2022 Sec 3 Express A Math EOY Anglo Chinese School with Answer

Visit FREETESTPAPER.com for more papers Website: freetestpaper.com Facebook.com/freetestpaper Twitter.com/freetestpaper

BP-3 Full Name Class lndex No Class ?unda.U!',tuEF**l (&rtr&"1) ENO.OF-YEAR EXAMINATION 2022 SECONDARY THREE EXPRESS ADDITIONAL T{ATHEMATICS 4049 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. lf working is needed for any queslion it must be sho\^ln with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. lf the degree of accuracy is not specified in the question, and if the answer is not exaci, give the answer to three signmcant figures- Give answers in degrees to one decimal place. For z , 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 as 90. IHt ItBtsT It ytr ,o This question paper consists of 19 printed pages and I blank page PartnerlnLeaming 1 For Examineis Use

BP-5 2 I Given that M =logzx and N=log+(2r), show that 2N-M=l The volume, I/ m3 ofa rectangular box is (ZO+f f.6) and the cross-sectional area of the box is (Z. "6) m2 . Without the use of a calculator, find the height of the box in the form o + b.li , where a and 6 are integers. PartnerlnLeaming 3 t3l t4l

BP-6 t4l PartnerlnLeaming 4 3 Solve the equation e"*' = 9e"\ -18e.

BP.7 4 The equation ofa circle is x2+y2-l0x- 4y+25=0 (a) Find the radius and coordinates ofthe centre ofthe circle (b) Given that the circle touches the.r-axis, state the equation ofthe circle which is a reflection of the original circle in the.r-axis. t4l tll PartnerlnLeaming 5

BP-8 5 Thefirnctionfisdefinedby r1r1=,-rr-(l) ,a. n <r<360'. (a) O) State the period of f (x) . (c) Sketch the graph of I = f(r) for 0' <.r < 540' State the maximum and minimum values of f (x) t2l ttl t3l PartnerlnLeaming 6

BP.9 6 A cup of Milo is heated until it reaches a temperature of !"'C. It is then allowed to cool. Its temperature, y'C , when it has been cooled for , minutes, is given by the formula r'= 2o+ n( z ,\() (r) Find (D the value of ?1 the initial temp€rature, (ii) the time taken, correct to the nearest minute, for the cup of Milo to reach 50'c (b) Is it possible for the cup of Milo to reach a temperahue of 0'C ? Explain your reasoning by showing yow workings clearly. t1l t3l t2) PartnerlnLeaming 7

BP'1 O 7 (a) The remainder when zx'-5x'+7 is dividedby 2;r-l is twice the remainder when it is divided by .r - 2. Find the value of the constant z. O) Given that the root ofthe quadratic equation x2 =2x-l isa, showthat ot *1 =(2a' - a +t)(+a' - +a' - a' + a +1) t4l t3l PartnerlnLeaming I

BP-1I 8 During a basketball match, Lavin was fouled and took a free throw. The height ofthe ball, i m, when leaving his hand is given by h = -;(t -5t + k),where r is the time in seconds after the ball left his hand and k is a constant. Given fiuther that the height ofthe ball was 4 m after I second (e) Show that the value of /r = -4 and hence find the height of the ball when it first left Lavin's hand. (b) Deduce the maximum height of the ball and the time it takes to reach the maximum height. PartnerlnLeaming I t3l t4l

BP-1? 9 (a) Show that *' - r*1is always positive for all real values of x. O) Find the set of values of the constant c fot which the line y-5.r-c = 0 meets the cuwe I =2x -:- . x t3l t4l PartnerlnLeaming '10