2022 Sec 2 Express Math EOY Outram Secondary with Answers

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BP - 295 Class lndex Number Name E5TO r&6 OUTRAM SEGONDARY SCHOOL EN D.OF.YEAR EXAMINATION 2022 : Mathematics :l : SecondaryTwo Express : 6 October2022 50 Subject Paper No. Level(Stream) Date Duration : t hour 30 minutes Marks : 50 READ THESE INSTRUCTIONS FIRST Candidates answer on the Question Paper. Write your name, class and index number 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. Do not use staples, paper clips, highlighters, glue or conection fluid. Answer all questions. lf 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. lf 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 r, use either your calculator value ot 3.142, unless the question requires the answer in terms of ,r. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [] at the end of each question or part question This document onsists of 10 printed pages, including this cover page. Setter: Ms Chua Yi Ping PartnerlnLeaming 295 For Examiner's Use

Answer all the questions 1 Expand and simplifu the following expressions. (a) (a-c)(3a+2c), O) (2m+n\2. BP-?97 t2) tll Answer Answer 2 (al Make 6 the subject of the formula a =ry5-b (b) Find the value ofD when a = - l. Answer lzl PartnerlnLeaming 297 Answer t1l

f (a) Factorise 2x' -llx-21 completely. Answer O) By factorisng 1p'z +3 p - 6 completely, explain whether there is any integer p such that 3p2 +3p -6 is a prime number. Answer BP - 298 t2l tzl 4 1 It is given that 72 is inversely proportional to .x and y = 4 when 2 (a) Find the equation connecting -y and x. Answer (b) Find the value of .r when y = S. t2l Answer t1l PartnerlnLeaming 258

5 3 people can fold 360 pieces oft-shirts in 3 hours. (a) How long does it take I person to fold 480 pieces oft-shirts? Answer O) State the assumption that you have made for your answer in part (a). Answer hours t)1 BP - 299 tll 6 Simplifu the following expressions. 2xz\ 3(x- l) 2x+\ry'(a) ._,x -l 7 (b) (x-6) x2 -4x-12. 5 Answer t2) Answer t3l PartnerlnLeaming 299

7 Given that a-b=5 and a6=3, evaluate a'+D' using algebraic identities. Answer 8 Alina and Chloe were asked to solve the equation 2x(4x + 5) = 4x(x + l) . The following showed the partial workings presented by Alina and Chloe: BP - 300 l2l Alina's partial working 2x(4x + 5) = 4{7 all 8x2 +10x = 4x2 + 4x 4x2 + 6x =0 Chloe's partial working 2x(4x + 5) = !{y a11 lxz +llx = 4x2 + 4x 4x2 = -6x 4x -- -6 (a) Whose partial working is correct? Answer O) Complete the working for the one you have chosen in pa( (a) and solve equation to find the value(s) for x. t1l Answer l2l PartnerlnLeaming 300

BP - 301 9 It is given that 3 cm on a map represents 4.5 km on the $ound. (a) Express the scale ofthe map in the form I : n, where n is an integer Answer tll O) The achul length of a road is 12 km. Catculate the length of this road on the map Answer cm tll (c) On the map, a football field has an area of 6 cm2. Calculate, in krnz, the actual area ofthe football field. Answer km2 121 PartnerlnLeaming 301

10 Solve the simultaneous equations. BP - 302 t3l 4x-3y=-1, l5x-2y =)Q. Answer x = tl There are z balls in a bag. 8 are blue, 4 are green and the rest are yellow. The probability of drawing a yellow ball is I . J (a) Find the number ofballs in the bag. (c) Find the probability of getting a black ball (b) Find the probability of getting either a green or yellow ball. Answer Answer 12) t1l Answer tlI PartnerlnLeaming 302

BP- 303 I 12 lnlrrtangle ABC, angle AB( = 90". Dis a point on BC suchthat BD is I of-BC. BD is l5 cm- 3 A 53 (a) Find the length oflB, @) Find angle lCB. (c) Find the area of the tnangle ACD. (d) Find the shortest length from D to AC. C D 15 cm B Answer Answer Answer cm t2l t2) cm t1l Answer cm t1l PartnerlnLeaming 303

BP- 304 13 A group of swimmers took part in the 50 m fieestyle heats. The stem-and-leaf diagram shows the time taken, in seconds, taken by this group of swimmers to complete the heats. 2t 22 2.) 24 899 r33345667 26677 156 Key: 2118 means 21.8 seconds (a) Find the number of swimmers who took part in the heats. Answer Ans:wer (c) Find the median time taken by this group of swimmers. Anstver (d) Write down the time taken by the fastest swimmer to complete the heats. Answer (e) swtmmers tll seconds l2l seconds t1l seconds tll Top 40% of the swimmers will be selected to enter the finals. Write down the timing taken by the last swimmer who qualifies for the finals. PartnerlnLeaming 304 Answer seconds t2l (b) Find the mean time taken by this group of swimmers.