Provice of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 01 MATHEMATICS P MARKS: 150 TIME: 3 hours *MATHE* This questio paper cosists of 13 pages, icludig diagram sheets ad a iformatio sheet.
MATHEMATICS P (NOVEMBER 01) INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios. 1. This questio paper cosists of 1 questios. Aswer ALL the questios.. Clearly show ALL calculatios, diagrams, graphs, et cetera, which you have used i determiig the aswers. 3. A approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. 4. Roud off your aswers to TWO decimal places if ecessary, uless stated otherwise. 5. Diagrams are NOT ecessarily draw to scale. 6. Two diagram sheets for aswerig QUESTION., QUESTION 4.1 ad 4., QUESTION 7.. ad QUESTION 11. are attached at the ed of this questio paper. Write your ame o them ad isert them i your aswer book. 7. Number the aswers correctly accordig to the umberig system used i this questio paper. 8. Write legibly ad preset your work eatly.
Fuel Cosumptio i l/100km (NOVEMBER 01) MATHEMATICS P 3 QUESTION 1 14 1 10 8 6 4 0 0 0 40 60 80 100 10 140 160 Speed i km/h 1.1 State whether a liear, quadratic or expoetial fuctio would best fit the data i the above scatter plot. (1) 1. A researcher says that if you drive at 160 km/h, you are likely to cosume more tha 1 l/100km. Do you agree with the researcher? Justify your aswer. () 1.3 What advice would you give to drivers about their drivig speed i order to keep fuel cosumptio to the miimum? () [5] QUESTION The followig are the marks (out of 50) obtaied by10 radomly selected grade 11 learers i a test: 31 5 11 44 35 36 4 18 49.1 Determie the followig:.1.1 the media ().1. the semi-iterquartile rage (3). Draw a box ad whisker diagram usig the iformatio i QUESTION.1. Use DIAGRAM SHEET 1. (4).3 Hece, commet o the distributio of data. (1) [10]
4 MATHEMATICS P (NOVEMBER 01) QUESTION 3 The mea age of the first 13 spectators who wet to St George s Park to watch a ODI (South Africa versus Australia) cricket match is 7. The 13 ages are give below: 0 3 5 14 x 38 30 19 8 34 40 5 3.1 Calculate the value of x. () 3. Hece, determie the stadard deviatio for the ages. (3) 3.3 Determie how may of the spectators had a age which is withi oe stadard deviatio of the mea. () [7] QUESTION 4 The followig table represets the marks achieved by 65 grade 11 learers i a Mathematics test out of 40 marks: Iterval Frequecy Cumulative frequecy 5 9 14 17 11 7 4.1 Complete the cumulative frequecy table usig DIAGRAM SHEET 1. () 4. Draw the ogive (cumulative frequecy graph) for the above data usig DIAGRAM SHEET 1. (3) 4.3 The school decided to reward learers who obtaied 80% ad above. How may learers were rewarded? (3) [8]
(NOVEMBER 01) MATHEMATICS P 5 QUESTION 5 I the diagram below, STAR is a quadrilateral with vertices S, T, A ad R. B is the midpoit of RT. SBA is a straight lie. S(-6 ; 4) T(-1 ; 3) y x R(-7 ; -1) A(p ; -17) 5.1 Show that ΔSTR is isosceles. (4) 5. Determie the coordiates of B, the midpoit of RT. (3) 5.3 Determie the equatio of lie SA. (4) 5.4 Hece, calculate the umerical value of p. (3) 5.5 Determie whether AS is perpedicular to TR or ot. (3) 5.6 What type of quadrilateral is STAR? Give reasos for your aswer. (3) [0]
6 MATHEMATICS P (NOVEMBER 01) QUESTION 6 P, Q(7 ; 6) ad R(4 ; 6) are the vertices of ΔPQR. P is o the x-axis. The equatio of PR is x + y + = 0. ad α are the agles of icliatio of PQ ad QR respectively as show i the diagram. y Q(7 ; 6) P O α x R(4 ; -6) 6.1 Determie the equatio of a lie parallel to PR passig through Q. (3) 6. Determie the gradiet of QR. () 6.3 Determie the coordiates of P. () 6.4 Determie the coordiates of T, if TPRQ is a parallelogram. (3) 6.5 Determie the size of. (5) [15]
(NOVEMBER 01) MATHEMATICS P 7 QUESTION 7 7.1 R(6 ; -1) is a poit o the Cartesia plae. Determie the co-ordiates of R /, the image of R, if: 7.1.1 R is rotated about the origi through 90 i a clockwise directio. () 7.1. R is reflected i the lie y = 0. () 7. ΔDEF is trasformed to its image ΔD // E // F // as follows: Reflectio i the x-axis (y = 0), Followed by a traslatio of 3 uits to the left. 7..1 Determie a sigle rule that trasformed ΔDEF to ΔD // E // F //. (4) 7.. Hece or otherwise, draw ΔD // E // F // if the vertices of ΔDEF are D(4 ; 3), E(0 ; -1) ad F(5 ; -). Use DIAGRAM SHEET. (4) 7..3 Commet o the rigidity of the trasformatio of ΔDEF to ΔD // E // F //. () 7.3 Quadrilateral KLMN is elarged to K / L / M / N / usig a scale factor of 3. 7.3.1 Write dow the coordiates of N / if N is the poit N(½ ; -). () 7.3. Determie the perimeter of K / L / M / N / if the perimeter of KLMN is 10 uits. () 7.4 Describe i words the rule for rotatig T(-4 ; 1) to T / ( -1 ; -4 ). () [0]
8 MATHEMATICS P (NOVEMBER 01) QUESTION 8 The diagram below shows a ew cotaier used for oil that is to be sold at garages. The cotaier is made up of a cylider ad a coe. The height, h, of the cylider is 15 cm ad the slat height, s, of the coe is 10 cm. (Formulae: V = area of base H, V = π r h, SA = π r + π r h, SA = π r s) H s h 8.1 Determie the radius, r, if the volume of the cylider is 4 000 cm 3. (3) 8. Hece, determie the total volume of the cotaier. (4) 8.3 Calculate the total surface area of the cotaier. (4) [11]
(NOVEMBER 01) MATHEMATICS P 9 QUESTION 9 9.1 If si 9 = p determie the followig i terms of p: 9.1.1 cos 9 (3) 9.1. ta (-569 ) () 9.1.3 1 cos 61 () 9. Prove the followig idetity: ( ) (5) [1] QUESTION 10 10.1 Simplify without usig a calculator: (8) 10. Determie the geeral solutio of: si x 3cos x = 0 (4) 10.3 Solve for α if: = 1 for α [90 ; 70 ] (3) [15]
10 MATHEMATICS P (NOVEMBER 01) QUESTION 11 Give: f(x) = si x ad g(x) = cos ( x 30 ) 11.1 Write dow the maximum value of 3.g(x). (1) 11. Sketch the graphs of f ad g o the same system of axes o DIAGRAM SHEET for x [ 180 ; 180 ]. (6) 11.3 Use your graph to determie the values of x, for x [ 180 ; 180 ], for which: g(x) f(x) 0 (4) 11.4 Aswer the followig questios: 11.4.1 Write dow the equatio of h if h is the traslatio of g by 60 to the right ad 1 uit up. () 11.4. Determie the maximum value of h(x) f(x). () 11.5 Explai why the reflectio of f i the x-axis ad the reflectio of f i the y-axis will both result i the same graph. () [17] QUESTION 1 Trapezium PQRT is a plot of lad bought by a farmer. RST is a straight lie. ΔQRS is right-agled at R ad PQST is a parallelogram. QR = 40 m, ad. P Q 40 m T 85 S 30 R 1.1 Calculate the legth of QS. () 1. Calculate the legth of PQ. (3) 1.3 Determie the area of the trapezium PQRT. (5) [10] TOTAL: 150
(NOVEMBER 01) MATHEMATICS P 11 b b 4 ac x a A P( 1 i) A P( 1 i) INFORMATION SHEET: MATHEMATICS A P( 1 i) A P( 1 i) ( 1) 1 i T a ( 1) d S a ( 1) d i 1 i 1 1 T ar a r 1 a S ; r 1 S ; 1 r 1 r 1 1 r x 1 i 1 F x[1 (1 i) ] P i i f ( x h) f ( x) f '( x) lim h 0 h ( ) ( ) x1 x y1 y d x x1 y y1 M ; y y1 y mx c y y1 m( x x1 ) m m ta x x1 x a y b r a b c I ABC: a b c 1 bc. cosa area ABC ab. si C si A si B si C si cos si.cos cos. si si si.cos cos. si cos.cos si. si cos cos.cos si. si cos si cos 1 si cos 1 si si. cos ( x ; y) ( xcos ysi ; ycos xsi ) ( x ; y) ( xcos ysi ; ycos xsi ) xi x fx i 1 x ( A) P( A) P(A or B) = P(A) + P(B) P(A ad B) S
1 MATHEMATICS P (NOVEMBER 01) NAME: DIAGRAM SHEET 1 QUESTION. 10 15 0 5 30 35 40 45 50 55 60 x QUESTION 4.1 QUESTION 4. Iterval Frequecy Cumulative frequecy 5 9 14 17 11 7 y 80 70 60 50 40 30 0 10 5 10 15 0 5 30 35 40 45 50 55 60 65 70 75 80 85 90 95 x
(NOVEMBER 01) MATHEMATICS P 13 NAME: DIAGRAM SHEET QUESTION 7.. y 5 4 3 1-5 -4-3 - -1 1 3 4 5 x -1 - -3-4 -5 QUESTION 11. y 1-180 -150-10 -90-60 -30 30 60 90 10 150 180 x -1