SEPTEMBER 2017 MATHEMATICS P1/WISKUNDE …

1 NATIONAL. SENIOR CERTIFICATE/. NASIONALE. SENIOR SERTIFIKAAT. grade /GRAAD 12. SEPTEMBER 2017 . MATHEMATICS P1/WISKUNDE V1. memorandum . MARKS/PUNTE: 150. Hierdie memorandum bestaan uit 13 This memorandum consists of 13 pages. 2 MATHEMATICS P1/WISKUNDE V1 (EC/ SEPTEMBER 2017 ). NOTE/LET OP: If a candidate answered a question TWICE, mark the FIRST attempt ONLY. Indien kandidaat vraag TWEE keer beantwoord het, merk SLEGS die EERSTE poging. Consistent accuracy applies in ALL aspects of the memorandum . Volgehoue akkuraatheid geld deurgaans in ALLE aspekte van die memorandum . If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out attempt. Indien kandidaat poging vir vraag deurgetrek het en nie die vraag weer beantwoord het nie, merk die poging wat deurgetrek is.

2 The mark for substitution is awarded for substitution into the correct formula. Die punt vir substitusie word toegeken vir substitusie in die korrekte formule. QUESTION 1/VRAAG 1. 2 ( + 1) 7( + 1) = 0. ( + 1)(2 7) = 0 factors/faktore 7 -value/waarde = 1 or / =. 2 -value/waarde (3). 2 5 1 = 0. 2 4 . = substitution into correct 2 . formula/substitusie in korrekte ( 5) ( 5)2 4(1)( 1). = formule 2(1). = 5,19 or = 0,19 -values/waardes (3). 4 2 + 1 5 . 4 2 5 + 1 0 standard form/standaard (4 1)( 1) 0 vorm factors/faktore + - +. 1. 1 1. 4 4. 1 1. 4 or/ of 1 (4). 54 +3 . 100 2 +1 = 50 000. 54 +3 . (52 . 22 ) 2 +1 = 50 000. 54 +3 . 5 4 +2 . 2 4 +2 = 50 000 5 4 +2. 55 . 2 4 . 22 = 50 000 2 4 +2. 2 4 = 22 4 = 2. 4 = 2. 1 answer/antwoord = (4).

3 2. Copyright reserved Please turn over (EC/ SEPTEMBER 2017 ) MATHEMATICS P1/WISKUNDE V1 3. = 2 ..(1). 2 + 2 2 = 36 .(2). = 2 . sub into (2)/vervang in (2). (2 )2 + 2(2 ) 2 = 36 substitution/vervanging 4 2 + 4 2 = 36. 3 2 + 3 36 = 0. 2 + 12 = 0 standard form/standaardvorm ( 3)( + 4) = 0 factors/ faktore = 3 or = 4 y values/ . = 6 or = 8 x values/ . (5). 2 + 1 = 0. = 2 4 substitution/vervanging = ( )2 4(1)( 1) simplification/vereenvoudiging = 2 4 + 4 ( 2)2. = ( 2)2 conclusion/gevolgtrekking 0 roots are real and rational(perfect square) (4). [23]. QUESTION 2/VRAAG 2. = 4 1 = 4 1. 483 = 4 1 equating/gelykstelling 483. 484 = 4 answer/antwoord = 121. 121 terms in series/ 121terme in reeks (3). 121. (4 1) answer/antwoord =1 (2). ( 3) (2 4) = (8 2 ) ( 3) setting up equation/opstel van + 1 = 3 + 11 vergelyking 2 = 10 simplification/vereenvoudig =5 answer/antwoord (3).

4 ; ; 6 ; 2 ; 2 ; ; ; numerical values of 10 = 6 or /of = 4 + 46 10 ; 11 ; 12 / numeriese waardes + 9 = 6 1 = 4(1) + 46 van 10 ; 11 ; 12. + 9( 4) = 6 1 = 42 difference / verskil 4. = 42 a-value/a-waarde (3). Copyright reserved Please turn over 4 MATHEMATICS P1/WISKUNDE V1 (EC/ SEPTEMBER 2017 ). 2 + 3 = 4. + = 1 setting of equations/ opstel van vergelykings 2 (1 + ) = 4. (1 + ) = 1 common factor/gemene faktor 2 = 4. = 2 = 2. + (2) = 1. + 2 = 1. 3 = 1 value of a/waarde van a 1. = first three terms/eerste drie 3. terme ry 1 2 4. First three terms: 3 ; 3 ; 3. Eerste drie terme: (6). [17]. QUESTION 3/VRAAG 3. 41 ; 43 ; 47 ; 53 ; 61 ; 71 ; 83 ; 97 ; 113 ; 131. 2 4 6 8 10 12 14 16 18. 2 2 2 2 2 2 2 2 2nd difference/ tweede verskil 2 = 2 + =2 + + = 41 = 1.

5 =1 = 1 = 41 = 1. 2 = 41. = + 41. = 2 + 41. (5). 41 = 412 41 + 41 41 = 1681. 41 = 1681. factors / faktore Factors of 1681: 1 ; 41 and 1681. Faktore van 1681 : 1 ; 41 en 1681 conclusion/. gevolgtrekking 1681 is not a prime number/ 1681 is nie priemgetal nie (3). Consider the unit digits only/kyk na die ene syfers alleenlik. 1 ; 3 ; 7 ; 3 ;1 ;1 ; 3 ; 7 ; 3 ;1 ; unit digits/ene syfers groups of 5/ groepe van 5 groups of 5/. 49999998 groepe van 5. = 9999999,6 conclusion/. 5. 0,6 5 = 3 gevolgtrekking 49999998 will end in 7/ sal met 7 eindig (3). [11]. Copyright reserved Please turn over (EC/ SEPTEMBER 2017 ) MATHEMATICS P1/WISKUNDE V1 5. QUESTION 4/VRAAG 4. = (1 + ) . 7,2 12 sub into formula/ vervang in = 500 000 (1 + ) formule 1200.

6 = 500 000( )12 12 . (2). = 500 000( )12 . = 500 000( )12 5 = 60. = answer/ antwoord (2). = (1 + ) . 1000000 = 500000( )12 setting up equation/opstel van log 2 vergelyking 12 = using logs/ gebruik van log log 12 = = 9,66 . Will exceed R1 000 000 in 10 years. conclusion/gevolgtrekking Sal R1 000 000 oorskry in 10 jaar. (3). 36. 15 and/ . 10 000 [1 (1 + 1200) ]. sub into formula/ vervang in = 15 formule 1200. = 288 472,67. = 288 472,67. / = 350 000 288 472,67. / = 61 527,33. subtracting/ . answer/antwoord (5). 18,5 60 18,5. = 1200. [1 (1 + 1200) ]. 350 000 = 18,5 = 60. 1200 substitution/substitusie = 8 983,17 answer/antwoord (4). [16]. Copyright reserved Please turn over 6 MATHEMATICS P1/WISKUNDE V1 (EC/ SEPTEMBER 2017 ). QUESTION 5/VRAAG 5.

7 ( 3; 0) answer/antwoord (1). ( ) = 2 + 3 .. = 3. 2 = 2. 3. = . 2. 3 3 2 3. ( ) = ( ) + 3 ( ). 2 2 2 substitution/ vervanging 9. = . 4. 3 9. ( ; ) answer/ antwoord 2 4 (3). ( 5) = 10 and / en ( 3) = 0 calculating ( 5) and ( 3). bepaling van ( 5) ( 3). 10 0 substitution/substitusie =. 5 ( 3) -value/waarde = 5 (3). < 3 or / of > 0 answer/ antwoord (2). 3 9. ( ; ). 2 4. 3 9. ( 2 ; ). 2 4. 1 9 answer/ antwoord ( ; ). 2 4. or/of ( 2) = ( 2)( 2 + 3). ( 2) = 2 2 ( 2) = 2 2. ( 1). = . 2(1). 1. 1 = 2. = . 2 (2). Copyright reserved Please turn over (EC/ SEPTEMBER 2017 ) MATHEMATICS P1/WISKUNDE V1 7. 1. = + 2 ( 2 + 3 ). 2 ( ) ( ). 1. = + 2 2 3 . 2 standard form/standaardvorm 7. = 2 + 2. 2. 2. 7. = ( + 2). 2 completing the square/. 7 2 81 voltooing van kwadraat = [( + ) ].

8 4 16. 7 2. 81 answer/antwoord = ( + ) +. 4 16. OR/OF. 1 ( ) ( ). = + 2 ( 2 + 3 ). 2. 1 standard form/standaardvorm = + 2 2 3 . 2. 7. = 2 + 2. 2 7. 7 = 4. = 2 . 2. 7. 2 = 0. 2. 7 81. = = 16. 4. 7 2 7 7. = ( ) ( ) + 2. 4 2 4. 81. =. 16. 7 2 81. = ( + ) +. 4 16. OR/OF. ( ) ( ). = . 2 standard form/standaardvorm 7. 2. = . 2( 1). 7. = 7. 4 = 4. 7 2 7 7. = ( ) ( ) + 2. 4 2 4. 81. =. 16 81. = 16. 7 2 81. = ( + ) +. 4 16. (4). [15]. Copyright reserved Please turn over 8 MATHEMATICS P1/WISKUNDE V1 (EC/ SEPTEMBER 2017 ). QUESTION 6/VRAAG 6. shape / vorm 1. y intercept/ . point on graph/punt op 1 grafiek . 1. (3). ( ) = 2 answer/antwoord (1). 1 = 2 . log . = interchange and . log 2. log . = log 2 / = log 2 / = log 1 ruil en . 2. equation/vergelyking (2).

9 0 ; (1). See sien shape and x-intercept/vorm en x-afsnit (2). log 1 = 3. 2. 1 3. ( ) = = 8. 2. =8 0 < 8. 0< 8 (2). [11]. Copyright reserved Please turn over (EC/ SEPTEMBER 2017 ) MATHEMATICS P1/WISKUNDE V1 9. QUESTION 7/VRAAG 7. =5 = 5. =2 = 2. (2). 5 . =. 2. ( 2) + 3 5 . = 2. =. ( 2). 3 ( 2)+3. = 1 =. 2 ( 2). (2). (5; 0). = 3. = +3 = 3. (0 + 3; 5 3) = 2. (3; 2) (2). [6]. Copyright reserved Please turn over 10 MATHEMATICS P1/WISKUNDE V1 (EC/ SEPTEMBER 2017 ). QUESTION 8/VRAAG 8. ( ) = 2 2 + . ( + ) ( ). ( ) = lim formula/formule 0 . 2( + )2 + ( 2 2 + ) substitution of/substitusie van = lim ( + ). 0 . 2( 2 + 2 + 2 ) + + 2 2 ). = lim 0 . 2 2 4 2 2 + + 2 2 simplification to/. = lim 0 vereenvoudiging na ( 4 2 2 ). 4 2 2. = lim 0 . ( 4 2 ) common factor/gemene = lim 0 faktor = lim ( 4 2 ).

10 0. Answer ONLY: 0 marks/. = 4 SLEGS antwoord: 0 punte answer/antwoord Penalise 1 mark for incorrect use of formula. Must show ( ). Penaliseer 1 punt vir verkeerde gebruik van formule. Moet ( ) toon. (5). 3 1. [4 + + 2]. 3 . 1 1. 1 1. [4 3 + 3 1 + 2] Penalise 1 mark for 4 3 1. incorrect notation. / 3. 4 2 1. = 3 2 Penaliseer 1 punt vir 4 2. 1. 3 3 verkeerde notasie. 3 3 3 2. (4). [9]. Copyright reserved Please turn over (EC/ SEPTEMBER 2017 ) MATHEMATICS P1/WISKUNDE V1 11. QUESTION 9/VRAAG 9. ( ) = ( 1)2 ( + 3). ( ) = 3 + 2 5 + 3 ( ) = 3 + 2 5 + 3. ( ) = 3 2 + 2 5 ( ) = 0. 3 2 + 2 5 = 0 factors/faktore (3 + 5)( 1) = 0. 5. = 3 or / of = 1 -values/waardes (1) = 0 -values/waardes 5 256. ( ) =. 3 27 (5). 256 shape / vorm 27 intercepts/.