ACSBR 2024 4E5N Prelim Math P2 QP

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMINARY EXAMINATION 2024 SECONDARY FOUR EXPRESS / FIVE NORMAL (ACADEMIC) MATHEMATICS 4052 PAPER 2 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 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 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 1 On a particular day in 2023, the exchange rate between Singapore dollars (SGD) and United States dollars (USD) was USD 1 = SGD x. (a) Write down an expression, in terms of x, for the USD received in exchange for SGD 10 000. Answer USD = ___________________ [1] In 2022, the rate was such that USD 1 would exchange for SGD 0.030 less than in 2023. The difference in exchanging SGD 10 000 in 2023 and SGD 10 000 in 2022, is USD 166. (b) Write down an equation to represent this information and show that it reduces to 283 2.49 150 0xx− − = . Answer [3] (c) Solve the equation 283 2.49 150 0xx− − = , giving your solutions correct to three decimal places. Answer x = ______________ or ______________ [3] (d) Find the amount of USD received in exchange for SGD 20 000 in 2022. Give your answer correct to the nearest dollar. Answer USD = ___________________ [2]

Anglo-Chinese School (Barker Road) 4 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 2 (a) It is given that 22 3sq r q=− . (i) Evaluate s when q = –3 and r = 5. Answer s = _______________________ [1] (ii) Express q in terms of r and s. Answer q = _______________________ [2] (b) (i) Show that 22 (7 1) ( 1)nn− − − is a multiple of 12 for all integer values of n. Answer [2]

Anglo-Chinese School (Barker Road) 5 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 (b) (ii) Simplify 2 22 3 12 4 (7 1) ( 1) p n n np nn − + − − − − . Answer _____________________________ [3]

Anglo-Chinese School (Barker Road) 6 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 3 The diagram shows a circle ABCDEF, with centre O. TA and TE are tangents to the circle. BGF and COT are straight lines. OA intersects BF at G. CT is parallel to BA. Angle OTE = 32°. (a) Identify the triangle that is congruent to triangle TOE and show that they are congruent. Give a reason for each statement you make. Answer _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ [3]

Anglo-Chinese School (Barker Road) 7 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 (b) Find, giving reasons for each step of your working, (i) angle OFG, Answer angle OFG = ___________ [3] (ii) angle CDE. Answer angle CDE = ___________ [3] (c) Explain why points O,E,T and A can also be points on the circumference of another circle. Answer_________________________________________________________ _______________________________________________________________ _______________________________________________________________ [1]

Anglo-Chinese School (Barker Road) 8 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 4 The position vectors of A and B, relative to O, are a and 2b respectively. 3 4BC BA= and 1 2AD BO= . (a) Find, in terms of a and b, (i) AB , Answer AB = ___________ [1] (ii) OC . Answer OC = ___________ [2] (b) (i) P is a point outside of triangle ABO. Find OP , such that 3BP OA= . Answer OP = ___________ [1]

Anglo-Chinese School (Barker Road) 9 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 (ii) Show that O, C and P lie on a straight line. Answer_____________________________________________________ ___________________________________________________________ [2] (c) Find the ratio (i) area of triangle OCB : area of triangle OCA, Answer _______ : _______ [1] (ii) area of triangle OAC : area of triangle OAD. Answer _______ : _______ [1]

Anglo-Chinese School (Barker Road) 10 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Mathematics 4052 Paper 2 5 A stone is thrown from the top of a cliff next to the sea. The height, h metres, of the stone above the sea level t seconds after it is released can be modelled by the equation 216 5 80h t t= − + . Some corresponding values of t and h are given in the table below. t 0 1 2 3 4 5 6 h 80 91 92 83 64 35 p (a) Calculate the value of p. Answer p = _____________ [1] (b) On the grid, draw the graph of 216 5 80h t t= − + for 06 t . [3] (c) Explain how the graph shows that the stone will not reach a height of 100m. Answer __________________________________________________________ ________________________________________________________________ [1]