NATIONAL SENIOR CERTIFICATE GRADE 12

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1 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P FEBRUARY/MARCH 0 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, 5 diagram sheets ad iformatio sheet. Please tur over

2 Mathematics/P DBE/Feb. Mar. 0 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios This questio paper cosists of questios. Aswer ALL the questios. Clearly show ALL calculatios, diagrams, graphs, et cetera that you have used i determiig the aswers. Aswers oly will ot ecessarily be awarded full marks. A approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. Roud your aswers off to TWO decimal places if ecessary, uless stated otherwise. Diagrams are NOT ecessarily draw to scale. 8. FIVE diagram sheets for QUESTION., QUESTION., QUESTION., QUESTION 3., QUESTION 8. ad QUESTION.3 are attached at the ed of this questio paper. Write your cetre umber ad eamiatio umber o these sheets i the spaces provided ad isert them iside the back cover of your ANSWER BOOK A iformatio sheet, with formulae, is icluded at the ed of this 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/P 3 DBE/Feb. Mar. 0 QUESTION The table below gives a breakdow of the PSL log stadigs for the 8 top teams at the ed of 008/009. POSITION TEAM POINTS SuperSport 55 Orlado Pirates 55 3 Kaizer Chiefs 50 4 Free State Stars 47 5 Golde Arrows 6 Bidvits Wits 7 Aja Cape Tow 8 Amazulu 4 [Source: log]. If the average poits for these 8 teams is 48,375, show that = 46. (). Draw a bo ad whisker diagram of the iformatio give o DIAGRAM SHEET. (4) [6] QUESTION The idividual masses (i kg) of 5 rugby players are give below: Complete the followig table o DIAGRAM SHEET MASS (kg) 60 < < < < 00 FREQUENCY CUMULATIVE FREQUENCY 00 < 0 (4). Draw a ogive (cumulative frequecy curve) of the above iformatio o the grid provided o DIAGRAM SHEET. (3).3 Calculate the mea mass of the rugby players. ().4 How may rugby players have masses withi oe stadard deviatio of the mea? From your calculatios, calculate the percetage of the rugby players who have masses withi oe stadard deviatio of the mea. (5) [4] Please tur over

4 Mathematics/P 4 DBE/Feb. Mar. 0 QUESTION 3 A group of learers was asked to measure their arm spa (from figertip to figertip) ad their height. The data below was gathered. Arm spa (cm) Height (cm) Represet the data as a scatter plot o the grid provided o DIAGRAM SHEET 3. (4) 3. Draw a lie of best fit for this scatter plot. () 3.3 Would you epect a perso with below average arm spa to be below average i height? Give a reaso for your aswer. () [8] QUESTION 4 I the diagram below PQR with vertices P( ; ), Q( ; ) ad R(3 ; 0) is give. 5 y 4 3 P O R - Q Calculate the agle that PQ makes with the positive -ais. (3) 4. Determie the coordiates of M, the midpoit of PR. () 4.3 Determie the perimeter of PQR to the earest whole umber. (5) 4.4 Determie a equatio of the lie parallel to PQ that passes through M. (3) [3] Please tur over

5 Mathematics/P 5 DBE/Feb. Mar. 0 QUESTION 5 5. The equatio of a circle is + y 8 + 6y = Prove that the poit ( ; 9) is o the circumferece of the circle. () 5.. Determie a equatio of the taget to the circle at the poit ( ; 9). (7) 5. Calculate the legth of the taget AB draw from the poit A(6 ; 4) to the circle with equatio ( 3) + ( y + ) = 0. (5) [4] QUESTION 6 The circle, with cetre A ad equatio ( 3) + ( y + ) = 5 is give i the followig diagram. B is a y-itercept of the circle. y B C O A 6. Determie the coordiates of B. (4) 6. Write dow the coordiates of C, if C is the reflectio of B i the lie = 3. () The circle is elarged through the origi by a factor of. Write dow the equatio of the ew circle, cetre A /, i the form ( a) + ( y b) = r. () 6.4 I additio to the circle with cetre A ad equatio ( 3) + ( y + ) = 5, you are give the circle ( ) + ( y 0) = 00 with cetre B Calculate the distace betwee the cetres A ad B. () 6.4. I how may poits do these two circles itersect? Justify your aswer. () [] Please tur over

6 Mathematics/P 6 DBE/Feb. Mar. 0 QUESTION 7 The poit ( ; ) is rotated about the origi through a agle of 50 i a aticlockwise directio to give the poit ( 3 ; y). Calculate the values of ad y. [5] QUESTION 8 I the diagram below MNP is give with vertices M( 5 ; ), N (6 ; 4) ad P( ; 4). / / / MNP is elarged by a factor of,5 to M N P. 7 y N(6 ; 4) M( 5 ; ) 3 O P( ; 4) Draw / / / M N P o the grid provided o DIAGRAM SHEET 4. (3) 8. Write dow the values of: MN 8.. / M / N area MNP 8.. / / / area M N P 8.3 If the above trasformatio is applied to MNP more times to get the image M // // // N P, write dow the value of area MNP. // // area M N P // () () () [9] Please tur over

7 Mathematics/P 7 DBE/Feb. Mar. 0 QUESTION 9 Cosider the poit A ( ; 6). The poit is reflected about the -ais to A /. 9. Write dow the coordiates of A /. () 9. A alterative trasformatio from A to A / is a rotatio about the origi through α, where α Calculate α. (6) [7] QUESTION 0 0. If si 8 = a ad cos 3 = b, determie the followig i terms of a ad/or b : 0.. cos 8 () 0.. cos 64 (3) 0..3 si 4 (4) 0. Prove without the use of a calculator, that if si 8 = a ad cos 3 = b, the b a a b =. (4) 0.3 Evaluate each of the followig without usig a calculator. Show ALL workig si 30.ta 60 cos 540.ta 30.si 400 (7) 0.3. ( si 75 )( si 75 + ) (4) 0.4 Determie the geeral solutio of: si + cos cos = 0 (7) 0.5 Cosider: cos.ta si 0.5. For which values of, [ 0 ; 80 ], will this epressio be udefied? (3) cos.ta cos 0.5. Prove that = ta for all other values of. si si (5) [39] Please tur over

8 Mathematics/P 8 DBE/Feb. Mar. 0 QUESTION The sketch below shows oe side of the elevatio of a house. Some dimesios (i metres) are idicated o the figure. 7,5 E D 3 G C 3,5 A F B 9,4 Calculate, rouded off to ONE decimal place:. EC (3). D ĈE (3).3 Area of DEC ().4 The height EF (3) [] Please tur over

9 Mathematics/P 9 DBE/Feb. Mar. 0 QUESTION The graph of f ( ) = si is draw below. y f Write dow the period of f. (). Write dow the amplitude of h if h() =.3 Draw the graph of ( ) = cos( 30 ) f (). () 4 g for [ 80 ; 80 ] o the grid provided o DIAGRAM SHEET 5. (3).4 Use the graph to determie the umber of solutios for si = cos( 30 ),. ().5 For which values of is g() 0? () / /.6 For which values of is f ( ) < 0 ad g ( ) > 0? (3) [] TOTAL: 50

10 Mathematics/P DBE/Feb. Mar. 0 CENTRE NUMBER: EXAMINATION NUMBER: DIAGRAM SHEET QUESTION QUESTION. MASS (kg) 60 < 70 FREQUENCY CUMULATIVE FREQUENCY 70 < < < < 0

11 Mathematics/P DBE/Feb. Mar. 0 CENTRE NUMBER: EXAMINATION NUMBER: DIAGRAM SHEET QUESTION. CUMULATIVE FREQUENCY CURVE 30 5 Cumulative frequecy Mass (kg)

12 Mathematics/P DBE/Feb. Mar. 0 CENTRE NUMBER: EXAMINATION NUMBER: DIAGRAM SHEET 3 QUESTION 3. Scatter plot showig arm spa vs height Height (cm) Arm spa (cm)

13 Mathematics/P DBE/Feb. Mar. 0 CENTRE NUMBER: EXAMINATION NUMBER: DIAGRAM SHEET 4 QUESTION y M( 5 ; ) N(6 ; 4) O P( ; 4) -7

14 Mathematics/P DBE/Feb. Mar. 0 CENTRE NUMBER: EXAMINATION NUMBER: DIAGRAM SHEET 5 QUESTION.3 y

15 Mathematics/P DBE/Feb. Mar. 0 INFORMATION SHEET: MATHEMATICS b ± b 4 ac = a A = P( + i) A = P( i) A = P( i) A = P( + i) i= = i= ( + ) i = T = ar a( r ) S = F = f [( + i) ] i f ( + h) f ( ) '( ) = lim h 0 h r T a + ( ) d = S = ( a + ( d ) ; r [ ( + i) ] P = i ( ) ( ) + y + y d = + y y M ; y = m + c y y = m ) ( a) + ( y b) = r I ABC: si a A area ABC ( b c = = a = b + c bc. cos A si B si C = ab. si C S ) a = ; < r < r y y m = m = taθ ( α + β ) = siα.cosβ cosα. si β si( α β ) = siα.cosβ cosα. si β si + cos ( α + β ) = cosα.cosβ siα. si β cos ( α β ) = cosα.cosβ + siα. si β cos α si α cosα = si α si α = siα. cosα cos α ( ; y) ( cosθ + y siθ ; y cosθ siθ ) ( ; y) ( cosθ y siθ ; y cosθ + siθ ) ( i ) = σ = i= f ( A) P( A) = P(A or B) = P(A) + P(B) P(A ad B) y ˆ = a + b ( S ) b ( ) ( ) ( y y) =

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P FEBRUARY/MARCH 009 MARKS: 50 TIME: 3 hours This questio paper cosists of 0 pages, a iformatio sheet ad 3 diagram sheets. Please tur over Mathematics/P DoE/Feb.