ACSBR 2023 3EXP Math EYE P2

Full Name Class Index No Class Anglo-Chinese School (Barker Road) END-OF-YEAR EXAMINATION 2023 SECONDARY THREE EXPRESS MATHEMATICS 4052 PAPER 2 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 18 printed pages. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 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 2 1 (a) The price of a game console in Singapore is $620. The price of the same game console in Japan is 42 980 yen. The exchange rate between Singapore dollar ($) and Japanese yen (¥) is $1 = ¥104.2. Calculate how much more expensive the game console is in Singapore than in Japan. Answer $ _________________________ [2] (b) Mr Ong invests $10 000 at a rate of r% per year compound interest. At the end of 3 years the value of his investment is $11 313. Calculate the value of r. Answer r = ________________________ [2]

Anglo-Chinese School (Barker Road) 4 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 (c) The cash price of a television set is $2480. The hire-purchase price of the television set is $2772. The hire-purchase price is a deposit of 15% of the cash price plus 12 equal monthly payments. Calculate one monthly payment. Answer $ ________________________ [3] 2 In the diagram, A is the point ( )0,3 , B is the point ( )3,0 and C is the point ( ),5k . (a) Calculate the length of the line AB. Answer _____________________ units [1] y x O A ( )0,3 B ( )3,0 C ( ),5k

Anglo-Chinese School (Barker Road) 5 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 (b) Show that the value of k is 7 if the gradient of BC is 5 4 . Answer [2] (c) Hence find the equation of the line BC. Answer _________________________ [2] (d) A point D lies on the y-axis such that AC = CD. Find the coordinates of D. Answer (____________ , ___________) [1]

Anglo-Chinese School (Barker Road) 6 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 3 (a) In the diagram, A and B are two geometrically similar cylindrical cans. The ratio of the base area of A to that of B is 9 : 16. (i) Find the ratio of the capacities of A and B. Answer _____________ : ____________ [1] (ii) If the capacity of can B is 768 cm3 and the height of can A is 9 cm, find the base radius of can A. Answer _______________________ cm [2] A B

Anglo-Chinese School (Barker Road) 7 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 (b) In the diagram, ABCD is a square. P and Q are the mid points of AD and AB respectively. (i) Show that triangle APB and triangle BQC are congruent. Answer ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ [2] (ii) QC and PB intersect at X. Show that angle BXC = 90°. Answer [2] A B C D P Q X

Anglo-Chinese School (Barker Road) 8 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 4 The diagram shows the speed-time graph of a lorry and a racing car that travelled along the same road during an interval of t seconds. Both vehicles started from the same place but the racing car started 8 seconds later than the lorry. (a) At the tth second, the distance covered by both vehicles is the same. (i) Form an equation in t and solve the equation. Answer t = ________________________ [3] (ii) Hence calculate the average speed by the lorry for the whole journey. Answer _______________________ m/s [2] Speed (m/s) Time (s) 0 8 t 20 50 r racing car lorry

Anglo-Chinese School (Barker Road) 9 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 (b) Calculate the acceleration of the racing car at 10 seconds. Answer ______________________ m/s2 [1] (c) Find the value of r when the two vehicles are at the same speed. Answer r = _______________________ [2]

Anglo-Chinese School (Barker Road) 10 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 2 5 (a) The diagram shows a circle, ABCDE, centre O. BE and AC are the diameters of the circle and F lies on CA produced. Angle ABE = 31°. Find, giving reasons for each answer, (i) angle BCA, Answer _________________________ ° [1] (ii) angle CDE, Answer _________________________ ° [1] (iii) angle COE. Answer _________________________ ° [2] A B C D E O 31°