NATIONAL SENIOR CERTIFICATE GRADE 11

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1 NATIONAL SENI CERTIFICATE GRADE MATHEMATICS P NOVEMBER MEMANDUM MARKS: 5 This memoradum cosists of pages. Copright reserved Please tur over

2 Mathematics/P DBE/November CAPS Grade Memoradum QUESTION or 7 () 5 stadard form b ± 5 ± b a 5 ± 5,7 or 5 ()( ) ac,7 correct substitutio ito correct formula 5, 7, 7 () ± 5 5,7 or 5,7 completig the square 5, 7, 7 ().. 5 ( ) (9) 8 8 isolatig squarig both sides simplif aswer ().. 7 ( )( ) CV's : ; factors method or ( ; ] [; ) otatio critical values otatio critical values () Copright reserved Please tur over

3 Mathematics/P DBE/November CAPS Grade Memoradum Copright reserved Please tur over. ( ) ( ) ( ) or ) ( () 6...() or ) )( ( substitutio of simplificatio stadard form factors both values both values (6) substitutio of simplificatio stadard form factors both values both values (6) []

4 Mathematics/P DBE/November CAPS Grade Memoradum QUESTION.. ( ). 8 ( ).. (8). ( ) 6 [( )] 6 6 ( ) 6 ( ) ( ) commo factor aswer () commo factor simplificatio aswer () applig ep. law simplifig aswer () squarig applig ep. law simplificatio aswer () Copright reserved Please tur over

5 Mathematics/P 5 DBE/November CAPS Grade Memoradum ` 8 applig surd law applig surd law simplifig aswer () [] QUESTION AC.( ) 8 AC.( ) ( )( ) AC ( ) cm FD ( ) cm ED ( ) ED 6 cm statemet factors AC ( ) cm method aswer (6) [6] QUESTION Copright reserved a a () b 7 b () () c 7 c T a a T b() c b c T b() c 9 b c () () b c () T () () b 7 b () a c 7 c a avalue bvalue c value () a avalue bvalue c value () Please tur over

6 Mathematics/P 6 DBE/November CAPS Grade Memoradum. ( )( ) T T ( ) d. d ( )( ) 7 ( ) ( )( ) or ivalid formula substitutio simplificatio () equatio factors aswers for (choice) (). 7 ; ; 9 ; ; first differece7 9 secod differece F c F () c 7 c 5 F 5 first differeces Aswer ol: Full Marks c 5 (). F this differece will be betwee term 97 ad term 98 equatig 97 98() [] QUESTION 5 5. Patter White squares aswer() 5. W W 57 (57) 96 (57) W substitutio aswer () Copright reserved Please tur over

7 Mathematics/P 7 DBE/November CAPS Grade Memoradum 5. < 6 6 < 6 < ( 7)( 8) < settig up iequalit factors method 5. 6 P () () is eve for all Z Total squares used i the P ( ( ( ) ) is odd for all Z ) is odd for all Ζ Total squares used i the th th patter is alwas odd. patter is alwas odd. aswer () P rewritig P coclusio () P rewritig P coclusio () [] QUESTION () 8.it : 8 8 ( ) it ; ; 8 ( ; ) ().it : ( ; ) Copright reserved Please tur over

8 Mathematics/P 8 DBE/November CAPS Grade Memoradum 6. / O asmptotes itercepts with aes shape () 6. k k ( ) k substitute aswer () aswer () [] QUESTION 7 7. q 6 aswer () 7. 5 a. a a 6 substitute substitute simplifig aswer () 7. it : (;) it :. 6 ; Average Gradiet 9 or subst. ito gradiet formula aswer (5) aswer () [] Copright reserved Please tur over

9 Mathematics/P 9 DBE/November CAPS Grade Memoradum QUESTION 8 8. C( ; ) C( ; ) () 8. ( )( ) ( ) ( ) () TP : () () R: [ ; ) m ( ) 6 [ ; ) () substitutig ito gradiet formula m equatio () 8.5. or ( ; ] [; ) 8.5. < < or > > ; ( ;) (; ) 8.5. < < or > ( ;) (; ) () ( ; ] [ ; ) () critical values otatio () > () ( ;) ( ; ) () critical values otatio () ( ;) ( ; ) () Copright reserved Please tur over

10 Mathematics/P DBE/November CAPS Grade Memoradum 8.6 p ( ) ()( p) p for o - real roots < p < p < p < A(; ) p p > p < 8.7 PM ( 6) ( ) b a ( ) ( ) ( ) uit Ma. PM PM 6 ( ) ( ) ( ) [( ) ] ( ) Ma. PM uit p < p < () p > p < () subtractio quadratic epressio method maimum value () subtractio quadratic epressio method maimum value () [] QUESTION 9 9. A P( i) 9, ( i) 9, i Thus i, Rate of Depreciatio 8% substitutio makig i subject i value as decimal aswer () Copright reserved Please tur over

11 Mathematics/P DBE/November CAPS Grade Memoradum 9. i eff i m m,98,5... rate,5% formula substitutio ito formula,5% () 9. A P( i ) ( i ).75 8 R768,6 6,75 A ,65..,9,9 A 7689,65 R768, ,9 multiplicatio aswer () 6,75 A 6,9 aswer () 9.. Ivestmet : ed of third ear : A P( i),65 96,65 subst. ito correct formula R59,7 aswer () 9.. T T T5 T8,65,65 A A R878,6 differece 878,6 59,7 R68,6 96 6, ,65 6,65 6,65 R 878, 6 subtractig aswer (7) Copright reserved Please tur over

12 Mathematics/P DBE/November CAPS Grade Memoradum Ivestmet: ed of third ear : A P ( i),65 R6,88 Pricipal(ew) : R6,88 R, R6,88 Ivestmet: ed of fifth ear : A P ( i), R, Pricipal(ew) : R, R, R, Ivestmet: ed of eighth ear : A P ( i),65, R878,6 Tashil had a deficit of R68,6 6 subst. ito formula aswer subst. ito formula aswer subst. ito formula aswer coclusio(7) [] QUESTION. 5 customers aswer (). P(C ad Thus evets B ad C are ot mutuall eclusive P(C ad coclusio ().. P(V ol) 58 9 aswer ().. 9 aswer () P(C ad.. P( ot C) P(C) P(ot C) 8 59 formula substitutio aswer () umerator ad deomiator aswer () Copright reserved Please tur over

13 Mathematics/P DBE/November CAPS Grade Memoradum.. P(B or V) P( P(V) P(B ad V) QUESTION P(B or V) 5 ( A or P P( A) P( P( A,8,,5 P( A P( A, P( A) P(,,5, P( A P( A) P( Thus A ad B are idepedet evets () umerator ad deomiator aswer () [] substitutio value of P( A value of P ( A) P( coclusio () [] Copright reserved Please tur over

14 Mathematics/P DBE/November CAPS Grade Memoradum QUESTION. There are % 6% % % red marbles 8 red marbles % () R Y G R Y G R Y G R Y G Outcome R,R R,Y R,G Y,R Y,Y Y,G G,R G,Y first brach secod brach values o diagram (). P(G ad Y) P(G, Y) P(Y, G) multiplicatio rule additio aswer () [8] TOTAL: 5 Copright reserved

Basic Education MATHEMATICS P1 PREPARATORY EXAMINATION SEPTEMBER 2016 MEMORANDUM NATIONAL SENIOR CERTIFICATE GRADE 12

Basic Education MATHEMATICS P1 PREPARATORY EXAMINATION SEPTEMBER 2016 MEMORANDUM NATIONAL SENIOR CERTIFICATE GRADE 12 Basic Educatio KwaZulu-Natal Departmet of Educatio REPUBLIC OF SOUH AFRICA MAHEMAICS P PREPARAY EXAMINAION SEPEMBER 6 MEMANDUM NAIONAL SENI CERIFICAE GRADE MARKS: his memoradum cosists of pages. Mathematics