ACSBR 2023 4EXP Prelim MA P2

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMIMARY EXAMATIONS SECONDARY FOUR EXPRESS 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. 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 24 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 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 Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 1 (a) It is given that 21 .2s ut at=+ (i) Find s when u = 0, a = 0.5 and t = 13. Answer s = _______________________ [1] (ii) Rearrange the formula to make a the subject. Answer a =_______________________ [2] (b) Solve 9 2 1.4 xx =−− Answer x =________ or x = _________ [2]

Anglo-Chinese School (Barker Road) 4 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 (c) Solve these simultaneous equations. 4 3 18 6 2 1 xy xy −= += You must show your working. Answer x = _______________________ Answer y = _______________________ [3]

Anglo-Chinese School (Barker Road) 5 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 2 The diagram shows a circle ABCD, centre O. E is the midpoint of the chord AB. ED passes through O. F is the point of intersection of BD and diameter AC. Angle 48 .BDC= (a) (i) Show that triangle CFD is similar to triangle BFA. Give a reason for each statement you make. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ [2]

Anglo-Chinese School (Barker Road) 6 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 (ii) AE = 5 cm. Find the area of triangle ABC. Answer _______________________cm2 [4]

Anglo-Chinese School (Barker Road) 7 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 (b) An odometer keeps track of the distance travelled by a vehicle by keeping track of the revolutions of a car tyre. The diagram below shows a car tyre and a simplified graphical representation of it. In real life, this tyre has the following technical information on its sides: 215/60 R16 R16 indicates the rim has diameter 16 inches.d = 215/60 means the tyre has a width of 215 mm, and the thickness h is 60% of the width. Taking 1 inch = 2.54 cm, (i) Find the circumference of the tyre in metres. Answer _________________________m [2] (ii) If the odometer registers 50 complete revolutions, calculate the distance travelled by the vehicle. Answer _________________________m [1]

Anglo-Chinese School (Barker Road) 8 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 3 The number of micro-organisms, y, in a test tube after t days is shown in the table below. The relationship between y and t can be modelled by the equation 10(2 )ty= . (a) Find the value of q. t 0 1 2 3 4 5 6 y 10 20 40 80 q 320 640 Answer q = ______________________ [1] (b) On the grid opposite, draw the graph of 10(2 )ty= for 0 6.t [3] (c) (i) By drawing a tangent, find the gradient of the curve when t = 3. Answer ______________________ [2] (ii) What does this gradient represent? _______________________________________________________________ _______________________________________________________________ [1] (d) The number of micro-organisms in another test tube is given by the equation 80 600.yt=− + By drawing the line 80 600yt=− + , find the number of days for the number of micro-organisms in the two test tubes to be the same. Answer t = ___________________days [2]

Anglo-Chinese School (Barker Road) 9 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2

Anglo-Chinese School (Barker Road) 10 Preliminary Examinations 2023 Secondary 4 Express Mathematics 4052 Paper 2 4 (a) The cumulative frequency curve shows the distribution of the scores of a Geography test (Test 1) taken by 80 students. Test 1 was marked out of 60. (i) Use the curve to estimate (a) the 40th percentile for Test 1, Answer________________ [1] (b) the interquartile range for Test 1. Answer ________________ [2] 10 20 30 40 50 60 Marks 100 80 60 40 20 0 Cumulative frequency