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1 Downloaded from Downloaded from Downloaded from Downloaded from Downloaded from NATIONAL. SENIOR CERTIFICATE/. NASIONALE. SENIOR SERTIFIKAAT. GRADE/GRAAD 11. MATHEMATICS P1/WISKUNDE V1. NOVEMBER 2019. MARKING GUIDELINES/NASIENRIGLYNE. MARKS/PUNTE: 150. These marking guidelines consist of 17 Hierdie nasienriglyne bestaan uit 17 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics/P1/Wiskunde V1 2 DBE/November 2019. CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne NOTE: If a candidate answered a question TWICE, mark only the FIRST attempt. If a candidate crossed out an answer and did not redo it, mark the crossed-out answer.

2 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. 2 x ( x 3) = 0. 2 x = 0 or/of x = 3 x = 0. x= 3. x=0. (2). 2. 3x 2 x = 4. standard form/standaardvorm 3x 2 2 x 4 = 0.

3 B b 2 4ac x=. 2a substitution into correct formula/. ( 2 ) ( 2)2 4(3)( 4) vervanging in korrekte formule =. 2(3). x =1,54 or x = 0,87. answer/antw. answer/antw. (4). ( x 1)(4 x) 0. critical values/kritieke waardes 1 4. 1 x 4. 1 x 4 (3). 5 x = x +1. squaring both sides/. 5 x = ( x +1). 2. kwadreer beide kante 5 x = x 2 + 2 x +1. standard form/standaardvorm x 2 + 3x 4 = 0 factors or using formula/. (x + 4)(x 1)= 0 faktore of gebruik formule x 4 or x =1 both solutions to/. beide oplossings x rejecting/verwerp x = 4. (5). Copyright reserved/Kopiereg voorbehou Downloaded from Mathematics/P1/Wiskunde V1 3 DBE/November 2019.

4 CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne x+4 = 2y and y 2 xy + 21 = 0. x= 2y 4 x= 2y 4. y 2 ( 2 y 4) y + 21 = 0 substitution /verv. y 2 2 y 2 + 4 y + 21 = 0. y 2 + 4 y + 21 = 0 std form/stand. vorm 2. y 4 y 21 = 0. ( y 7 )( y + 3) = 0 factors or using formula/. faktore of gebruik formule y = 7 or y = 3. y-values/wrdes x = 2(7 ) 4 or x = 2 ( 3) 4. x = 10 or x = 10 x-values/wrdes (6). 2(x 3) + 2 = 0. 2. ( x 3) = 1. 2. (x 3) 2. = 1. conclusion/gevolgtrekking (2). roots are non - real/wortels is niere l g ( x) =. 2 x 2 px + 3. b ( p ) p x= p x= = = . 2a 2 ( 2 ) 4 4. 2. p p . y= 2 p + 3. 4 4 . 2. p p 1.

5 2 . 2. p p 1 p +3 =3. 2 p + 3 =3 4 4 8. 4 4 8. p2 2 p2 1 simplification/vereenvoudiging + =. 8 8 8. p2 = 1 p = 1. p = 1 OR/OF. 4ac b 2 4ac b 2. max value/maks waarde = max value =. 4a 4a 4( 2)(3) p 2 25 4( 2 )(3) p 2. 25. = =. 4( 2 ) 8 4( 2 ) 8. 24 p 2 25. =. 8 8. 2. simplification 192 8 p = 200. 8p2 = 8 p = 1. p = 1 (4). [26]. Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Mathematics/P1/Wiskunde V1 4 DBE/November 2019. CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2. 32 x + 2 x 3. 27 x 2 x 4. 32 x + x 2 x 3 prime bases/priembasis = base/basis 3. 33 x 2 x 4.

6 Adding and subtracting = 32 x +1+ 2 x 3 3 x + 3 x . 5 2 x 3 2 x + 4 exponents/optel en aftrek van = eksponente = 15 answer/antw. (4). 1 . x = 32. 2 . x 1 5. =2. 2.. same base/dieselfde basis 2 x = 25. x=5 equating indices/. x = 5 gelykstelling van eksponente answer/antw. OR/OF. x OR/OF. 1 . = 32. 2 . x 1 5. =2. 2. same base/dieselfde basis x 5. 1 1 . = simplification/vereenv 2 2 . answer/antw. x = 5 (3). 1. 3 =4. x2. 2 exp form/eksp. vorm x3 = 22. 3. x= ( ). 2 2 2. x = (2 2 ) 2. 3. x = 2 3. 1 answer/antw. x= (3). 8. Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Downloaded from Mathematics/P1/Wiskunde V1 5 DBE/November 2019.

7 CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne 12. 2x = 4. 2x (2 ) 12 = x 2 x mult by LCD/KGN. (2 ) + 12 = 0. x 2 x ( ) 2. 2 x + x 12 = 0. (2 + 6)(2 2) = 0. x x factors/faktore 2 x 6. 2 x 6 or 2x = 2 x =1. no solution/geen oplossing or/of x =1 (5). OR/OF OR/OF. Let 2 x = k 12. k = 4. k k 2 12 = 4k mult by LCD/KGN. k 2 + 4k 12 = 0 k 2 + 4k 12 = 0. (k 2)(k + 6) = 0 factors/faktore k = 2 or k = 6. 2 x = 2 or 2 x 6 2x 6. x =1 or no solution x =1. (5). 2 4. +. 2 +1 2. =. 2. 2. +. (. 4 2 +1 ) LCD/KGN. ( ) 2(. 2 2 +1 2 +1 ). =. ( 2) +4 2 + 2. 2 2. perfect square trinomial volkome vierkant drieterm 2+ 2 simplification denominator/.

8 Vereenvoudigingsnoemer =. ( 2 +2 ) 2. factors/faktore 2+ 2. = 2+ 2 answer/antwoord (5). [22]. Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Mathematics/P1/Wiskunde V1 6 DBE/November 2019. CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3. -5 0 5. 5 5. Tn = an + b 5n 10. = 5n 10. (2). T12 = 5(12 ) 10 substitution/verv. = 50 answer/antw. (2). 5n 10 = 130 substitution/verv. 5n = 140. n = 28 answer/antw. 28 term(T28 ). th (2). [6]. Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Downloaded from Mathematics/P1/Wiskunde V1 7 DBE/November 2019.

9 CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4. 13 27 45 67. 14 18 22. 4 4. It is a quadratic number pattern/ Dit is 'n kwadratiese getalpatrron quadratic/ kwadratiese Second difference is verskil is konstant. justification/. regverdiging (2). 2a = 4. a=2 a =2. 3(2) + b = 14. b=8 b =8. 2 + 8 + c = 13. c =3. c=3. 2. Tn = 2n 2 + 8n + 3 Tn = 2n + 8n + 3. (4). Tn = 2n 2 + 8n + 3. substitution/vervanging T100 = 2(100) + 8(100) + 3. 2. = 20803 answer/antwoord (2). 4n + 10 = 110 4n +10 = 110. 4n = 100. n = 25 n = 25. T25 = 2(25) + 8(25) + 3. 2. T25 =1453. = 1453. T26 = 2(26 ) + 8(26 ) + 3.

10 2. T26 = 1563. =1563. (5). Copyright reserved/Kopieregvoorbehou Please turn over/Blaai om asseblief Mathematics/P1/Wiskunde V1 8 DBE/November 2019. CAPS/KABV Grade/Graad 11 Marking Guidelines/Nasienriglyne The first and second differences are all even but the first term is argument Die eerste en tweede verskille is gelyk maar die eerste term is onewe. conclusion/gevolgtr Thus when adding an even to an odd number the answer will always be 'n ewe by 'n onewe getal gevoeg word, sal die antwoord altyd onewe wees. OR/OF. OR/OF. Tn = 2n 2 + 8n + 3. 2n 2 has an even coeficient thus it even 8n has an even coeficient thus it even argument 3 is an odd number conclusion/gevolgtr the values will always be odd OR/OF OR/OF.