NATIONAL SENIOR CERTIFICATE GRADE 11

Transcription

1 NTIONL SENIOR ERTIFITE GRDE THETIS P3 EXEPLR 007 RKS: 00 TIE: hours This questio paper cosists of 8 pages, diagram sheet ad a -page formula sheet. Please tur over

2 athematics/p3 DoE/Exemplar 007 INSTRUTIONS ND INFORTION Read the followig istructios carefully before aswerig the questios: This questio paper cosists of 8 questios. swer LL the questios. Some of the questios have to be aswered o the attached diagram sheet. Write your ame/examiatio umber i the space provided ad had i the diagram sheet with your aswer book. learly show LL calculatios, diagrams, graphs, et cetera you have used i determiig the aswers. approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. If ecessary, aswers should be rouded off to TWO decimal places, uless stated otherwise. Number the aswers correctly accordig to the umberig system used i this questio paper. Diagrams are NOT ecessarily draw to scale. It is i your ow iterest to write legibly ad to preset the work eatly. Please tur over

3 athematics/p3 3 DoE/Exemplar 007 QUESTION. The probability that evet will occur, is 0, ad the probability that evet will occur, is 0,6. The probability that both evets ad will occur, is 0,..... re evets ad mutually exclusive? Explai your aswer. re evets ad idepedet? Explai your aswer. () (). survey was coducted about the broadcastig of a certai televisio programme. 50 males ad 00 females were iterviewed. The table below shows some of the results: LE FELE TOTL Liked the programme 60 (a) 30 Did ot like the programme (b) 30 (c) TOTL (d).... QUESTION alculate the values of the letters (a, b, c ad d) i the table. Is a perso's preferece for the programme idepedet of the perso's geder? Support your aswer with appropriate calculatios. [] Zama is plaig o spedig the eveig with her frieds. She is udecided about what she should wear. She has to choose from the followig items that she placed o her bed: Two pairs of pats: blue jeas or white pats Three tops: a white T-shirt, a red T-shirt or a blue shirt Two pairs of shoes: a black pair or a white pair.. Draw a tree diagram to show LL the possible combiatios of pats, tops ad shoes. Each pair of pats, each top ad each pair of shoes have a equal chace of beig chose. Zama chooses her outfit at radom. (6).... What is the probability that Zama will wear her blue jeas ad black shoes? What is the probability that she will wear a red T-shirt ad white shoes? () () [0] Please tur over

4 athematics/p3 4 DoE/Exemplar 007 QUESTION 3 t the Natioal School of the rts there are 00 learers i Grade. Learers completed their registratio forms ad the followig iformatio was extracted: 07 learers take rt 90 learers take Dace 63 learers take Graphic Desig 35 learers take Dace ad rt 3 learers take rt ad Graphic Desig 5 learers take rt ad Dace ad Graphic Desig 90 learers take rt or Dace or Graphic Desig x learers take Graphic Desig ad Dace, but NOT rt Draw a Ve diagram to represet the give iformatio. (Let D Dace; rt ad G Graphic Desig.) How may learers have NOT registered for ay of rt or Dace or Graphic Desig? How may learers have registered for Graphic Desig ad Dace, but NOT rt? What is the probability that a Grade learer selected at radom has registered for at least two of the followig subjects: rt, Dace or Graphic Desig? (Idicate your aswer correct to THREE decimal places.) (8) () [6] QUESTION 4 abayaa oys' School has a studet populatio of 00. Fifty boys were selected at radom ad iterviewed about their favourite sport. The table below shows the prefereces of these 50 boys: SPORT PREFERENES Soccer 0 Rugby 7 ricket 0 Golf 5 Hockey Use the iformatio above to predict the total umber of boys who prefer soccer at abayaa oys' School. Is the predictio accurate? Give a reaso for your aswer. () [5] Please tur over

5 athematics/p3 5 DoE/Exemplar 007 QUESTION 5 The sales figures of two motor maufacturers i South frica for a six-moth period were released. The umber of vehicles sold by these two maufacturers is show below: ONTH Jauary February arch pril ay Jue Sales for maufacturer Sales for maufacturer Refer to the table above ad determie which maufacturer had a better growth rate i sales over the give period. (5) 5. The iformatio below regardig the car sales was preseted by two lie graphs: Sales figures for for maufacturer Sales figures for for maufacturer Number umber of of uits uits sold sold Number umber of uits of sold uits sold Ja Feb ar pr ay Ju oths moths 4000 Ja Feb ar pr ay Ju oths moths Determie, with the aid of the graphs above, which maufacturer gives the impressio of a higher growth rate i sales over the give period. Explai how this perceptio is created. () () [9] Please tur over

6 athematics/p3 6 DoE/Exemplar 007 QUESTION 6 6. Eri draws the figures DEF, UVWXYZ ad PQRST o the square grid below ad shows them to her fried, Saras. Saras says that UVWXYZ is similar to DEF, but PQRST is ot similar to DEF. Do you agree with Saras? Give reasos why you agree or disagree with Saras. D U V W X F E Z Y S R P Q T 6. The diagram below has Δ with: N,5 cm, 5 cm, 5 cm, 5 cm ad N 5 cm 5 cm N alculate N. alculate N. Prove that,5 cm 5 cm Δ is a right-agle triagle. [5] Please tur over

7 athematics/p3 7 DoE/Exemplar 007 QUESTION 7 7. I the isosceles triagle below,, E ad D. E D 7.. Prove that Δ E Δ D. 7.. Prove that E D D E. 7. Give rectagle DEGF such that D is o ad F is o of Δ ad D:D :. D 3 F 3 E G swer the followig, givig reasos for LL statemets: F 7.. Determie. 7.. Prove that Δ DF Δ. (6) 7..3 If EG 8 cm, calculate the legth of. (6) [] Please tur over

8 athematics/p3 8 DoE/Exemplar 007 QUESTION 8 X P Q Y R Z I the figure above, R is the midpoit of YZ of Δ XYZ. If PX XY ad QY 4 cm, 3 determie with reasos the umerical value of the followig: 8. PY YX 8. rea of rea of ΔXQR ΔXYR 8.3 rea of ΔXZ rea of ΔXYZ (5) [] TOTL: 00

9 athematics/p3 DoE/Exemplar 007 DIGR SHEET NE/EXINTION NUER: QUESTION cm 5 cm 5 cm,5 cm N QUESTION 7 7. E 7. D D 3 F 3 E G QUESTION 8 X P Q Y R Z

10 athematics/p3 DoE/Exemplar 007 INFORTION SHEET: THETIS INLIGTINGSLD: WISKUNDE b ± b 4 ac x a P( + i) P( i) P( i) P( + i) i i i ( + ) ( a + i ) d ) ( i i ar F f '( i x x) ( a + ( ) d ) ( r ) a r [( + i) ] i lim h 0 f ( x + h) f ( x) h ; r i a r i ar ; < r < x[ ( + i) ] P i d ) + ( y ( x x y ) x + x y + ; y y mx + c y y m x ) y y m m taθ x x ( x a) + ( y b) r I Δ: a si a b si c si b + c bc. cos area Δ ab. si ( x ( α + β ) siα.cos β cosα. siα si( α β ) siα.cos β cosα. siα si + cos ( α + β ) cosα.cos β siα. si β cos ( α β ) cosα.cos β + siα. si β cos α si α cos α si α cos α si α siα. cosα

11 athematics/p3 DoE/Exemplar 007 x x fx x var i ( xi x) ( xi x) var i s. d i ( x x) i P( ) ( ) () s P( or ) P() + P() P( ad )