NATIONAL SENIOR CERTIFICATE GRADE 12
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1 NATIONAL SENI CERTIFICATE GRADE TECHNICAL MATHEMATICS P MARKING GUIDELINES EXEMPLAR 08 MARKS: 50 These markig guidelies cosist of pages.
2 Techical Mathematics/P DBE/08 QUESTION.. ( ) 0 0or 0.. ( ) Graphical represetatio b ( ) b 4ac a ( ) (5) 4(5)( ) 0,74 or 0, 54. m t 0 m t m t 5 ( t ) t 5 t t t 5 0 t t 4 0 t t 0 ( t )( t ) 0 t or t m = or m = m t 0 t m m t 9 m ( m ) 5 m m m 5 0 m m 4 0 m m 0 ( m )( m ) 0 m or m t = or t = 4 0 Stadard form Substitutio ito the quadratic formula 0, 74 0, 54 Makig m the subject Substitutio Simplificatio Factors Both values of t Both values of m Makig t the subject Substitutio Simplificatio Factors Both values of m Both values of t (4 (6)
3 Techical Mathematics/P DBE/ LL L L L L L L L L L L L 8 L L L L L L L L L L multiply with LCD commo factor divide by factor 0,8 0 cm cm Substitutio Simplificatio , 006 0,04 4,0 00, 0, 04 4, 0 [5] QUESTION.. p p.. 9 p 0 9 p p 9 p 0 p ( k ) 0 For equal roots, b 4ac 0 ( 4) 4()( k ) 0 6 4k 4 0 4k 0 k 5 For equal roots, 0 Substitutio Simplificatio Value of k () () [8]
4 Techical Mathematics/P 4 DBE/08 QUESTION Commo factor Simplificatio log 6 6 log 0, 00 log 6 6 log 000 log 6 6 log0 log6 6 log0 9 5 Dividig each term by the deomiator Simplificatio Additio Simplified surd Simplified surd Simplificatio log log0 6 6 log 6 6 log0 Simplificatio.. log( 8) log ( 8) log ( 8) Apply log property Chage from log form to ep. Form Simplificatio Value of
5 Techical Mathematics/P 5 DBE/08. z i z r y ta 0 Calculatig the modulus Simplificatio ta Argumet z cis0 z cos 0 isi 0.4 yi ( 5 i)( 7i) yi 6 i 5i yi 6 i 5( ) yi 6 i 5 yi 4i 4 ad y Correct polar form 6 i 5i i 4 y (5) [4]
6 Techical Mathematics/P 6 DBE/08 QUESTION itercepts, f ( ) ( )( ) 0 ( )( ) 0 or B( ; 0) 4.. f ( ) 4 6 b 4 ; ac b 4 4( 6) ; a 4a 4 D( ; 8) b 4 a f ( ) ( ) 4( ) 6 8 D( ; 8) D f ( ) ( ) 4( ) 6 8 D( ; 8) Fidig other factor Coordiates of B. Substitutio i formula Coordiates of D Substitutio i formula Substitutio to fid y Coordiates of D Usig -itercepts Substitutio to fid y Coordiates of D f ( ) 4 6 ' f ( ) f ( ) ( ) 4( ) 6 8 D( ; 8) 4.. g( ) k q 0 k 6 k 4 k 4..4 y 6 y 6 Usig the derivative Substitutio to fid y Coordiates of D Substitutig coordiates of Q Simplified equatio Correct value of k Correct critical values Correct otatio ()
7 Techical Mathematics/P 7 DBE/ ad y 0 y 4.. h ( ) 0 Substitutig coordiates of Q Value of 4.. r r () 4..4 Shape of h Asymptote -itercept Ay other poit o the graph of h Shape of g -itercepts of g y-itercept of g (7) y 0 y y [5]
8 Techical Mathematics/P 8 DBE/08 QUESTION 5 5. i eff m i m i eff 0,07 0,0796 aual effective iterest rate is 7,% 5. A P( i) 70 0( 0,08) 7 (0,9) 7 log 0, 9,7666 It will take approimately 4 miutes. 5.. Value of A after years: A P( i) 4 0,5% A R R 04705,40 Value of P after withdrawal: P R ,40 R0 000 R74 705,40 Amout received at the ed of the ivestmet period: Correct substitutio Simplificatio Effective rate as % Correct formula Correct substitutio Simplified power form Usig logarithms Nearest miute Correct formula Correct substitutio R04705,40 P R74 705,40 (5) 0,5% A R74705, 40 4 A R 4 947, 5 4 Correct substitutio Fial amout (6) [4]
9 Techical Mathematics/P 9 DBE/08 QUESTION 6 6. f ( ) Average gradiet f f [() 5 ] [( ) ( ) ] Correspodig y-value Correspodig y-value Substitutio i formula Simplificatio 6. f ( ) 4 / f ( h) f ( ) f ( ) lim h 0 h [4 ( h)] (4 ) lim h 0 h lim 4h4 h0 h h lim h 0 h lim( ) 6. h 0 y y 4 dy 6 d 6.4 g( ) g 6 The poit of cotact is (; 6) / g ( ) / mta g 5 y m c y y m( ) 6 5 c y ( 6) 5( ) c 4 y y 5 4 Defiitio Substitutio i the defiitio Simplificatio (removig brackets) Simplificatio ( divisio) Simplificatio 4 6 value of y mta 5 Correct substitutio Value of c (simplificatio) Equatio (ay form) (5) (5) [8]
10 Techical Mathematics/P 0 DBE/08 QUESTION 7 7. f ( ) 7 4 f () () () 7() 4 f ( ) 0 is a factor of f 7. -itercepts: f ( ) ( )( 4) 0 ( )( )( 4) 0 or 4 7. f ( ) f f / ( ) / ( ) ( 7)( ) 0 7 or (, ; 8,5) ad ( ;0 ) Substitutio 0 ( 4) (quadratic ) ( )( )( 4) (liear) -itercepts Derivative / f ( ) 0 Factorisatio Both values of Coordiates of the turigs (5) Shape Itercepts with -ais y-itercept Turig poits [4]
11 Techical Mathematics/P DBE/08 QUESTION After hrs D 4 0,5 0, 5 m 4m 8.. D 4 0,5t 0, 5t / D ( t) t 0,75t At :00 ( hours later): / D 0,75,75m.h 8.. P v 0v Neither profit or loss at P 0 v 0v 0 v ( v 0) 0 v 0 or v 0 v 0 km.h 8.. P v 0v dp dv 6v 0 0 v 5km.h 8.. P ma (i R000) (5) 0(5) 75 R Substitutig Simplificatio Derivative Substitutio of Simplified rate P 0 Factors Correct value of v Derivative Equatig to 0 Value of v Substitutio Profit i R 000 []
12 Techical Mathematics/P DBE/08 QUESTION d d 7 d d 4 7l C 9. h( ) 6 0 ( 6) d 0 (0) (0) uits square ( ) ( ) l C ; Substitutig 0 Substitutig Simplificatio (5) [9] TOTAL: 50
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