NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 008 MARKS: 00 TIME: hours This questio paper cosists of 0 pages, a iformatio sheet ad diagram sheets. Please tur over
Mathematics/P DoE/November 008 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios.... 4. 5. 6. 7. 8. This questio paper cosists of 0 questios. Aswer ALL the questios. Clearly show ALL calculatios, diagrams, graphs, et cetera, which you have used i determiig the aswers. A 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. Diagrams are NOT ecessarily draw to scale. THREE diagram sheets for aswerig QUESTION 6., QUESTION 6., QUESTION 7., QUESTION 8, QUESTION 9 ad QUESTION 0 are attached at the ed of this questio paper. Write your examiatio umber o these sheets i the spaces provided ad had them i together with your ANSWER BOOK. Number the aswers correctly accordig to the umberig system used i this questio paper. It is i your ow iterest to write legibly ad to preset the work eatly. Please tur over
Mathematics/P DoE/November 008 QUESTION Cosider the sequece: ; 6 ; 0 ; 4 ; 8 ; ;. Write dow a recursive formula for the sequece. (). Write dow aother formula for the sequece. () [5] QUESTION After protracted uio protests, a compay aalysed its salary structure for employees. They foud that the salaries are symmetrically distributed with a mea of R8 850 per moth ad a stadard deviatio of R 950 per moth. Research has idicated that if the mothly salary is below R 000, the employee will ot maitai a acceptable quality of life. sd sd sd R8 850 sd sd sd It is also kow that: Approximately 68% of the mothly salary recorded is withi oe stadard deviatio of the mea: 4% above ad 4% below. Approximately 96% of the mothly salary recorded is withi two stadard deviatios of the mea: 48% above ad 48% below. Approximately 00% of the mothly salary recorded is withi three stadard deviatios of the mea: 50% above ad 50% below.. Estimate the percetage of employees who will struggle to maitai a acceptable quality of life. (). Estimate the percetage of employees who ear more tha R 800 per moth. (). Do you thik that the compay has a fair salary structure? Use the give data to motivate your aswer. () [7] Please tur over
Mathematics/P 4 DoE/November 008 QUESTION Durig August 007 a televisio statio carried out a survey durig a programme o Souther Africa. They asked viewers to respod to the questio: 'Should South Africa do somethig to help the refugees from Zimbabwe?' Respodets were required to aswer either 'yes' or 'o' to the questio by meas of a Short Message Service (SMS). The results at the ed of the programme idicated that 65% of the respodets had voted 'o'. The statio thaked the 7 800 respodets who participated i the survey.. Calculate the umber of people who voted 'o' to the questio. (). Ca you coclude from this survey that 65% of all South Africas believe that South Africa should ot help Zimbabwea refugees? Discuss by makig referece to the validity of the results of this survey. () [5] QUESTION 4 4. A survey of 80 studets at a local library idicated the readig prefereces below: 44 read the Natioal Geographic magazie read the Getaway magazie 9 read the Leadership magazie read both Natioal Geographic ad Leadership magazies 9 read both Getaway ad Leadership magazies 9 read all three magazies 69 read at least oe magazie 4.. How may studets did ot read ay magazie? () 4.. Let the umber of studets who read Natioal Geographic ad Getaway, but ot Leadership, be represeted by x. Draw a Ve diagram to represet readig prefereces. (5) 4.. Hece show that x = 5. () 4..4 What is the probability, correct to THREE decimal places, that a studet selected at radom will read at least two of the three magazies? () 4. A smoke detector system i a large warehouse uses two devices, A ad B. If smoke is preset, the probability that it will be detected by device A is 0,95. The probability that it will be detected by device B is 0,98 ad the probability that it will be detected by both devices simultaeously is 0,94. 4.. If smoke is preset, what is the probability that it will be detected by device A or device B or both devices? () 4.. What is the probability that the smoke will ot be detected? () [6] Please tur over
Mathematics/P 5 DoE/November 008 QUESTION 5 5. The Matric Dace Committee has decided o the meu below for the 008 Matric Dace. A perso attedig the dace must choose oly ONE item from each category, that is starters, mai course ad dessert. MENU STARTERS MAIN COURSE DESSERT Crumbed Mushrooms Fried Chicke Ice-cream Garlic Bread Beef Bologaise Malva Puddig Fish Chicke Curry Vegetable Curry 5.. How may differet meal combiatios ca be chose? () 5.. A particular perso wishes to have chicke as his mai course. How may differet meal combiatios does he have? () 5. A photographer has placed six chairs i the frot row of a studio. Three boys ad three girls are to be seated i these chairs. I how may differet ways ca they be seated if: 5.. Ay learer may be seated i ay chair () 5.. Two particular learers wish to be seated ext to each other () [9] Please tur over
Mathematics/P 6 DoE/November 008 QUESTION 6 A traiig maager wats to kow if there is a lik betwee the hours i traiig (x) spet by a particular category of employee ad their productivity (uits produced per day, y) o the job. The data below was extracted from the files of 0 employees. Employee 4 5 6 7 8 9 0 Hours i traiig (x) Productivity (uits produced per day) (y) 6 6 0 8 40 0 5 40 4 45 70 44 56 60 48 75 60 6 8 6. Use the grid provided o DIAGRAM SHEET to draw a scatter plot for the data. () 6. Usig the least squares method, establish a liear relatioship betwee traiig hours ad productivity for these employees. (4) 6. Draw the least squares lie for the data o the scatter plot diagram draw i QUESTION 6. (DIAGRAM SHEET ). () 6.4 Estimate the productivity level for a particular employee who has received oly hours of traiig. () 6.5 Determie the correlatio betwee productivity ad hours of traiig. () 6.6 Is the associatio strog? Advise the maager. () [6] Please tur over
Mathematics/P 7 DoE/November 008 QUESTION 7 7. Complete the statemets below by fillig i the missig word(s) so that the statemets are CORRECT: 7.. The agle subteded by a chord at the cetre of a circle is. () 7.. The agle betwee the taget ad a chord is. () 7.. The opposite agles of a cyclic quadrilateral are. () 7. I the figure below, RDS is a taget to circle O at D. If BC = DC ad CD S = 40, calculate, with reasos, the measures of: 7.. BD C () 7.. 7.. C () A () 7..4 O () A B O C 4 5 40 R D S [9] Please tur over
Mathematics/P 8 DoE/November 008 QUESTION 8 I the diagram below, poits R, P, A, Q ad T lie o a circle. RA bisects R ad AB = AQ. RA ad TQ produced meet at B. R P T Q A B Prove that: 8. AQ bisects PQ B () 8. TR = TB () 8. P = T R P () [8] Please tur over
Mathematics/P 9 DoE/November 008 QUESTION 9 I the figure below, PQ is a diameter to circle PWRQ. SP is a taget to the circle at P. Let P = x P x Q T W R S 9. Why is PR Q = 90? () 9. Prove that P = S. () 9. Prove that SRWT is a cylic quadrilateral. () 9.4 Prove that QWR /// QST. () 9.5 If QW = 5 cm, TW = cm, QR = 4 cm ad WR = cm, calculate the legth of: 9.5. TS () 9.5. SR () [6] Please tur over
Mathematics/P 0 DoE/November 008 QUESTION 0 I the figure below, ABC has D ad E o BC. BD = 6 cm ad DC = 9 cm. AT : TC = : ad AD TE. A T F C B D E CE 0. Write dow the umerical value of ED () 0. Show that D is the midpoit of BE. () 0. If FD = cm, calculate the legth of TE. () 0.4 Calculate the umerical value of: 04. 0.4. Area of ADC Area of ABD Area of TEC Area of ABC () () [9] TOTAL: 00
Mathematics/P DoE/November 008 b ± x = b 4 ac a A = P( + i) A = P( i) INFORMATION SHEET: MATHEMATICS INLIGTINGSBLAD: WISKUNDE A = P( i) A = P( + i) i= i= = ar x F = f i ( r ) a = r [( + i) ] i f ( x + h) f ( x) '( x) = lim h 0 h i= ; r i= ( + ) i = x[ ( + i) ] P = i a r ( a + ( i ) d ) = ( a + ( ) d ) i= i ar = ; < r < d = ( x ) ( ) x + y y M x + x y + y ; y = mx + c y y = m x ) ( x a) + ( y b) = r ( x y y m = m = taθ x x I ABC: si a A b c = = a b c = + bc. cos A area ABC = ab. si C si B si C ( α + β ) = siα.cos β cosα. si β si( α β ) = siα.cos β cosα. si β 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 si α = siα. cosα cos α ( xi x) = σ = i= fx x ( A) P( A) = P(A or B) = P(A) + P(B) P(A ad B) y ˆ = a + bx ( S ) ( x x) ( y y) b = ( x x)
Mathematics/P DoE/November 008 EXAMINATION NUMBER: DIAGRAM SHEET QUESTIONS 6. ad 6. 80 y 70 60 50 40 0 0 0 x 0 0 0 40 QUESTION 7. A B O C 4 5 40 R D S
Mathematics/P DoE/November 008 EXAMINATION NUMBER: DIAGRAM SHEET QUESTION 8 R P T Q A B QUESTION 9 P x Q T W R S
Mathematics/P DoE/November 008 EXAMINATION NUMBER: DIAGRAM SHEET QUESTION 0 A T F B D E C