ACSBR 2023 4EXP Prelim MA P1

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMINARY EXAMINATION 2023 SECONDARY FOUR EXPRESS 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. 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 90. This question paper consists of 26 printed pages and 2 blank pages. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 Preliminary Examinations 2023 Secondary 4 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 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 1 Simplify ( )5 3 2 .aa−− Answer __________________________ [1] 2 (a) Calculate 212.5 .5.48 2.47− Write down the first five digits of your answer. Answer _________________________ [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer __________________________ [1]

Anglo-Chinese School (Barker Road) 4 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 3 The sine of an angle is 0.6420. Give two possible values for the angle. Answer _________  or __________  [2] 4 (a) Express 168 as the product of its prime factors. Answer _________________________ [1] (b) The number 168k is a perfect square. Find the smallest positive integer value of k. Answer k = _______________________ [1]

Anglo-Chinese School (Barker Road) 5 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 5 (a) Factorise completely 3 6 5 10 .xy ay x a− − + Answer __________________________ [2] (b) Solve ( )( )2 1 3 0xx+ − = . Answer x = _______ or x = _________ [1] (c) (i) Solve the inequalities 9 1 11 3 7 21x x x−  +  + . Answer __________________________ [3] (ii) Represent the solution on the number line below. Answer [1]

Anglo-Chinese School (Barker Road) 6 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 6 A gardener wants to plant flowers in his garden and he wants to arrange them in rows. He has 60 red flowers, 72 yellow flowers and 84 blue flowers. He wants to make the same number of rows of each color. (a) Find the largest number of rows he can make of each colour. Answer __________________________ [2] (b) Write down the number of red, yellow and blue flowers in each row. Answer _______________________red yellow ______________________blue [1]

Anglo-Chinese School (Barker Road) 7 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 7 (a) Express 2 8 18 y x x= − + in the form y = (x+a)2 + b. Answer _____________________ [2] (b) Write down the equation of the line of symmetry of the graph of 2 8 18 .y x x= − + Answer _____________________ [1] (c) Explain why the graph 2 8 18y x x= − + will not pass through the x-axis. Answer_________________________________________________________ _______________________________________________________________ [1]

Anglo-Chinese School (Barker Road) 8 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 8 In the triangle, AC = 20.5 cm, BC = 13.3 cm and angle ABC = 90 . (a) Calculate AB. Answer AB =___________________cm [1] (b) (i) Explain why it is possible to draw a circle that passes through A, B and C. Answer _____________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [1] (ii) State the radius of this circle. Answer ___________________________cm [1] B A C 13.3 20.5

Anglo-Chinese School (Barker Road) 9 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 9 The diagram shows a triangle ABC. (a) Construct the angle bisector of angle ACB. [1] (b) Construct the perpendicular bisector of BC. [1] (c) Shade the region closer to AC than to BC and closer to C than to B. [1] 10 Joe and Jack each have a savings account. The ratio Joe’s savings : Jack’s savings = 29 : 8 . They each spend $15 from their savings. The new ratio Joe’s savings : Jack’s savings = 4 : 1 . Find how much money Joe now has in his account. Answer $_____________________ [4]

Anglo-Chinese School (Barker Road) 10 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 1 11 Simplify 22 22 23 44 a ab b ba −− − . Answer _____________________ [3] 12 Solve ( ) ( ) 53 403 1 2 1xx + + =−− . Answer _____________________ [3]