NATIONAL SENIOR CERTIFICATE GRADE 12

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1 NTIONL SNIOR RTIFIT GR MTHMTIS P3 NOVMR 00 MRKS: 00 TIM: hours This questio paper cosists of 7 pages, 3 diagram sheets ad iformatio sheet. Please tur over

2 Mathematics/P3 /November 00 INSTRUTIONS N INFORMTION Read the followig istructios carefully before aswerig the questios This questio paper cosists of 0 questios. swer LL the questios. learly show LL calculatios, diagrams, graphs, et cetera, that you have used i determiig your aswers. swers oly will ot ecessarily be awarded full marks. You may use a approved scietific calculator (o-programmable ad o-graphical), uless stated otherwise. If ecessary, roud your aswers off to TWO decimal places, uless stated otherwise. iagrams are NOT ecessarily draw to scale. THR diagram sheets for aswerig QUSTION 4., QUSTION 7, QUSTION 8., QUSTION 8., QUSTION 9 ad QUSTION 0 are attached at the ed of this questio paper. Write your cetre umber ad examiatio umber o these sheets i the spaces provided ad isert them iside the back cover of your NSWR OOK. iformatio sheet, with formulae, is icluded at the ed of the questio paper. Number the aswers correctly accordig to the umberig system used i this questio paper. Write legibly ad preset your work eatly. Please tur over

3 Mathematics/P3 3 /November 00 QUSTION school orgaised a camp for their 03 Grade learers. The learers were asked to idicate their food prefereces for the camp. They had to choose from chicke, vegetables ad fish. The followig iformatio was collected: learers do ot eat chicke, fish or vegetables 5 learers eat oly vegetables learers oly eat chicke learers do ot eat fish 3 learers eat oly fish 66 learers eat chicke ad fish 75 learers eat vegetables ad fish Let the umber of learers who eat chicke, vegetables ad fish be x.. raw a appropriate Ve diagram to represet the iformatio. (7). alculate x. ().3 alculate the probability that a learer, chose at radom: QUSTION.3. ats oly chicke ad fish, ad o vegetables. ().3. ats ay TWO of the give food choices: chicke, vegetables ad fish. () [3] supermarket coducted a survey o its service to customers. This was doe o a Wedesday morig. The survey idicated that 78% of the customers were satisfied with the service offered by the supermarket ad 90% of the customers agreed that the supermarket was a stress-free place to do their shoppig. The total umber of customers iterviewed was 30.. Would you agree that the supermarket could regard the fidigs of the survey as reliable? Motivate your aswer. (). How may customers thought that the supermarket's service was ot satisfactory? ().3 Give TWO recommedatios to the supermarket o usig surveys to gather iformatio regardig its customer service. () [6] Please tur over

4 Mathematics/P3 4 /November 00 QUSTION 3 toothpaste maufacturer fills toothpaste tubes with a average of 8 grams of toothpaste. The stadard deviatio of a cotrol sample is 0,454 grams. 3. If tubes of toothpaste are maufactured daily, how may tubes will fall withi ON stadard deviatio of the mea? () 3. alculate the rage of the weight of toothpaste tubes i the cotrol sample. (4) [6] QUSTION 4 The data below shows the pulse rate of a sample of people whe they rest ad the agai after miutes of joggig. Restig heart rate (beats per miute) Heart rate after joggig (beats per miute) raw a scatter plot of the data give o the grid provided o IGRM SHT. (3) 4. alculate the equatio of the least squares lie for this data. (4) 4.3 alculate the correlatio coefficiet. () 4.4 ommet o the correlatio of the data. () 4.5 If Joa's heart rate after joggig is 86 beats per miute, what is her restig heart rate, i beats per miute? () [3] QUSTION 5 I Gauteg umber plates are desiged with 3 alphabetical letters, excludig the 5 vowels, ext to oe aother ad the ay 3 digits, from 0 to 9, ext to oe aother. The GP is costat i all Gauteg umber plates, for example TTT 0 GP. Letters ad digits may be repeated i a umber plate. 5. How may uique umber plates are available? (3) 5. What is the probability that a car's umber plate will start with a Y? (3) 5.3 What is the probability that a car's umber plate will cotai oly oe 7? (3) 5.4 How may uique umber plates will be available if the letters ad umbers are ot repeated? (3) [] Please tur over

5 Mathematics/P3 5 /November 00 QUSTION 6 Give: Tk + = Tk + (5 4k) where T = 3 ad k 6. etermie the FIRST FOUR terms of the sequece. (3) 6. What type of sequece will this formula geerate? Give a reaso for your aswer. () [5] QUSTION 7 I the diagram below is a diameter of the circle with cetre O. ad chord itersect at., ad are also chords of the circle. O is joied.. 3 O 33 If Ĉ = 33, calculate, with reasos, the size of: 7. Â (3) 7. ˆ () 7.3 Show that bisects Â (3) [8] Please tur over

6 Mathematics/P3 6 /November 00 QUSTION 8 8. I the diagram below O is the cetre of the circle. GH is a taget to the circle at T. J ad K are poits o the circumferece of the circle. TJ, TK ad JK are joied. G J O T K Prove the theorem that states H Tˆ = TĴK. (5) 8. is a diameter of the circle, with cetre O. is exteded to. is a taget to the circle at. O itersects at F. O. Ê = x O F x 8.. Write dow, with reasos, THR other agles equal to x. (4) 8.. etermie, with reasos, ˆ i terms of x. (3) 8..3 Prove that F is the midpoit of. (4) 8..4 Prove that. () 8..5 Prove that F. =.. (3) [] Please tur over

7 Mathematics/P3 7 /November 00 QUSTION 9 I the diagram below,, ad are poits o the circumferece of the circle. ad itersect at. lso, = 8 cm, = 8 cm ad : = 4 : 7. x 8 y 8 If = x uits ad = y uits, calculate x ad y. [6] QUSTION 0 I the diagram below M is the cetre of the circle. F is a taget to the circle at. is the midpoit of. F M 0. Prove M is a cyclic quadrilateral. (3) 0. Prove that M = M +. (3) 0.3 alculate if = 60 mm, M = 40 mm ad = 0 mm. (4) [0] TOTL: 00

8 Mathematics/P3 /November 00 NTR NUMR: XMINTION NUMR: IGRM SHT QUSTION 4. Scatter plot showig restig heart rate vs heart rate after joggig Heart rate after joggig (beats per miute) Restig heart rate (beats per miute)

9 Mathematics/P3 /November 00 NTR NUMR: XMINTION NUMR: IGRM SHT QUSTION 7 QUSTION 8. G J 3 O O T 33 K H QUSTION 8. QUSTION O y x 8 8 F x

10 Mathematics/P3 /November 00 NTR NUMR: XMINTION NUMR: IGRM SHT 3 QUSTION 0 F M

11 Mathematics/P3 /November 00 INFORMTION SHT: MTHMTIS b ± b 4 ac x = a = P( + i) = P( i) = P( i) = P( + i) i= = i= ( + ) i = T = ar a( r ) S = F = f x [( + i) ] i f ( x + h) f ( x) '( x) = lim h 0 h r T a + ( ) d = S = ( a + ( d ) ; r x[ ( + i) ] P = i ( ) ( ) x + x y + y d = x x + y y M ; y = mx + c y y = m x ) ( x a) + ( y b) = r I Δ: si a area Δ ( x b c = = a = b + c bc. cos si si = ab. si S ) a = ; < r < r y y m = m = taθ x x ( α + β ) = siα.cosβ cosα. si β si( α β ) = siα.cosβ 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 ( x ; y) ( x cosθ + y siθ ; y cosθ x siθ ) ( x ; y) ( x cosθ y siθ ; y cosθ + x siθ ) ( xi x) = σ = i= fx x ( ) P( ) = P( or ) = P() + P() P( ad ) y ˆ = a + bx ( S ) b ( x x) ( x x) ( y y) =

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 1 MATHEMATICS P FEBRUARY/MARCH 014 MARKS: 150 TIME: 3 hours This questio paper cosists of 1 pages, 3 diagram sheets ad 1 iformatio sheet. Please tur over Mathematics/P