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.... 7 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 5 5 5 ± 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
Mathematics/P DBE/November CAPS Grade Memoradum Copright reserved Please tur over. ( ) ( ) ( ) or ) ( 5 5 6 6 6...() 6...() or ) )( ( 5 5 6 substitutio of simplificatio stadard form factors both values both values (6) substitutio of simplificatio stadard form factors both values both values (6) []
Mathematics/P DBE/November CAPS Grade Memoradum QUESTION.. ( ). 8 ( ).. (8). ( ) 6 [( )] 6 6 ( ) 6 ( ) ( ) 6 6 96 96 commo factor aswer () commo factor simplificatio aswer () applig ep. law simplifig aswer () squarig applig ep. law simplificatio aswer () Copright reserved Please tur over
Mathematics/P 5 DBE/November CAPS Grade Memoradum.. 7 8 7 8. 8 7. ` 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. 7 9 7 9 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
Mathematics/P 6 DBE/November CAPS Grade Memoradum. ( )( ) T T ( ) d. d ( )( ) 7 ( ).7. 7 7 7 8 ( )( ) 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 5 599 59 97 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
Mathematics/P 7 DBE/November CAPS Grade Memoradum 5. < 6 6 < 6 < ( 7)( 8) < - 8 7 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 6 6. 6. () 8.it : 8 8 ( ) it ; ; 8 ( ; ) ().it : ( ; ) Copright reserved Please tur over
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) 7.. 6 aswer () [] Copright reserved Please tur over
Mathematics/P 9 DBE/November CAPS Grade Memoradum QUESTION 8 8. C( ; ) C( ; ) () 8. ( )( ) ( ) ( ) () 8. 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
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,999... Rate of Depreciatio 8% substitutio makig i subject i value as decimal aswer () Copright reserved Please tur over
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 8 7689,65..,9,9 A 7689,65 R768,6 6 6 6 6.75 6,9 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 96,65 6,65 6,65 R 878, 6 subtractig aswer (7) Copright reserved Please tur over
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),65 6.88 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) 59 5 58 5 P(ot C) 8 59 formula substitutio aswer () umerator ad deomiator aswer () Copright reserved Please tur over
Mathematics/P DBE/November CAPS Grade Memoradum.. P(B or V) P( P(V) P(B ad V) 8 8 5 5 QUESTION 7 5 9 58 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 8 8 5 5 () umerator ad deomiator aswer () [] substitutio value of P( A value of P ( A) P( coclusio () [] Copright reserved Please tur over
Mathematics/P DBE/November CAPS Grade Memoradum QUESTION. There are % 6% % % red marbles 8 red marbles % (). 8 8 8 8 8 R Y G 8 8 7 8 8 7 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) 8 8 8 8 8 8 8 95 multiplicatio rule additio aswer () [8] TOTAL: 5 Copright reserved