Math - Sec 2 - SA 2 - 2021 - Beatty Sec

8P.45 BEATTY SECONDARY SCHOOL END.OF.YEAR EXAMINATION 202 1 SUBJECT: Mathematics PAPER :1 LEVEL : DURATION: DATE : Sec 2 Express t hour 30 minutes 8 October 2021 CLASS : NAME: REG NO : ;;;;;;;;;;' !''I'! r'| r ! r, r r''l i'i'i r r i'l i'i r i r r r' r ! r,'!'i r i, Write your name, class and index number in the spaces on the top of this page. 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. 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 n, use either your calculator value or 3.142, unless the question requires the answer in terms of a. 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 50. For Examiner's Use 50 This paper consists of 14 printed pages (including this cover page) PartnerlnLearning 45 [Turn over

8P.46 Mensuration ) Mathematical Formulae Curved surface area of a cone: trl Surface area of a sphere : 47tr2 Volumeofacone:!*'h J Volume of a sphere : 1r'J PartnerlnLearning 46

8P.47 3 I A map is drawn to the scale of 1: 25 000. (a) The distance between two towns on the map is 30 cm. Find the actual distance. Give your answer in metres. Answet" ..... m l2l (b) Aparkhas anactual arcaof 2.5kmz. Calculate the area of the park on the map. Give your answer in cm2. Answer ..... cm2 l2l PartnerlnLearning 47 [Turn over

BP-48 2 Expand and simplifiy (a) (i) (x -sy)(z - ty + r1x), (i,) ?r- +)' (b) Express as a single fraction in its simplest form. 92 @-^ Answer .. 12) Answer l2l L2)Answer PartnerlnLearning 48 4

BP-49 3 (a) Solve the inequality 2l -2x < x + 36. Answer Represent your answer in (a) on the number line below. An,swer 121 (b) (c) Write down the smallest integer x that satisfies the inequality 2l - 2x < x + 36. Answer tll PartnerlnLearning 49 [Turn over 5

BP-50 6 A group of students was asked to measure the length of the pencils they were using. The results are shown in the grouped frequency table below. (a) Complete the histogram with the information provided from the table above. Answer Describe one aspect of the distribution of the length of pencils found in the histogram. Answer.. tll (b) Length of pencil (cm) 2< x<4 4<x<6 6<xS8 8<xS10 10 <.x S l2 Number of pencil(s) 3 8 9 7 3 Le*gth of pencil tcrnl t1l PartnerlnLearning 50

BP. 51 7 (c) Arini concluded that more than a third of the pencils are 6 cm or less. Explain with a supporting reason if she is correct. Answer. (d) Bill was overheard saying that a dot diagrarn would also be able to accurately represent the distribution of pencils above. Do you agree with Bill? Why or why not? Answer. t1l t1l fTurn over PartnerlnLearning 51

BP- 52 s (a) Triangle PQT is similar to triangle SRZ. PT: (x + 5) cm, QT: (x + 3) cm, TR= 9 cm and SI: 12 cm. Calculate PrR. Answer ...... cl1t t3] Given thatl: i5 inversely proportional to the cube of .x and thaty : p for a particular value of x. Findy, in terms ofp, when;r is tripled. Answer y: l2l PartnerlnLearning 52 8

BP-53 ion ABD is a righrangled triangle and BC : BD. AB : 9 cm, AD: 4l cm, angle ABD = 90o and angle BDC : 66". Calculate (a) angle DAB, Answer (b) BD, t ' 121 (c) the shortest distance from ^B to DC. Answer ...... cm l2l Answer . .... c1lt l2l PartnerlnLearning 53 [Turn over 9 6

BP .54 t0 (b) (a) Consider the equation 3x + )y = 3. Find the value of a in the table above. Answer cl : ... ;llftrJilfi lC i;'rr:'r': in the axes berow. on rhe same axes, draw andlabel the graph ,i Z* * 2y : 3. 3x + )y:3and x*y-1. t1l t2l (c) x -1 0 1J v a 1.5 *3 By using the graphs, solve the simultaneous equations PartnerlnLearning Answer r = ....,. ......,! : l1l