NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 11/GRAAD 11

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1 NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE /GRAAD MATHEMATICS P/WISKUNDE V NOVEMBER 0 MEMORANDUM MARKS/PUNTE: 50 This memorandum consists of pages. Hierdie memorandum bestaan uit bladsye.

2 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum NOTE: If a candidate answered a question TWICE, mark the FIRST attempt ONLY. If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out question. Consistent accuracy applies in ALL aspects of the memorandum. LET WEL: As 'n kandidaat 'n vraag TWEE keer beantwoord het, merk SLEGS die EERSTE poging. As 'n kandidaat 'n antwoord deurgehaal het en nie oorgedoen het nie, merk die deurgehaalde antwoord. Volgehoue akkuraatheid (werk met die fout) moet op ALLE aspekte van die memorandum toegepas word. QUESTION/VRAAG ( + )( ) 0 or ( ) ± ( ) ( )( ) () standard form factors s substitution into correct formula.. ± 0, or, + < 0 ( + )( ) < OR simplification s standard form factors method < < OR ( ; ) ( 5 ) (accept 5 or 5 ) ()

3 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum.. ( + ) simplification.. y + y + y 0 ( + ) 0 OR ( + ) + ( + ) 0( + ) + + y + y y + y or y 5 or y 0 ( + ) ( )( + ) 0 y + y 0( + ) ( y ) y + y 0( y + ) y y + y y 0 0 0y y y 6y ( y 5)( y ) 0 y 5 or y or substitution simplification standard form factors -values y-values substitution simplification standard form factors -values y-values (6) (6) [5]

4 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG ( + 5)( + ) 5 or Answer : only.. Shift is one unit RIGHT/Skuif is een eenheid na REGS + square both sides standard form factors 5 Shift is one unit RIGHT +.. f () Undefined if: < (5) () () () () []

5 Mathematics P/Wiskunde V 5 DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG. Perimeter is 60 cm. Hypotenuse is 5 cm. Omtrek is 60 cm. Skuinssy is 5 cm. Let the third side of the triangle be y: Laat die derde sy van die driehoek y wees: y 60 y 5. By Pythagoras: + y r + (5 ) ( 5)( 0) 0 5 or 0 Other sides have lengths of 5 and 0. Ander sye het lengtes van 5 en 0. QUESTION/VRAAG y 60 Pythagoras Subs 5 Standard form factors () (5) [6]. A P( + i). + i 0, R 09,55 i eff eff n 5 0,5 + 0,556 5,56% subs into correct formula 0,5 i n 0 formula substitution into correct formula () OR 09, A P n ( + i) ( + i) 09, ( + i),060 + i 5 i 0,556 5,56% 5 formula 09, i ( ) 5 () [7]

6 Mathematics P/Wiskunde V 6 DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG 5 n 5. A P( i) 000( 0,5) R8,0 n 5. A P( + i) 000( + 0,066) R 660, Value of fund needed R 660, R 8,0 Waarde van die fonds benodig 0,07 05,8 P + R0 5,8 P R 6,69 60 subs into correct formula () subs into correct formula () method (subtraction) n 60 0,07 i substitution into correct formula (6) [0]

7 Mathematics P/Wiskunde V 7 DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG 6 Pattern number Number of sticks () If the new sequence terms are given by a a + b 5 a + b + c Hence: a + b 5 b + + c c 0 T n + n n OR T n an + bn + c substitutions a b c 0 If the new sequence terms are given by a a By inspection, c 0 T n n + bn Substitute T () + b() b T n + n n T n an + bn + c a c 0 substitution b

8 Mathematics P/Wiskunde V 8 DBE/November 0 CAPS Grade /KABV Graad Memorandum T 6 9 ( 6) + ( 6) n + n < 6 n + n < 5 substitution setting up inequality () n + n 5 < 0 ( n + 8)( n 9) < 0 standard form factors method 8 < n < 9 n 8 (5) []

9 Mathematics P/Wiskunde V 9 DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG 7 Given the sequence: y 6 n T n n + ; ; ; 5 ; y numerator denominator () () [] QUESTION/VRAAG 8 Given: ; ; 5 ; 6 ; 9 ; 8 ; ; 5 ; 8. 7 ; 6 7 NOTE: If the answers are in the 6 incorrect order: / marks LET WEL: As die antwoorde in die verkeerde volgorde is: / punte () 8. st term of the sequence is LINEAR. It will be the 6 th linear term. ste term van die ry is LINEÊR. Dit sal die 6 de lineêre term wees. T ( 6) 6 OR ; ; 5 ; 6 ; 9 ; 8 ; ; 5 ; 7 ; 6 ; ; 86 ; 5 ; 58 ; 9 ; 7 ; ; ; 7 ; 9 66 ; ; ; 5 ; 5 9 ; 9 ; ; 5 ; ; 57 ; ; 6 The st term of the sequence is 6. n 6 n correct epansion () () [5]

10 Mathematics P/Wiskunde V 0 DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG 9 9. R () 9. f ( ) 0 ( )( + ) 0 ( )( + ) 0 or or AB AB () 9. C(0; ) 0 Average gradient 0 ( ) C(0; ) correct formula () 9. TP : ( ) b () a y y H( ; ) () 9.5 mline m m g g Point :( ; 0) subs ( ; 0) formula y (0) ( + ) y y OR [0 ; ] 0 < () ()

11 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum 9.7 DE 5 7,5 DE 5 7, ( )( ) standard form factors or Answer: only 9.8 k< k< (5) () [] QUESTION/VRAAG 0 + y Given: f ( ) y + ( 0 ; ) ;0 0. ( ) y 0 y 0 shape -intercept y-intercept asymptote () () ()

12 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum 0.5 y + + () [] QUESTION/VRAAG. p 5 q. h ( ) QUESTION/VRAAG p 5 q 6 5 () () []. f ( ) a + b + c m - 5 and m + are roots of Ma valueat m 5 + m + m m f ( ) 0 m 5 + m + (). For m the roots are : 5 and + 6 f 5 () y a 5 a 5 5a a y y ( y ( + )( 6) ( + )( 6) ( + )( 6) ) + + roots: and 6 y a( + )( 6) subs f () 5 a y + + (5) [8]

13 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG Given: HIV POSITIVE HIV NEGATIVE TOTAL Male 06 b Female a d c TOTAL 9 e a 86 b 58 c d 6 e 768. Let M be the event 'student is male'. Laat M die gebeurtenis 'student is manlik' wees. Let H be the event 'student is HIV positive'. Laat H die gebeurtenis 'student is MIV-positief' wees P( M ) P( H ) , 06 P( M and H ) 960 0, Since P ( M ) P( H ) P( M and H ), the events M and H are independent, i.e. HIV status is independent of gender. Aangesien P( M ) P( H ) P( M en H ), is die gebeurtenisse M en H onafhanklik, d.i. MIV-status is onafhanklik van geslag. a 86 b 58 c d 6 e P ( M ) or P ( H ) P ( M ) P( H ) 0, P ( M and H ) 0, conclusion () (5) [0]

14 Mathematics P/Wiskunde V DBE/November 0 CAPS Grade /KABV Graad Memorandum QUESTION/VRAAG. Let H be the event 'customers said they were happy'. Let A be the event 'customers said they would shop at the store again'. Laat H die gebeurtenis 'klante sê hulle is gelukkig' wees. Laat A die gebeurtenis 'klante sê hulle sal weer by die winkel koop' wees. 0,7 H 0,95 0,05 A not A P(H and A) 0,665 P(H and not A) 0,05 level one of tree second level first tier second level, second tier outcomes given probabilities given on tree (5) 0, not H 0,6 A P(not H and A) 0,078 0,7 not A P(not H and not A) 0,. P(A) P(H and A) + P(not H and A) 0, ,078 0,7 P(H and A) + P(not H and A) () [7] QUESTION/VRAAG 5 P(A and B) P(A) P(B) 9 7 P(A or B) P(A) + P(B) P(A and B) ,5% P(A) P(B) P(A or B) P(A) + P(B) P(A and B) substitution [] TOTAL/TOTAAL: 50