NATIONAL SENIOR CERTIFICATE GRADE 11

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1 NATIONAL SENI CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 0 MEMANDUM MARKS: 50 This memoradum cosists of pages.

2 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum QUESTION.. ( )( + 5) 0 5 s ( 5 ) 5 5 ( ) ± ( ) ( )( ) ( ) ± 8 ±. ± ± ( ± ).. ( )( + ).. substitutio ito correct formula s 5 (accept 5 or 5 ) ( ) ( ).. ( )( ) ( )( ) () () () () () () [5]

3 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum QUESTION.. ( + )( ) 6 + < < 0 ( + )( ) < 0 < + stadard form factors or.. < < + 8 < 0 < < Sum of itegers ( ) + ( ) + ( ) + ( 0) + ( ) 5 < < < <,,, 0, () () ( + ) factorise umerator. simplificatio of umerator 7 to.....t t or. () ()

4 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum. y 8 ad y y y y ( 9)( ) or ( 9) or ( ) 6 or y y stadard form factors -values y-values ( ; y) ( 9 ; 6) or ( ; ) (7) [9] QUESTION p 0 8p 0 8p p 8p < 0 8p < 0 p > ad ad Hece ad () () () ( + )( ) 0 or Sice 5, oly square both sides stadard form factors s selectio of.. (5) () []

5 Mathematics/PI 5 DBE/0 NSC Grade Eemplar Memoradum QUESTION. A P( i) 5000[ ( 0,7 )( 5) ].. R 750 8% % per quarter.. ( ). A P + i After year, ( ) Hece + i eff ( + 0.0) ( + 0.0) A P + i ad ( ) eff A P substitutio ( ) i + 0,0 ieff 0,08 The effective iterest rate is 8,% p.a. 0,09 0,075 0, 09 A R 0 755,08 0, , 07 + eff () () () (5) [0]

6 Mathematics/PI 6 DBE/0 NSC Grade Eemplar Memoradum QUESTION 5 5. R Simple iterest 5. A P( + i) 5( + 6i) + 6i 5 i ,778 7,78% A P + i w 5 + 0,778 7 A P + i 5. ( ) ( ) i i ( ) ( + i) 7 5 0, ,99% substitutio of (6 ; ) ito correct formula w 7 substitutes ( ; w) 7 5 () () () () [8]

7 Mathematics/PI 7 DBE/0 NSC Grade Eemplar Memoradum QUESTION Multiply 8 by multiply T a () () T () T 6.. Cotiuig the patter: ; ; ; ; ; ; ; ; Hece 0 5 ; 0 epad sequece 0 () () T < 0 6 < 8 0,5 < Hece T is the first term to be egative < 0 0,5 < () () () ()

8 Mathematics/PI 8 DBE/0 NSC Grade Eemplar Memoradum 6.. ( ) ( 5) + 68( 5) a 8 a a + b 56 + b 56 b 68 T 5 T c a substitutios b 68 substitutio c 76 (5) T 5 (give) T T + b c b 00 6b 68 b c 76 ( 5) + b( 5) ( 6) + b( 6) () () () () T 6 00 a substitutios b 68 c 76 (5) T 5 (give) T 56 T + b c b 56 9 b 68 b c 76 ( 5) + b( 5) ( ) + b( ) () () () () T 56 a substitutios b 68 c 76 (5) [7]

9 Mathematics/PI 9 DBE/0 NSC Grade Eemplar Memoradum QUESTION 7 T 0 T 0 y + T 0 + AND T + y 0 y AND y + y itroduce variables T y y + Hece [6] a a 6 T 6 + b a 6 ad + b b b 0 b 7 b 6 : + b b 0 b c 8 c 8 T T 6 6() ( ) + 8 [6]

10 Mathematics/PI 0 DBE/0 NSC Grade Eemplar Memoradum QUESTION 8 8. y 8. R ; ( ; ) ( ; ) R ( ; ) ( ; ) d ta 76 d ta 76 d d 6 ( ) + e e 6 e 6 g( ) 6 6 equatig 5 simplificatio ( ) 5( ) stadard form 0 ( )( ) factors -values or y 6 or y ( ) 6 y-values y 7 or y Poits of itersectio are A ( ; ) ad C ; 7 < or [; ) ; < 8.6 y ( ) y y Substitute ( ; ) c y substitute ( ; ) () () () () (6) () () () [9]

11 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum QUESTION 9 9. (; ) f: shape -it y-it turig poit g: shape -it y-it asymptote 0 ( )( + ) 0 or y y 0 0 ( ) ( ) + ( ) + y (9) 9. f (0) f ( ) correct formula Average gradiet 0 ( ) f ( ) ( ) 5 () 9. 0 or < < 0 > () 9. Give: f ( ) 0 has oe solutio/equal roots i.e. f ( ) c has oe solutio c f ( ) c f ( ) c () h is f traslated uits dow y-itercept of h will the be at c 9.5 (0 ; ) (0 ; ) 9.6 k( ) () () () [0]

12 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum QUESTION 0 Rage of f ( ;7] y-part of turig poit [Ma value of ( ) a <0 ad shape f ] is 7 b < 0 b egative ais of symmetry o left of y-ais roots real, uequal & opposite sigs -its o opposite sides of y-ais y 7 shape turig poit at y 7 ais of symmetry o left of y-ais roots are o opposite sides [] QUESTION. No, W ad T are ot mutually eclusive Because P(W ad T) 0 No, W ad T are ot mutually eclusive Because P(W or T) 0,6 0,75 P(W) + P(T). P(W ad T) 0, (give) ot mutually eclusive P(W ad T) 0 () ot mutually eclusive P(W or T) P(W) + P(T) () ad P(W) P(T) 0, 0,5 0, P(W ad T) P(W) P(T) Therefore yes, W ad T are idepedet evets P(W) P(T) 0, P(W ad T) P(W) P(T) coclusio (yes) () [5]

13 Mathematics/PI DBE/0 NSC Grade Eemplar Memoradum QUESTION.. a 5 b c 8 d e 6 a 5 b c 8 d e a + b 6 (5) () () (). 0,5 Mathematics P(G ad M) 0,7 girl 0,6 0,55 Mathematical Literacy P(G ad ML) 0, 0, boy 0,5 0,65 Mathematics Mathematical Literacy P(B ad M) 0, P(B ad ML) 0,6 0, 0,5 0,5 P(Mathematics) P(G ad M) + P(B ad M) ( 0,6)( 0,5) + ( 0,)( 0,5) 0,7 + 0, 0, P(G ad M) 0,7 P(B ad M) 0, (6) [] TOTAL: 50

NATIONAL SENIOR CERTIFICATE GRADE 11

NATIONAL SENIOR CERTIFICATE GRADE 11 NATIONAL SENI CERTIFICATE GRADE MATHEMATICS P NOVEMBER MEMANDUM MARKS: 5 This memoradum cosists of pages. Copright reserved Please tur over Mathematics/P DBE/November CAPS Grade Memoradum QUESTION....