GRADE 11 NOVEMBER 2012 MATHEMATICS P3

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1 Provice of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 01 MATHEMATICS P3 MARKS: 100 TIME: hours This questio paper cosists of 14 pages, icludig a formula-sheet ad diagram sheets.

2 MATHEMATICS P3 (NOVEMBER 01) INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios. 1. This questio paper cosists of NINE questios. Aswer ALL the questios.. Show clearly ALL calculatios, diagrams, graphs, et cetera which you have used i determiig the aswers. 3. A approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. 4. If ecessary, aswers should be rouded off to TWO decimal places, uless stated otherwise. 5. Number the aswers correctly accordig to the umberig system used i this questio paper. 6. Diagrams are NOT ecessarily draw to scale. 7. It is i your ow iterest to write legibly ad to preset the work eatly. 8. A iformatio sheet with formulae is attached. 9. Diagram sheets are icluded to assist i aswerig QUESTIONS 1..1, 7.1, 7., 8 ad 9. Write your ame i the space provided ad had it i with your script.

3 (NOVEMBER 01) MATHEMATICS P3 3 QUESTION Complete the followig statemets: If A ad B are idepedet evets, the P(A ad B) = (1) 1.1. If A ad B are mutually exclusive evets, the P(A or B) = (1) 1. Two tests amely a Mathematics test (M) ad a Sciece test (S) are give to a group of 300 learers. It is foud that 110 learers failed (f) both tests, 10 learers passed (p) both tests, 30 learers passed the Mathematics test but failed (f) the Sciece test, ad 40 learers passed (p) the Sciece test but failed (f) the Mathematics test Summarise the give iformatio i a two way cotigecy table below by calculatig the values of a, b, c, d, e ad f as provided i DIAGRAM SHEET 1. Write the aswers o the aswer sheet provided o DIAGRAM SHEET 1. (6) TWO TESTS Maths (p) Maths (f) Total Sciece (p) 10 c e Sciece (f) a 110 f Total b d What is the probability that a learer chose at radom, passed both tests? (1) 1..3 What is the probability that a learer chose at radom, passed the Mathematics test, but failed the Sciece test? (1) 1..4 Determie whether passig the Mathematics test (M) ad passig the Sciece test (S) are idepedet, or depedet evets. Support your aswer with appropriate calculatios. (5) [15]

4 4 MATHEMATICS P3 (NOVEMBER 01) QUESTION A idepedet survey was coducted amogst 160 parets of a particular school to determie their choices for chairma of the School Goverig Body (SGB) amog three cadidates, amely Cadidate A, Cadidate B ad Cadidate C. The Ve-diagram below shows the preferred choices of the parets. S A B x C 5.1 How may parets would like to see that ay oe of the three cadidates become the chairma of the SGB? (). What is the probability of a umber of parets selected radomly, beig udecided i makig a decisio of who should be the chairma of the SGB? (1).3 Calculate the probability that a paret selected at radom will be i favour of Cadidate B to be the chairma of the SGB. Express your aswer as a decimal. (3).4 Show that at least 33% of the parets chose at radom would have at least TWO of the cadidates selected for chairma of the SGB. (3) [9]

5 (NOVEMBER 01) MATHEMATICS P3 5 QUESTION The Huma Scieces Research Coucil (HSRC) coducted a survey amogst 1000 people selected radomly i all the ie provices about who they will support to become the ext presidet of South Africa with a voter populatio of about 3 millio people. 550 of the participats of the survey said they will vote for cadidate X. Headlies i the ewspaper claimed: 55% of all voters support cadidate X. Discuss the validity of this statemet alog with ay limitatios it may have ad the miscoceptios it could create. (4) 3. The swimmig team of South Africa cosists of EIGHT swimmers, amely three me ad five wome, for the Olympic Games. They have to swim i two qualifyig rouds before they ca go through to the fials. As part of their rotatio policy they must select a captai for each qualifyig roud Draw a tree diagram to determie all the probabilities of me or wome beig selected as captai with a colum for the first roud, the the secod roud, the the possible outcomes ad the probabilities as fractios. Label each brach with its probability. (7) 3.. What is the probability, expressed as a decimal fractio, that both the people chose will be wome? () 3..3 Express as a percetage, the probability that the two swimmers selected to be captai, will cosist of oe ma ad oe woma. (3) [16]

6 6 MATHEMATICS P3 (NOVEMBER 01) QUESTION 4 The estimated umber of HIV-positive ifectios, as per persos tested by the Departmet of Health, was released i a ews report ad is show i a table below: Age group Estimated ifectios Estimated uifected Estimated populatio TOTAL If you were to pick a perso at radom what is the probability that he/she would be HIV-positive? Express your aswer as a percetage. () 4. What is the probability that a perso would be betwee 5 9 years old ad be HIV-positive? Express your aswer as a percetage. () 4.3 What is the probability that a perso would be betwee years old ad ot ifected? Express your aswer as a percetage. () 4.4 What percetage of the total populatio that was tested, is HIV-positive? () 4.5 Which age group has the highest ifectio rate? Motivate your aswer by expressig the highest ifectio rate as a percetage. (3) 4.6 By comparig the differet ifectio rates of the differet age groups, give THREE importat messages that this ews report is tryig to covey to the broader public. (3) [14]

7 (NOVEMBER 01) MATHEMATICS P3 7 QUESTION 5 The graphs below (Graph A ad Graph B) show the umber of illegal immigrats (i thousads) from a eighbourig state that has etered the borders of South Africa i a three moth period sice Jauary 01 to March 01. This is accordig to the Departmet of Home Affairs Graph A 4 0 Jauary February March Graph B Jauary February March 5.1 Which graph (Graph A or Graph B) do you thik, displays the iformatio more clearly? What is causig the effect that the oe graph is clearer tha the other graph? () 5. If you were asked by a televisio statio as the Miister of Home Affairs to discuss the illegal immigrat problem, which graph (Graph A or Graph B) would you use i your discussio? Motivate your aswer. () 5.3 If you were asked by the same televisio statio as a member of the oppositio to discuss the illegal immigrat problem, which graph (Graph A or Graph B) would you use i your discussio? Motivate your aswer. () [6]

8 8 MATHEMATICS P3 (NOVEMBER 01) QUESTION 6 The vertices of a certai triagle PQR are P(4;7), Q(4; ) ad R(1; ). 6.1 If the vertices of PQR is elarged by a factor of, write dow the vertices of PQR i the followig order: P(x;y) (1) 6.1. Q(x;y) (1) R(x;y) (1) 6. If the vertices of PQR is reduced by a factor of, write dow the vertices of PQR i the followig order: 6..1 P(x;y) (1) 6.. Q(x;y) (1) 6..3 R(x;y) (1) 6.3 Is PQR /// PQR? Give a reaso for your aswer. () 6.4 If the area of PQR is 16x uits, the the area of the elarged PQR with factor would be...x uits. () [10]

9 (NOVEMBER 01) MATHEMATICS P3 9 QUESTION I the figure below, PMN has V the midpoit of PM. RT VN ad =. P R V T W M N Determie the followig: () 7.1. () ()

10 10 MATHEMATICS P3 (NOVEMBER 01) 7. I the figure below PQRT is a rectagle with PS QS ad P S = y. Q 1 1 P R S 1 T Calculate the followig agles i terms of y: 7..1 Q R (1) 7.. P (1) Prove that: 7..3 PSQ /// STP (3) 7..4 PS = ST (RS + ST) (3) [14] QUESTION 8 I the figure below, P is a poit such that S P = T S, TS = 51 mm, PS = 3,6 mm ad TP = 9 mm. T 9 mm 51 mm Q P 3,6 mm S 8.1 Prove that STP /// SQT. (3) 8. Show that SQ = 79,79 mm. (3) 8.3 Calculate the legth of QT correct to TWO decimal places. (3) [9]

11 (NOVEMBER 01) MATHEMATICS P3 11 QUESTION 9 I the figure below, OBEC is a rectagle with OA = 0 uits, OD = 10 uits ad CD = p uits. A y B E O C D x 9.1 If AOD /// ECD, show that OB = p uits. (3) 9. Write dow the legth of OC i terms of p. (1) 9.3 Hece, show that =. (3) [7] TOTAL: 100

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13 1 MATHEMATICS P3 (NOVEMBER 01) INFORMATION SHEET: MATHEMATICS b b 4 ac x a A P( 1 i) A P( 1 i) A P( 1 i) A P( 1 i) i1 F f 1 x 1 i 1 i i1 ( 1) i S a r 1 r 1 x[1 (1 i) ] P i f ( x h) f ( x) '( x) lim h 0 h d ( x ) ( ) x1 y y M x1 x y1 y 1 ; y mx c y y m x ) x a y b r I ABC: si a A 1 ( x1 ; r 1 ; 1 r 1 y y1 m m ta x x b c a b c 1 bc. cos A area ABC ab. si C si B si C si si.cos cos.si cos 1 si si.cos cos.si cos.cos si. si cos cos.cos si. si cos si cos 1 si si si. cos cos 1 xi x i1 fx x ( A) P( A) P (A or B) = P (A) + P (B) P (A ad B) y a bx S b x x y y x x

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15 (NOVEMBER 01) MATHEMATICS P3 13 NAME AND SURNAME: DIAGRAM SHEET 1 QUESTION 1..1 TWO TESTS Maths (p) Maths (f) Total Sciece (p) 10 c = e = Sciece (f) a = 110 f = Total b = d = 300 QUESTION 7.1 QUESTION 7. P Q 1 1 P R V T 1 W R S T M N

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17 14 MATHEMATICS P3 (NOVEMBER 01) NAME AND SURNAME: DIAGRAM SHEET QUESTION 8 T 9 mm 51 mm Q P 3,6 mm S QUESTION 9 A y B E O C D x