Mathematics Grade 10 Paper 1 National November 2019 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10 MATHEMATICS P1/WISKUNDE V1 NOVEMBER 2019 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 100 These marking guidelines consist of 11 pages./ Hierdie nasienriglyne bestaan uit 11 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 2 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne NOTE:  If a candidate answered a QUESTION/VRAAG TWICE, mark only the FIRST attempt.  If a candidate crossed out an answer and did not redo it, mark the crossed-out answer.  Consistent accuracy applies to ALL aspects of the marking guidelines.  Assuming values/answer in order to solve a problem is unacceptable. LET WEL:  As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na.  As 'n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde antwoord na.  Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing.  Dit is onaanvaarbaar om waardes/antwoorde te veronderstel om 'n probleem op te los. QUESTION/VRAAG 1 1.1.1 3y 2  y answer/antwoord (1)  y (3 y  1) 1.1.2 x 2  10 x  24  ( x  12)  ( x  12)( x  2)  ( x  2) (2) 1.1.3 9 x 2  y 2  10 y  25 grouping/groepering  9 x 2  ( y 2  10 y  25)  9 y 2  ( y  5) 2 factorising/faktorisering  (3 x  y  5)(3 x  y  5) answer/antwoord (3) 1.2.1  1  3  4   2    x  x  answer/antwoord (2) 10 3  8  2 x x 1.2.2 5x  5 5x 5( x  1)  factorising/faktorisering 5x x 1 answer/antwoord (2)  x OR/OF 5x 5  separation/skeiding 5x 5x 1 answer/antwoord  1 (2) x Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 3 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 1.2.3 3 x 1  3 x 27.3 1 x 3 x .3  3 x  separating bases/skei  27.3 1.3 x basisse 3 x (3  1) common factor/  gemeenskalike faktor 27 3 x. 3 4  answer/antwoord (3) 9 OR/OF 3 x 1  3 x 27.3 1 x 3 x .3  3 x  separating bases/skei  basiss 27.3 1.3 x 4.3 x  27 addition/optelling 3 x. 3 4  answer/antwoord (3) 9 [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 4 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1.1 2 x 2  10 x  0 common factor/ 2 x( x  5)  0 gemeenskaplike faktor x  0 or x  5 both values of/beide waardes van x (2) 2.1.2 px  kx  k  p x( p  k )  k  p common factor/ gemeenskaplike faktor kp x change of sign/verander kp teken x  1  answer/antwoord (3) 2.1.3 x 1 23  1 128  7 or/of 2 7 x 2 2  2 7 3 equating exponents/ x gelykstelling van  7 eksponente 3 answer/antwoord (3) x  21 2.2.1 x5  2 simplification/ 2 x  5  4 vereenvoudiging answer/antwoord (2) x  9 2.2.2 x number line/getallelyn –9 (1) 2.3 x( x  3)  y (3  x)  0 x( x  3)  y ( x  3)  0 change of sign/verander teken ( x  3)( x  y )  0 common factor/ x  3 or y  x  3 gemeenskaplike faktor x-value/-waarde y-value/-waarde (4) 2.4 Let the number of R50 notes be x/ Laat die getal R50-note x wees. Number of notes Total value of Getal note money/Totale warade van geld R10 x + 15 10(x+15) setting up R20 2x 20(2x) equation/vergelyking/ R50 x 50(x) opstel van vergelyking 10( x  15)  20(2 x)  50 x  10150 simplification/ 100 x  10000 vereenvoudiging x  100 x-value/-waarde answer/antwoord R10 Notes :100  15  115 R10 notes = 115 R 20 Notes : 2(100)  200 R20 notes = 200 R50 Notes :100  100 R50 notes = 100 (4) [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 5 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 3.1.1 5x  7 answer/antwoord (1) 3.1.2 Tn  mn  c Tn  ( x  2)n  q substitution/vervanging/ vervanging 4 x  5  xn  2n  q simplification/ 4 x  5  3x  6  q vereenvoudiging x 1  q answer/antwoord (3)  Tn  ( x  2)n  ( x  1) Tn  xn  2n  x  1 OR/OF For n  1: ( 1  1 )  ( 2( 1 )  1 ) investigating/onderso n  2: ( 2  1 )  ( 2( 2 )  1 ) ek n  3: ( 3  1 )  ( 2( 3 )  1 ) Tn  (n  1) x  (2n  1) answer/antwoord Tn  xn  2n  x  1 (3) 3.1.3 T13  95 95  13 x  2(13)  x  1 substitution/vervanging/ vervanging 95  13 x  26  x  1 14 x  70 x5 answer/antwoord (2) 3.1.4 Tn  5n  2n  5  1 Tn  7 n  4  7n  4  158 7n  4  158 7n  154 n  22  n  22  T21 is the first term less than 158./is die eerste term minder as 158  conclusion/gevolg- trekking (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 6 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 3.2.1 Height/ Hoogte  50  44 answer/antwoord (1)  2200 cm 3.2.2 Tn  0,1n  c T1  7,9 constant difference/ konstante verskil 7 ,9  0 ,1  c c  8  Tn Tn  0,1n  8 T45  0,1(45)  8 T45  3,5m answer/antwoord (3) OR/OF 7,9 ; 7,8 ; 7,7 ; .... 7,9  0,1  1  8 ............(1) 7,8  0,1  2  8 ...........(2) 7,7  0,1  3  8 ...........(3) Tn  0,1  n  8 equation/vergelykings Tn  0,1n  8 T45  0,1  45  8 substitution/vervanging answer/antwoord (3) T45  3,5m 3.2.3 1 Area of Trapezium / Oppervlakte van trapesium  ( AB  CD) Hformula/formule 2 1  (3,5  7,9)22 substitution/vervanging 2  125,4 m 2 answer/antwoord (3) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 7 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 4.1.1 25 Deposit   R 7950  R1987,50 deposit/deposito 100 Balance  R7950  R1987,50 balance/balans (2)  R5962,50 OR/OF 75 75% Balance   R 7950  R5962,50 100  answer/antwoord ¶(2) 4.1.2 A  P(1  in )  15  A  R5962,501   2 substitution/vervanging  100  A  R7751,25 R7751,25 dividing by/deel deur Monthly payment   R70,75 24 24 adding insurance/voeg  R393,72 versekering by answer/antwoord (4) 4.2.1 £55  R23,43 answer/antwoord (1)  R1288,65 4.2.2 5 500 5 500 Cost of a car/ Koste van ' n motor   14,58  14,58 23,43 23,43 £3 422,54  £3 422,54  Car is more expensive in England /Motor is duurder conclusion/gevolg- in Engeland trekking OR/OF 23,43 23,43 Cost of a car/ Koste van motor   3500   3500 14,58 14,58  $5624,49  $5624,49  Car is more expensive in England /Motor is duurder conclusion/ in Engeland gevolgtrekking (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 8 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 5.1.1 q 1 answer/antwoord (1) 5.1.2 x  ; x  0  x  x0 (2) OR/OF x    ; 0  0 ;  answer/antwoord (2) 5.2.1 y  x 1 negative gradient/ negatiewe gradiënt the value of/die waarde van c (2) 5.2.2 x20 x  2  x  2 k 0 1  substitution (2 ; 0) 2 k2 k  2 2  f ( x)   1 equation/vergelyking x (4) 5.2.3 f ( x)  g ( x) 2 equating/vergelyking 1  x  2 x 2  x  x 2  2x standard form/ x x20 2 standaardvorm factorising/ ( x  2)( x  1)  0 faktorisering  x  2 or x  1 x-values/-waardes at A : x  1 ; y  3 answer/antwoord (5) A(1; 3) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 9 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1.1 y  4 answer/antwoord (1) 6.1.2 q  5 answer/antwoord (1) 6.1.3 (2 ; 0) answer/antwoord (1) 6.2.1 g ( x)  ax 2  5 (2 ; 0) : 0  a (2) 2  5 0  4a  5 5 value of a a 4 equation/vergelyking/ 5  g ( x)  x 2  5 waarde van 'n 4 vergelyking (2) 6.2.2 f ( x)  k x  4 (2 ; 0) : 0  k  2  4  substitution (2 ; 0) 1 0 2 4 k 4k  1 2 1 k2  4 1 value of/waarde van k k 2 x 1  f ( x)     4 equation/vergelyking 2 (3) 6.3 1 0 y   4 substitution/vervanging 2 y  3 answer/antwoord (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 10 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne 6.4 f: asymptotes of/asimptote van f y-intercept of/y-afsnitte van f  shape of/vorm van f g: x-intercepts/x-afsnitte turning point of/draaipunt van g shape of/vorm van g (6) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P1/Wiskunde/V1 11 DBE/November 2019 CAPS/KABV – Grade/Graad 10 – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 7.1.1 P( A or B)  P( A)  P( B)  P( A and B) 0,74  0,30  0,65  P( A and B ) substitution/vervanging P ( A and B )  0,21 answer/antwoord (2) 7.1.2 A B 0,09 0,21 0,09 0,21 0,44 0,44 0,26 0,26 (4) 7.1.3 No ; P( A and B )  0 . No/Nee OR/OF reason/rede (2) No. There is an intesection 7.2.1 n( S )  12 n( square no.)  3 (i.e 1 ; 4 ; 9) 3 answer/antwoord P( square no.)  (1) 12 1  4 7.2.2 1 1 P(sum of the 2 numbers  2)   144 144 1 P(sum of the 2 numbers greater th an 2)  1  Complementary rule/ 144 Komplementêre reël 143  144  0,99 answer/antwoord (3) [12] TOTAL/TOTAAL: [100] Copyright reserved/Kopiereg voorbehou