 2 64y x x= − + . Answer ( _________ , ____________ ) [1] 8 In the diagram, ST // VW, angle TUV = 95° and angle UVW = 128°. Calculate angle STU. Give a reason for each step of your working. Answer _________________________ ° [3] S T U V W 95° 128°

Anglo-Chinese School (Barker Road) 7 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 9 The graph of 2 6y x x=− + + is drawn on the grid. (a) Write down the equation of the line of symmetry of the curve. Answer ___________________________ [1] (b) The equation 2 202 x x− + + = can be solved by drawing a suitable straight line on the grid. (i) Find the equation of the straight line. Answer ___________________________ [1]

Anglo-Chinese School (Barker Road) 8 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 (ii) By drawing this straight line, solve the equation 2 202 x x− + + = . Answer x = ___________ or __________ [3] 10 (a) Given that 22 4hkp n −= , express k in terms of h, n and p. Answer ___________________________ [3] (b) Hence, find the values of k when 1p=− , 9h= and 2n= . Answer k = ___________ or __________ [2]

Anglo-Chinese School (Barker Road) 9 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 11 The diagram shows the interior angles of each of three regular polygons, A, B and C. A is a square, B is a regular pentagon and C is a regular n-sided polygon. The polygons fit together at O. Find the value of n. Answer n = ________________________ [4] A B C O

Anglo-Chinese School (Barker Road) 10 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 12 (a) The diagram shows a bar graph of the number of students in Clubs in a school. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. Answer ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ [2] (b) The table shows the number of private buses in Singapore from 2020 to 2022. Year 2020 2021 2022 Number of private buses 2835 2717 2634 Suggest one advantage of using a line graph compared to using a pictogram to represent the above data. Answer ________________________________________________________ ________________________________________________________ ________________________________________________________ [1] 6 8 10 12 14 16 18 20 22 24 26 28 30 Aesthetics Club Chess Club Dance Club Guitar Club Debate Club Number of Students in Clubs