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

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1 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.

2 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) QUESION.. ( ) or AA Aswers () A equatio i std. form ( ) ±, or.. ( )( 9) / a ( ) () 7+ 9 ()( 7), + 9 or 9 CA substitutio Pealise roudig off CACA aswers A isolatig M squarig both sides CA stadard form CA factors CA both aswers CA rejectig (6).. + or No solutio (+ ) < 9 A stadard form CA factors CA CA CA aswer CA rejectig (6) > for all R + < < [Graphically] A > A + < A < for all R () A sketch of y < A sketch of y + A < () Please tur over

3 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) M for takig ( ) 99 as a commo 99 factor A ( ) A aswer. y () + y+ y () From() : y Subst. () + ( ) + ( ) + ito() 7 6 ( + )( 6) + or 7 y or y y () + y+ y () y+ From() : Subst. () ito() y+ y + 6y+ 9 + y y y y + 6y+ 9+ y + 6y + y 7 ( y+ 7)( y ) 7 y or or y+ + y + y y y + y + y+ y 6 A y as subject CA substitutio y CA std. form CA factors CA values CA y values A as subject CA substitutio CA std. form CA factors CA y values CA values + y () (6) (6) [] Please tur over

4 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) QUESION. a a a+ b b 6 a+ b+ c c 8 A a value CA b value CA c value 6+ 8 CA geeral term a a a+ b b 6 c A a value CA b value CA c value CA geeral term. + + ( ) ( )( ) + + d ( )( ) ( )( ) ( ) Betwee the 7 rd ad 7 th terms. d A formula A substitutig first ad secod differece values CA simplifyig CA geeral term A CA 888 CA( ЄN) 7 CA ( ЄN)coclusio [ ( ) 6( ) + 8] Betwee the 7 rd ad 7 th terms. 888 A 888 CA 896 CA ( ЄN) 7 CA ( ЄN)coclusio [8] Please tur over

5 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) QUESION.. 6 ; ; ; ; ; ;... 8 ; AA aswers ().. a adisa costat sequece.. S a 6; d ; S [ ( 6) + ( ) ] A () A for a, d ad values CA for substitutio ito formula CA. S S rs + a+ ar+ ar ar+ ar () () : ar + ar () () CA aswer A for equatio () A for equatio () rs S S S ( r ) a( r ) a( r ) ar r a A subtractio o LHS ad RHS A factorisig a( r ) if S r pealize mark [] QUESION.. a r a S r S S S [ ] [ () () ] A a ad r value CA substitutio of r ito formula CA aswer () M S S AA substitutio A aswer Please tur over

6 Mathematics P 6 September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) S a S S 8 8 d () + () a+ d + (6) A a value A secod term value CA d value CA aswer [7] QUESION..... A P( i) A R A P(+ i) (,) 7,,9 + R, [ ( + i) ] P i,9 +,,9,,9 +,86999 log,86999,9 log +,68 6,9 paymets 7,9 + A formula A correct substitutio CA aswer () A correct substitutio ito correct formula CA aswer () CA correct substitutio of P ito formula A CA as subject M usig logs CA( Є N) aswer () Please tur over

7 Mathematics P 7 September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN).. Balace o Loa after the th paymet,9 +,9, +,9 R668,9 R86, R8,6 M (A - F v ) formula A,9 CA, +,9 + CA,9 CA aswer () [ ( + i) ] P i,9 +,9 R8,6,68 A formula A subst.,9 CA subst CA subst, 68 CA aswer () [] QUESION 6 (For learers who did ot receive the errata ad used P(-;), should be marked accordigly) 6. p q A p value A q value () 6. a h ( ) + q. P(; ) is a poit o h + p a a CA subst. p, q ad poit P CA(egative) a value () 6. h( ) h() A substitutig CA(egative) aswer () ; 6. CACA aswer () Please tur over

8 Mathematics P 8 September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) 6. y ( + p) + q y ( ) CA substitutio of p ad q values ito equatio of lie of symmetry y + c CA aswer () y + c Poitof itersectio of + c c asymptotes ( ; ) CA substitutio of ( ; ) ito equatio of lie of symmetry CA aswer () [] QUESION 7 7. D( ; ) 7. ( + )( ) A(must be i coordiate form) aswer A CA factors or CACA(egative ad positive) A( ;) each value B(;) A( ;) B (; ) 7. a ad q CA(positive) a value A q value 7. b ( ) + b ( ) or A a () a () or 9 y /,/ + CA C(, ;,) CA substitutio CA miimum value () () () 7. (,; 9,) CA value CA y value () 7.6 CACA aswer () / / g ( ). h( ). CA product of derivatives ( ) CA(positive) aswer pealize mark for icorrect otatio Please tur over () []

9 Mathematics P 9 September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) QUESION 8 8. y log AA aswer () 8. y p O ( ; ) ( ; ) p - A Shape of p ad p - A y itercept of p A itercept of p - A poit o each graph 8. log 7 < 7 M settig up equatio CA 7 CACA for ed poits ad iequality ANSWER ONLY full marks [] QUESION 9 [Pealise oce for otatioal error i questios 9, ad ] 9. f ( ) f f ( ) lim 9.. h ( + h) lim h lim h h lim h lim h f( ) f ( ) ( + h) f( ) h h ( + h+ h ) ( + h+ h ) + h+ h h + 8 h + h A formula A substitutio ito correct formula CA simplifyig CA factors CA aswer () AA epoetial form CACA aswer Please tur over

10 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) 9.. y A squarig both sides y dy d 6 dy d A simplifyig CACA aswers AA derivative usig chai rule CACA aswers [] QUESION.. f ( ) ( ) 8 A y ( y value) ().. f ( ) A value of gradiet of taget () m f ( ) ( ) 6.. Equatio oftaget: - y m+ c 6( ) + c c 7 CA substitutio y 6 7 CA aswer ().. y 6( + ) y 6 8+ y 6 7 f ( ) f ( ) ( + )( ) or y or y A( ; ) B(; ) CA substitutio CA aswer A derivative ad equatig to () CA factors CA - values CA y - values Please tur over

11 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN).. PQ g( ) f( ) ( ) ( + PQ + ±,9 For,9 y (,9) ) + (,9), Maimum Legth of PQ,uits A epressio for PQ A P Q CA values CA y value for,9.. k or k k A k - CA aswers ().. f ( ) 6 > A 6 > A 6 > A aswer () + ( ) + () A midpoit formula CA > CA aswer () b a > () A formula A A aswer () [7] QUESION (Igore uits i the questio). V s ( t) t+ m/ s A aswer (). V s ( ) () + 6m/ s CA aswer (). V s ( t) t+ m/ s A s () ( t) m/ s CACA. / / A s () m/ s CA aswer (aswer oly mark) (). s( t) t + t A equatig s to t + t ( t+ )( t ) t s V s ( ) () + m/ s CA factors CA t CA aswer [9] Please tur over

12 Mathematics P September 6 Preparatory Eamiatio NSC-MEMANDUM(KZN) QUESION.. A aswer ()..(a) 7 7 A aswer () P(Male )..(b) P(Eatig Chocolate) P(Male eatigchocolate) P(Male) P(Eatigchocolate) 7 8 6,9, A aswer () A P(male eatig chocolate ) CA P(Male) P(eatig chocolate) value P(Male ad Eatig chocolate) P(Male) P(Eatig chocolate) Evets are ot idepedet CA coclusio () A () A A 6 6 () A 7.. Four digit codes divisible by :- A A Probability of a four digit code divisible by 6,,% 8 9 CA aswer () [] OAL MARKS: Please tur over

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NAIONAL SENI CERIFICAE GRADE MAHEMAICS P NOVEMBER 00 MEMANDUM MARKS: 50 his memoradum cosists of 7 pages. Mathematics/P DoE/November 00 QUESION.. x ( x 4) 5.... x 4x 5 0 ( x 5)( x + ) 0 x 5 or x 4x 0x