2022 Sec 2 Express Math EOY Broadrick Secondary with Answers

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BP- 101 Name lndex Number BROADRICK SECONDARY SCHOOL SECONDARY 2 EXPRESS END.OF.YEAR EXAMINATION 2022 MATHEMATICS Section 1 Candidates answer on the Question Paper 4052 Oclobet 2022 2 hours 15 minutes Section I Answer all the questions. Soction 2 Answer all the 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 z , use either your calculator value ot 3.142, unless the question requires the answer in terms of z. The number of marks is given in brackets [ ] at the end of each question or part question The total of the marks for Section 1 is 45. The total of the marks for this paper is 90. You are to hand in Section I and Section 2 separately. For Examineds Use Section I t45 Section 2 t45 Total 90 For Examiner's use Reason Question Number Marks Deductsd Roundinq-off Premature Roundino Others This document consists of 'l't printed pages Setter(s): Mrs Jasmine Chua PartnerlnLeaming 99 class I I 6 READ THESE INSTRUCTIONS F]RST 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, glue or correction fluid.

Compound interest Mensuration Tigonometry Statistics Mathematical Formulae BP- 102 Total amount = l+ ''100 Cuwed Surface area of a cone = r/ Surface area of a sphere = 4/P': Volume of a cone : Volume of a sphere = !,t,Area of frangle ABC = 2 sin C Arc length = r9, where d is in radians 0 Sector area : , where d is in radians l-!n''h3 4 3 n' 1 2 ab c sinl sinB sin C o' -- b2 +r'-2bccosA w*r=Z'ftSa Standard deviation = L-fr= (Zfr\' r/ -lrrJ PartnerlnLeaming 100

BP- 1 03 Answer all the questions in this section I Given thaty is directly proportional to the cube of (.r + 1) and thaty = l5 vyhsn x=2, (a) express y in terms ofx, Answer O) find the value of r when y = 120, Answer (c) find the value of y when.x : I I Answer y : I2l t2) PartnerlnLeaming 101 ttl

BP- 1 04 2 (a) Factorise completely (D 1sf-y-6, Answer (ii\ 2ac - 6ad + 10bc - 10bd Answer (b) Expand and simplifu (2x - 1)(2x + l) - 3(2x + 3)2 Awwer I2l 12) PartnerlnLeaming 102 l3l

BP- 105 3 Write as a single fiaction in its simplest form x -+ 2x -l Answer 2 .r+l t3l 4 Solve the following pair of simultaneous equations. 1x -2y --8 4x+3Y=5 Answer x v PartnerlnLeaming 103 t3l

BP- 1 06 5 In the diagram, triangle l-BP is congruent to trian gle AQP . BP and AQ are extended to meet at C. AB = 24 cm, AP = 25 cm and angle ABP = angle AQP = 90" . o (e) State the length of AQ. Answer AQ = (b) Hence, find (i) angle PAB, Answer angle PAts : (ii) angle ACB. Awwer angle ACB : C P B A cm Ul tzl 25 PartnerlnLeaming 104 12)

BP-107 6 The total number of hours spent using the computer in a week by 12 students are shown in the stem-andJeaf diagram below. Key: l l2means 12 hows (a) Given that the mode is 14 houn, find the value of ,t. Answer k = (b) Find (i) the mean number ofhours, Answer hours l2l (ii) the median number of hours. Answer hours tll LeafStem 8 244k8 55 08 19 0 1 2 3 4 tll 7 A trtangle ABC has sides lB = 5 cm, BC = 12 cm andlC= 13 cm. A l3 Bl2C (a) Prove that triangl e ABC is a right-angled triangle. Answer 5 PartnerlnLeaming 105 t2)

7 BP- 1 08 (b) Hence, find (i) sin BiC, $) ACB Answer Answer AeB tt l tl l 8 B +2xIt rs glven that x (a) Findywhen.r:-3 andB:6, @) Express x in terms ofy and.B. Answer y: l2l Answer PartnerlnLeaming 106 t2)

BP-109 9 Amos tkew a javelin. Ignoring the height of Amos, the trajectory ofthe arc is shown below. The highest point the iavelin reaches is 60 m and the distance from the throw is 80 m away. .l' The vertical height, y metres, ofthejavelin, and the horizontal distance, x metres, can be modelled by the equation ), = 4r(,r -80) . The value a, is a constant to be determined. (a) Write down the equation of the line of symmetry of the graph. Answer (b) Write down the coordinates ofthe highest point ofthe javelin. Answer ( (c) Hence or otherwise, find the value ofa. Answer 60 40 20 .T 800 .) trl tll PartnerlnLeaming 107 12) A