NATIONAL SENIOR CERTIFICATE GRADE 11

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1 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 007 MARKS: 50 TIME: 3 hours This questio paper cosists of pages, 4 diagram sheets ad a -page formula sheet. Please tur over

2 Mathematics/P DoE/Exemplar 007 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios: This questio paper cosists of questios. Aswer ALL the questios. Some of the questios have to be aswered o the diagram sheets attached. Write your ame/examiatio umber i the space provided ad had i ALL FOUR diagram sheets with your ANSWER BOOK. Clearly show ALL calculatios, diagrams, graphs, et cetera 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. 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

Write your ame/examiatio umber i the space provided ad had i ALL FOUR diagram sheets with your ANSWER BOOK.

3 Mathematics/P 3 DoE/Exemplar 007 QUESTION A(0; 4), B(3; ), C( 3; 5) ad D( 6; ) are the vertices of a quadrilateral i a Cartesia plae... Prove that ABCD is a rectagle. (Show ALL the calculatios.) Hece determie the coordiates of the poit of itersectio of the diagoals of rectagle ABCD. (9) () [] QUESTION P( ; 4), Q( 4; ) ad R(7 ; ) are vertices of PQR i a Cartesia plae as show below. is the agle of icliatio of PQ. y 4 Q( 4; ) x R(7; ) -4 P( ; 4) Prove that PQR is right-agled. Calculate the area of PQR. Calculate the size of to the earest degree. Determie the coordiates of midpoit M of QR. Hece determie the equatio of lie MN passig through M, which is parallel to PR. (7) (6) (3) () (5).6 Determie whether the midpoit of PQ lies o lie MN. (4) [7] Please tur over

is the agle of icliatio of PQ. y 4 Q( 4; ) -5 5-0 x R(7; ) -4 P( ; 4) -6...3.4.5 Prove that PQR is right-agled. Calculate the area of PQR. Calculate the size of to the earest degree.

4 Mathematics/P 4 DoE/Exemplar 007 QUESTION 3 The diagram below shows quadrilateral PQRS ad its trasformatios ABCD ad WXYZ. A 6 P 4 B Q D S C R -5 5 Y 0 Z - X -4 W State the geeral rule for the coordiates of ay poit represetig the trasformatio of quadrilateral PQRS to quadrilateral ABCD. Describe TWO possible trasformatios of quadrilateral PQRS to quadrilateral WXYZ. Give the coordiates of the reflectio of poit D i the lie y = x. () (6) () [0] Please tur over

3. 3.3 State the geeral rule for the coordiates of ay poit represetig the trasformatio of quadrilateral PQRS to

5 Mathematics/P 5 DoE/Exemplar 007 QUESTION 4 A(; 3), B(3; ), C(; ) ad D(; 0) are the coordiates of the vertices of quadrilateral ABCD i the Cartesia plae as show below. y A(; 3) B(3; ) 0 D(; 0) 4 6 x - C(; ) - 4. ABCD has to be elarged through the origi by a factor of Use the grid o the attached diagram sheet to draw this elargemet ad clearly idicate the vertices A / B / C / D /. Give the coordiates of vertices A / ad C / of the elargemet. If the area of ABCD is x square uits, determie the area of the elargemet A / B / C / D /. (5) () () 4. Quadrilateral ABCD is rotated 90 i a clockwise directio through the origi State the geeral rule for the coordiates of a poit satisfyig this type of rotatio. Give the coordiates of the vertices of A // B // C // D // for this rotatio. () (4) [5] Please tur over

Give the coordiates of vertices A / ad C / of the elargemet. If the area of ABCD is x square uits, determie the area of the elargemet A / B / C / D /. (5) () () 4.

6 Mathematics/P 6 DoE/Exemplar 007 QUESTION 5 5. Simplify, without usig a calculator, the followig expressios: (Show ALL the calculatios.) 5.. cos50.ta 5 si( 60).cos 480 (Leave the aswer i simplified surd form.) (5) 5.. cos(90 x) cos(360 x).ta(80 x) (5) 5..3 cos x si x si x (6) 5. Determie, without usig a calculator, the value of the followig i terms of t, if si 34 = t: cos 56 ta( 34 ) () (3) Solve for x if 7cos x + = 0 ad x [0 ; 360 ]. (6) 5.3. Determie the geeral solutio of cos x (si x ) = 0. (5) [3] Please tur over

.3 cos x si x si x (6) 5. Determie, without usig a calculator, the value of the followig i terms of t, if si 34 = t: 5.. 5.. cos 56 ta( 34 ) () (3) 5.

7 Mathematics/P 7 DoE/Exemplar 007 QUESTION 6 6. The diagram below is a represetatio of a 5 m vertical observatio tower TB ad two cars K ad L o a road. The agle of depressio from T to car L is 0. The agle of elevatio from car K to the top of the tower is 7. B, K ad L lie i a straight lie ad lie o the same horizotal plae as the base of the tower. T 0 5 m B 7 K L 6.. Calculate the size of Lˆ. () 6.. Calculate the legth of KT. (3) 6..3 Hece calculate the distace betwee the two cars. (4) 6. A game rager G is 8,3 km from cotrol cetre, C, at a bearig of 54 east whe he receives a call that there is a ijured atelope, A, that eeds attetio. The atelope is located 4,8 km at a bearig 5º south of east from the cotrol cetre. The diagram below is a represetatio of the above-metioed situatio. G 8, 3 km 54 C 5 4, 8 km A Calculate how far the game rager is from the ijured atelope. Calculate the area of GCA. (4) (3) [5] Please tur over

() 6.. Calculate the legth of KT. (3) 6..3 Hece calculate the distace betwee the two cars. (4) 6.

8 Mathematics/P 8 DoE/Exemplar 007 QUESTION 7 Volume 3 r h Surface Area r rh (where H is slat height) Volume 4 3 r 3 Surface Area 4 r A ower of a ice-cream parlor wats to istall a steel model of a ice-cream coe outside the etrace of the parlor. The shape of the model of the coe is costructed by usig a hemisphere ad a coe as show i the diagram below. The total height of the model is,4 m ad the radius of the coe is 40 cm. 40 cm, 4 m Calculate: The volume of the model i cm 3 The total exterior surface area of the model i m The mass of the steel model if m has a mass of,5 kg (5) (5) () [] Please tur over

The shape of the model of the coe is costructed by usig a hemisphere ad a coe as show i the diagram below.

9 Mathematics/P 9 DoE/Exemplar 007 QUESTION 8 The followig scores of a cricket player were recorded durig oe seaso: Determie the media score. Determie the lower ad the upper quartiles. Represet the scores of the cricket player usig a box ad whisker diagram. What iformatio about the player's performace ca be deduced relative to the lower quartile? () () (4) () [9] QUESTION 9 The table below represets the umber of people ifected with malaria i a certai area from 00 to 006: YEAR NUMBER OF PEOPLE INFECTED Draw the scatter plot to represet the above data. Explai whether a liear, quadratic or expoetial curve would be a lie of best fit for the above-metioed data. If the same tred cotiued, estimate, by usig your graph, the umber of people that will be ifected with malaria i 008. (3) () () [5] Please tur over

What iformatio about the player's performace ca be deduced relative to the lower quartile?

10 Mathematics/P 0 DoE/Exemplar 007 QUESTION 0 The frequecy table below represets the marks out of a maximum of 80 marks, obtaied by a group of Grade learers i a Accoutig examiatio. MARKS FREQUENCY OBTAINED 0 m < m < m < m < m < m < 80 0 CUMULATIVE FREQUENCY Use the table o the diagram sheet to complete the cumulative frequecy colum. Draw the ogive for the give data o the grid provided o the diagram sheet. Use the ogive to determie the media mark. () (3) () [6] Please tur over

MARKS FREQUENCY OBTAINED 0 m < 30 6 30 m < 60 60 m < 90 38 90 m < 0 4 0 m < 50 50 m < 80 0 CUMULATIVE FREQUENCY 0. 0. 0.3 Use the table o the diagram sheet to complete the cumulative frequecy colum.

11 Mathematics/P DoE/Exemplar 007 QUESTION A basketball team cosists of 0 players. The umber of poits each player scored durig the seaso are as follows: Determie the mea umber of poits scored by the team. (). Complete the followig table usig the table o the diagram sheet: (3) POINTS SCORED ( x i x ) ( x i x ) x i x i = Determie the variace of the poits scored. Determie the stadard deviatio of the poits scored. By makig use of the stadard deviatio obtaied i QUESTION.4, make a statemet about the performace of the team. TOTAL: () () () [9] 50

Complete the followig table usig the table o the diagram sheet: (3) POINTS SCORED ( x i x ) ( x i x ) 3 37 38 4

12 Mathematics/P DoE/Exemplar 007 NAME/EXAMINATION NUMBER: DIAGRAM SHEET QUESTION 4 Y A(; 3) B(3; ) < 0 D(; 0) 4 6 X > - C(; ) - Please tur over

13 Mathematics/P DoE/Exemplar 007 NAME/EXAMINATION NUMBER: DIAGRAM SHEET QUESTION 9 9. Please tur over

14 Mathematics/P DoE/Exemplar 007 NAME/EXAMINATION NUMBER: DIAGRAM SHEET 3 QUESTION 0 0. MARKS FREQUENCY OBTAINED 0 m < m < m < m < m < m < 80 0 CUMULATIVE FREQUENCY 0.3 Please tur over

MARKS FREQUENCY OBTAINED 0 m < 30 6 30 m < 60 60 m <

15 Mathematics/P DoE/Exemplar 007 NAME/EXAMINATION NUMBER: DIAGRAM SHEET 4 QUESTION POINTS SCORED ( x i x ) ( x i x ) x i x i =

16 Mathematics/P DoE/Exemplar 007 INFORMATION SHEET: MATHEMATICS INLIGTINGSBLAD: WISKUNDE b b 4 ac x a A P( i) A P( i) A P( i) i a ( i ) d a ( ) d i i ar i a r r x i F i f ; r f ( x h) f ( x) '( x) lim h 0 h A P( i) i i ( ) i a r r i ar ; x[ ( i) ] P i d x ) ( y ( x y ) x M x y ; y y mx c y y m x ) y y m m ta x x x a y b r I ABC: si cos a si A b si B c si C a b c bc. cos A area ABC ab. si C ( x si.cos cos. si si si.cos cos. si cos.cos si. si cos cos.cos si. si cos si cos si cos si si. cos Please tur over

x ) ( y ( x y ) x M x y ; y y mx c y y m x ) y y m m ta x x x a y b r I ABC: si cos a si A b si B c si C a b c bc.

17 Mathematics/P DoE/Exemplar 007 x x x fx x x var i i x x var i i x x d s i i. s A A P ) ( ) ( P (A or B) = P (A) + P (B) P (A ad B)

NATIONAL SENIOR CERTIFICATE GRADE 11

NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a -page formula sheet. Please tur over Mathematics/P DoE/November