GRADE 12 SEPTEMBER 2012 MATHEMATICS P2

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1 Provice of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE SEPTEMBER 0 MATHEMATICS P MARKS: 50 TIME: 3 hours *MATHE* This questio paper cosists of 4 pages, icludig a formula sheet ad 4 diagram sheets.

2 MATHEMATICS P (SEPTEMBER 0) INSTRUCTIONS AND INFORMATION Read the followig istructios carefull before aswerig the questios.. This questio paper cosists of questios. Aswer ALL the questios.. Clearl show ALL calculatios, diagrams, graphs, et cetera, which ou have used i determiig the aswers. 3. Aswers ol will ot ecessaril be awarded full marks. 4. A approved scietific calculator (o-programmable ad o-graphical) ma be used, uless stated otherwise. 5. Roud off our aswers to TWO decimal places if ecessar, uless stated otherwise. 6. Diagrams are ot ecessaril draw to scale. 7. FOUR diagram sheets for aswerig QUESTION., QUESTION., QUESTION., QUESTION 4.., QUESTION 7.4 ad QUESTION. are attached at the ed of this questio paper. Write our ame ad surame i the spaces provided ad isert the sheets i our aswer book. 8. Number the aswers correctl accordig to the umberig sstem used i this questio paper. 9. Write legibl ad preset our work eatl. 0. A iformatio sheet, with formulae, is icluded at the ed of this questio paper.

3 (SEPTEMBER 0) MATHEMATICS P 3 QUESTION The graph below shows the umber of people ad their ages who voted i the Local Govermet electios i oe votig statio. Use the graph to aswer the questios which follow. 60 Ogive for ages of people i oe votig statio Ages.. How ma people voted i that votig statio? (). Complete the frequec ad cumulative frequec colums of the frequec table o DIAGRAM SHEET. (4).3 Determie the media age. ().4 How ma voters were 35 ears or older? () [7]

4 4 MATHEMATICS P (SEPTEMBER 0) QUESTION The ages (i ears) of the oldest perso i each of homes that were couted b a Statistics South Africa official i Dutwa durig the 0 Cesus surve are give below: Draw a bo ad whisker diagram for the above data usig DIAGRAM SHEET. (4). Aother Statistics South Africa official couted i Alice. The data was summarised as follows: miimum age was 8, lower quartile was 3, the iterquartile rage was 8, the media was 4 ad the maimum age was the same as i Dutwa. Draw, o the same diagram (DIAGRAM SHEET ), the bo ad whisker diagram for the above data. ().3 Which tow had more families with older people? Justif our aswer. () [8] QUESTION 3 The followig are the pass percetages of 0 subjects doe at a high school: 65,3 8, , 56,5 94, , 75 79,4 3. Determie the mea percetage. () 3. Determie the stadard deviatio of the percetages. (3) 3.3 What is the lowest pass percetage that the subject must get i order to be withi oe stadard deviatio of the mea? () [7] QUESTION 4 I order to determie whether fatigue plas a role i the umber of tries scored i a match, the umber of tries scored i successive matches is compared. The followig table represets the umber of tries scored b oe rugb team i the IRB rugb world cup i each of their seve matches: Matches No. of tries Draw the scatter plot to represet the above data usig the DIAGRAM SHEET. () 4. Which of the followig fuctios has a graph which will be the best fit for the scatter plot: epoetial, quadratic or liear? () 4.3 Will the team score more tha 5 tries or less tha 5 tries i the 8th match? Justif our aswer. () [4]

5 (SEPTEMBER 0) MATHEMATICS P 5 QUESTION 5 I the figure, C( ; 7), A( ; 4) ad B(s ; ) are vertices of ΔCAB. E is the -itercept of lie AE with equatio =. C(-4 ; 7) A( ; 4) O E B(s ; ) 5. Determie the legth of AC. () 5. Determie the values of s ad t if M( 3 ; t) is the midpoit of BC. (4) 5.3 Prove that ΔCAB is a right agled triagle. (4) 5.4 Determie the equatio of a lie passig through C ad parallel to AB. (3) 5.5 Calculate the size of C. (5) 5.6 Determie p if CA is eteded to D(p ; ) such that C, A ad D are colliear. (3) []

6 6 MATHEMATICS P (SEPTEMBER 0) QUESTION 6 6. The diagram below shows two circles touchig at poit E( ; ). The smaller circle has its cetre at the origi ad a bigger circle has cetre D(a ; ). The legth of the radius of the bigger circle is twice the legth of the radius of the smaller circle. O E D 6.. Calculate the legth of the radius of the smaller circle. () 6.. Determie the value of a if a > 0. (4) 6..3 Determie the equatio of the bigger circle. (3) 6..4 Determie the equatio of a taget to both circles at E. (4) 6. The legth of the diameter of the circle k = 0 is 4. Determie: 6.. the co-ordiates of the cetre of the circle. (4) 6..3 the value of k. (3) [0]

7 (SEPTEMBER 0) MATHEMATICS P 7 QUESTION 7 Polgo MATHS has udergoe two trasformatios to obtai MATHS is first trasformed to M A T H S. M A T H S is the trasformed to M A T H S. M A T H S S // H // T // 3 M // A// S M M - S / H -3-4 H / -5 T A -6-7 A / T / Describe, i words, the trasformatio of MATHS to M A T H S. () 7. Write dow the rule of trasformig M A T H S to M A T H S. () 7.3 Write dow a sigle rule that trasforms MATHS to M A T H S. () 7.4 M A T H S is elarged b a scale factor of to M A T H S. Sketch polgo M A T H S usig DIAGRAM SHEET 3. (3) 7.5 Hece or otherwise determie a sigle rule that trasforms MATHS to M A T H S. () 7.6 Determie the ratio: area of MATHS: area of M A T H S. () 7.7 If MATHS is traslated to LUCID usig the rule ( ; ) ( 4 ; + 3), write dow the coordiates of L. () [5]

8 8 MATHEMATICS P (SEPTEMBER 0) QUESTION 8 T / is the image of T( ; ) after rotatig T i a ati-clockwise directio about the origi through a agle of. 8. Determie the value of. (6) 8. T( 3; ) is rotated about the origi through a agle of ( + ) i a aticlockwise directio to S(3 ; ). Write dow the value of. () [8] QUESTION 9 9. Give: 7cos β + 5 = 0 ad ta β > 0. Use a suitable diagram to determie: 9.. ta β (3) 9.. si(450 + β) () 9..3 si β () 9. Determie the geeral solutio of: (9) [6] QUESTION 0 0. Simplif without usig a calculator: 0. Cosider the idetit: 0.. Prove the idetit. () (7) 0.. Hece, or otherwise, determie the maimum value of (4) 0.3 Prove that: si cos si cos cos si (4) [7]

9 (SEPTEMBER 0) MATHEMATICS P 9 QUESTION Give: f ( ) ta ad g ( ) si. Write dow the equatios of the asmptotes of f for [ 90 ;80 ]. (). Sketch the graphs of f ad g o the same set of aes provided o DIAGRAM SHEET 4, for [ 90 ;80 ]. (7).3 Use our graphs to write dow the values of for which g() f() =. ().4 Determie the value of f(45 ) g(30 ). ().5 If h() = f( + m), write dow two possible values of m such that oe of the asmptotes of h is the lie = 30 for [ 90 ;80 ]. ().6 Write dow the period of f(). () [6] QUESTION The diagram below shows the side elevatio of a house. The roof of the house is a scalee triagle with P Q =. QT is a ladder such that UQT is a straight lie. The agle of elevatio Q R =. PQ = t ad QR = t. U P Q S R T. Prove that si U Q = si(α + θ) (). Prove that UT = t si( ) t si si (5).3 Determie the legth of UQ ad hece the area of ΔUPQ if t = 3m, = 4 ad = 83. (4) [] TOTAL: 50

10 0 MATHEMATICS P (SEPTEMBER 0) INFORMATION SHEET: MATHEMATICS b b 4ac a A P( i) A P( i) A P( i) A P( i) i i i ( ) T a ( ) d S a ( ) d T ar S a r r ; r S a r ; r F f '( ) i [ ( i) ] P i i lim h 0 f ( h) h f ( ) d ) ( ) M ( ; m c m ) ( m m ta area a I ABC: ABC a si A b r b si B ab. si C c si C a b c bc. cos A si si.cos cos.si si si.cos cos. si cos cos.cos si.si cos cos.cos si. si cos si cos si si si.cos cos ( ; ) ( cos si ; cos si ( ; ) ( cos si ; cos si ) ) f i ( A) P( A) P(A or B) = P(A) + P(B) P(A ad B) S i

11 (SEPTEMBER 0) MATHEMATICS P NAME: : SURNAME: DIAGRAM SHEET QUESTION. AGES FREQUENCY CUMULATIVE FREQUENCY QUESTION. ad

12 MATHEMATICS P (SEPTEMBER 0) NAME: : SURNAME: DIAGRAM SHEET QUESTION N u m b e r o f T r i e s MATCH NUMBER N U M B E R O F T R I E S

13 (SEPTEMBER 0) MATHEMATICS P 3 NAME: : SURNAME: DIAGRAM SHEET 3 QUESTION S // H // T // 3 M // A// S M M - S / H -3-4 H / -5 T A -6-7 A / T / -8-9

14 4 MATHEMATICS P (SEPTEMBER 0) NAME: : SURNAME: DIAGRAM SHEET 4 QUESTION

GRADE 11 NOVEMBER 2012 MATHEMATICS P2

GRADE 11 NOVEMBER 2012 MATHEMATICS P2 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