SA EXAM PAPERS

1 SA EXAM PAPERS . _____. YOUR LEADING PAST YEAR EXAM PAPER. PORTAL. Visit SA Exam PAPERS SENIOR CERTIFICATE EXAMINATIONS/. SENIORSERTIFIKAAT-EKSAMEN. NATIONAL SENIOR CERTIFICATE EXAMINATIONS/. NASIONALE SENIORSERTIFIKAAT-EKSAMEN. MATHEMATICS P1/. WISKUNDE V1. MARKING GUIDELINES/NASIENRIGLYNE. 2021. MARKS: 150. PUNTE: 150. These marking guidelines consist of 13 pages. Hierdie nasienriglyne bestaan uit 13 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 2 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne NOTE: If a candidate answers a question TWICE, only mark the FIRST attempt. Consistent Accuracy applies in all aspects of the marking memorandum. LET WEL: Indien 'n kandidaat 'n vraag TWEE keer beantwoord, merk slegs die EERSTE poging.

2 Volgehoue akkuraatheid is DEURGAANS op ALLE aspekte van die memorandum van toepassing. QUESTION/VRAAG 1. x 2 x 20 0. x 5 x 4 0 factors x=5. x=5 or x = 4. x = 4 (3). 3x 2 x 6 0. 2. 2 2 2 4 3 6 substitution x . 2 3 . 1 19. x simplification 3. x = 1,12. x = 1,12 or x = 1,79. x = 1,79 (4). ( x 1) 2 9. standard form x 2 2x 8 0. ( x 4)( x 2) 0. Critical values: x = 4 or x= 2 critical values 2 4. x 2 or x 4 x 2 or x 4. (4). OR/OF OR/OF. ( ; 2) or (4; ) ( ; 2) or (4; ). OR/OF OR/OF. x 1 3 or x 1 3 x 1 3. x 4 or x 2 x 1 3. x 4 or x 2. (4). Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 3 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne 2 x 6 2 x 2 x 6 x 2 isolating the surd 4( x 6) ( x 2) 2.

3 4 x 24 x 2 4 x 4. 4 x 24 x 2 4 x 4. x 2 8x 20 0. ( x 10)( x 2) 0. x 10. x 10 or x 2 x 2. (4). 4 x 2 y .. (1) 4x 2 y 4 x y 2 8 .. (2). substitution 2 y y2 8. standard form y2 y 6 0. ( y 3)( y 2) 0. y = 3 or y = 2 y-values 1 x-values x or x = 1. 4 (5). OR/OF OR/OF. y 4 x 2 .. (1) y 4x 2. 4 x y 2 8 .. (2). 4 x 4 x 2 8. 2. substitution 4 x 16 x 2 16 x 4 8 0. 16 x 2 12 x 4 0. 4 x 2 3x 1 0. 4x 1 x 1 0 standard form 1. x or x = 1 x-values 4. y = 3 or y = 2 y-values (5).. 2 x 3 y 23 3 6. 2 3. 3. 2 x 3 y 218 36. 218 or 3 6. 2 2. x 18. and 3 3 y 6. x = 18 or y = 6. x = 18 and y=6. x y 18 6. x y 12 answer (A). (4). [24]. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 4 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2.

4 72 ; 100 ; 120 ; 132 ; . 28 20 12. 8 8 second differences = 8. 2a = 8. a= 4. a= 4. 3a + b = 28. b = 40. b = 40. a + b + c = 72. c = 36. c = 36. Tn 4n2 40n 36 (4). T12 36 8n 36 8(12) 60 36 8n 4n 2 40n 36 60 60. standard form n 2 10n 24 0. (n 12)(n 2) 0 factors n 12 n 12. (5). Tn 8n 40 0. / 8n 40. n 5. n 5. Tn 4(5) 2 40(5) 36 136 136 (3). OR/OF OR/OF. b 40 substitution 5. 2a 8 n 5. Tn 4(5)2 40(5) 36. 136. 136. (3). Maximum value = 41 value (1). 2 sin 3x 11 15 2 sin 3x equating 4 sin 3x 4 4 sin 3x 4. sin 3x 1 sin 3x 1. 3x 90 . answer x 30 . (4). [17]. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 5 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3. n 1 n 1.

5 1 1 . Tn ar n 1 2000 2000 (1). 5 5 . 7 1 16. 1 16 (1). T7 2000 125. 5 125. n 1. 16 1 . 2000 equating 15625 5 . n 1. 1 1 .. 1953125 5 . 9 n 1. 1 1 1 same base / use of log OR n 1 log 1. 5 5 5. 1953125. n 1=9. n = 10 answer (3). a a S 27 S 27 . 1 r 1 r a(1 r 3 ) a(1 r 3 ). S3 26 S3 26. 1 r 1 r 27(1 r 3 ) 26 substitution 26. 1 r3 . 27. 1. r3 . 27. 1 1. r r . 3 3. (4). OR/OF OR/OF. a S 27 . 1 r a 27(1 r ) a 27(1 r ). But a ar ar 2 26 a ar ar 2 26. a(1 r r 2 ) 26. substitution 27(1 r )(1 r r 2 ) 26. 26. (1 r )(1 r r 2 ) . 27. 26. r 2 r 1 r3 r 2 r . 27. 26. r3 1 . 27. 1. r3 . 27. 1. r . 1 r (4). 3 3. [9]. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 6 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4.

6 X 1 x 7 x 1 x 7. 2 x 8 2 x 8. x 4 x 4. y 3 y 3. 2. f ( x) 3. x 4. p 4 and q 3 (4). OR/OF OR/OF. p + q = 1 (1) p+q=1. p + q = 7. q = p 7 .(2) q=p 7. subs. (2) into (1). p+p 7=1 substitution 2p = 8 simplification p=4. q = 3 (4). 2. y 3. x 4. 2. 0 3 y=0. x 4. 2 3( x 4) 0. 3x 14 0. 14 14. x x (2). 3 3. horizontal asymptote vertical asymptote 4,67 y intercept 4 O shape 3. 3,5. (4). [10]. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 7 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5. 2 x 2 4 x 16 0. x 2 2x 8 0. factors ( x 4)( x 2) 0. x = 4 or x = 2 x= 2 x=4. A( 2 ; 0) and B(4 ; 0) (3). f ( x) 2 x 2 4 x 16. b 4. 1 1. 2a 2(2). f (1) 2(1) 2 4(1) 16 18. C(1;18) 18 (2).

7 OR/OF OR/OF. f ( x) 2 x 2 4 x 16. f / ( x) 4 x 4. 4x 4 0. x 1 1. f (1) 2(1) 2 4(1) 16 18 18. C(1;18) (2). y 18 y 18. (1). OR/OF OR/OF. y ( ;18] y ( ;18]. (1). TP (1 ; 18) for f TP (2 ; 15) for h TP for h at (2 ; 15). p 1 q 3 p 1. q 3. (3). y 2x 4. x 2y 4 swop x and y 1. 1. y x 2 y x 2. 2 2. (2). 1. g ( x) 0 or g ( x) 0. x = 4 or x = 2 (product 0 at x-intercepts) x=4. x = 2. (2). Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 8 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne 2 x 2 4 x 16 k 2 x 4 equating 2 x 2 2 x 12 k 0 standard form b 2 4ac 0 b 2 4ac 0. substitution (2) 2 4( 2)(12 k ) 0. 4 8(12 k ) 0. 100 8k 0. k 12,5 answer (5). OR/OF. OR/OF. g ( x) 2. /. g / ( x) 2.))

8 F / ( x) 4 x 4 2 f / ( x) 4 x 4. 1. x . 2. 1 1 . f 17,5 f 17,5. 2 2 . 1 1 . g 5 g 5. 2 2 . k 12,5 answer (5). [18]. QUESTION/VRAAG 6. y 3x swop x and y x 3y y log 3 x equation (2). x 4. h( x) 3 2. Transformation: 4 units left, 2 units down x = 2 (A). P / (2 ; 9). y = 9 (A). (2). x p f ( x) 2 q q 16 q 16. 16 2 p 3 16. substitute (3 ; 16). 2 p 3 32. 2 p 3 2 5 2 p 3 25 or p 3 log2 32. p 3 5. p 2 p 2. (4). [8]. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 9 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7. i . 16. 13 080 10 000 1 substitution into correct 4 . 16. formula i 13080 n = 16. 1 . 4 10000. i 16 13080 simplification 1 . 4 10000. i 0, 4. i 0, i 6,77% answer (A).

9 (4). F .. x 1 i 1. n . i 0,075 60 0,075. 9 000 1 1 .. 12 12. F . 0,075. substitution into correct 12 Formula F R 652 743,95. answer (3). 60 9 000 R540 000 60 9 000 R540 000. A P(1 i) n n 0,075 . 652743,95 1 190 214,14 540000. 12 equation n 0, 075 . 730 214,14 652 743,95 1 . 12 . 1, 1, 00625 . n simplification n log1,00625 1,1186 use of logs n 18 months 18 months (6). Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 10 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne OR/OF OR/OF. Interest over 5 years = 652 743,95 9 000 60 60 9 000. = 112 743,95. interest on n years = 190 214,14 112 743, 95 = 77 470,19 answer n 0,075 equating 652 743,95 + 77 470,19 = 652743,95 1 . 12.

10 1, 1, 00625 simplification n n log1,00625 1,1186 use of logs n 18 months 18 months (6). [13]. QUESTION/VRAAG 8. f ( x) 3 x 2. f ( x h) f ( x ). f / ( x) lim h 0 h 3( x h)2 3x 2 substitution f / ( x) lim h 0 h 3x 2 6 xh 3h 2 3x 2. f / ( x) lim expansion h 0 h 6 xh 3h 2. = lim h 0 h simplification h(6 x 3h) h(6 x 3h). = lim lim h 0 h 0 h h = 6x 6x (5). 2 2. f ( x) x 3 9 x 2. 9x f / ( x) 2 x 18x 3 2x 18 x 3. (3). Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief Mathematics P1/Wiskunde V1 11 DBE/2021. SC/SS/NSC/NSS Marking Guidelines/Nasienriglyne g ( x) ( x 3)( x 1). 1. 1. x 2x 2. g ( x) x 2 x 3. 2. 1.. 1. g / ( x) 1 x 2. 1 x 2. (4). [12]. QUESTION/VRAAG 9. f / ( x) 6 x 2 6 x 12 6 x 2 6 x 12. 6 x 2 6 x 12 0 =0.