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.

2 Indien kandidaat poging vir vraag deurgetrek het en nie die vraag weer beantwoord het nie, merk die poging wat deurgetrek is. 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 + - +.

3 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). 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.

4 = ( 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). ; ; 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 ).

5 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. =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/.

6 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. = 500 000( )12 12 . (2). = 500 000( )12 . = 500 000( )12 5 = 60. = answer/ antwoord (2).

7 = (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 ).

8 QUESTION 5/VRAAG 5. ( 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 ).

9 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 = [( + ) ]. 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 ).

10 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). 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 ).