GRADE 12/GRAAD 12 - cdn.24.co.za

NATIONAL SENIOR CERTIFICATE/

NASIONALE SENIOR SERTIFIKAAT

GRADE 12/GRAAD 12

MATHEMATICS P1/WISKUNDE V1 FEBRUARY/MARCH/FEBRUARIE/MAART 2018

MARKING GUIDELINES/NASIENRIGLYNE

MARKS/PUNTE: 150

These marking guidelines consist of 17 pages./ Hierdie nasienriglyne bestaan uit 17 bladsye.

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Mathematics/P1

2 NSC ? Memorandum

DBE/November 2016

NOTE: If a candidate answers a question TWICE, only mark the FIRST attempt. Consistent accuracy applies in ALL aspects of the marking guidelines.

LET WEL: Indien 'n kandidaat 'n vraag TWEE KEER beantwoord, merk slegs die EERSTE poging. Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing.

QUESTION/VRAAG 1

1.1.1 x2 6x 16 0

x 8x 2 0

x 2 or x 8

1.1.2 2x2 7x 1 0

b b2 4ac x

2a

7 72 421

22

7 57 4

x 0,14 or x 3,64

factors

x 2

x 8

(3)

subs into correct formula

7 57 4

x 0,14 x 3,64

OR/OF

x2 7 x 49 1 49 2 16 2 16 x 7 2 57 4 16

NOTE: Penalise 1 mark if the rounding to TWO decimal places is incorrect.

OR/OF

for adding 49 on 16

both sides

x 7 57 44 x 7 57 4 x 0,14 or x 3,64

1.2

x2 25 0

x 5x 5 0

7 57 4

x 0,14 x 3,64

(4)

factors

+

-

+

+ -

+

5 x 5

inequality

NOTE:

x ={ ?4 ; ?3 ; ?2 ; ?1 ; 0 ; 1 ; 2 ; 3 ; 4} Final answer only answer

2 / 2

(4)

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3 NSC ? Memorandum

1.3

x 2y 1

2 y 1 2 7 y2 y

4y2 4y 1 7 y2 y

3y2 3y 6 0

y2 y 2 0

y 2( y 1) 0

y 2 or y 1

x 22 1 or x 21 1

x3

or x 3

OR/OF

y x 1 2

x2 7 y2 y

x2 7 x 12 x 1 2 2

x2

7

x2

2x 4

1

x 1 2

4x2 28 x2 2x 1 2x 2

3x2 27 0

x2 9 0

x 3x 3 0

x 3

or

y 3 1 or 2

y 1

or

x3 y 31 2 y2

1.4

32018 32016

32017

32017 31 31

32017

3 1 3

3 1 or 10 33

OR/OF

DBE/November 2016

x 2y 1 substitution

correct standard form factors y ? values

x ? values OR/OF y x 1

2

substitution

correct standard form factors x ? values

y ? values

(6)

common factor 32017 answer OR/OF

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Mathematics/P1

32018 32016 32017

32016 32 1

32017

10 3

OR/OF

32018 32016 32017

32018 32016 32017 32017

3 1 3

3 1 or 10 33

4 NSC ? Memorandum

1.5.1

3x 5 0 and x 3 x 5 and x 3 3

1.5.2

3x 5 1 x3

3x 5 x 3

3x 5 x 32

3x 5 x2 6x 9

x2 9x 14 0

x 7x 2 0

x 2 or x 7

NOTE: If x = 2 is not rejected, then maximum 3 / 4 marks

DBE/November 2016

common factor 32016

answer

OR/OF

dividing by 32017

answer (2)

3x 5 0 x5

3 x3

(3) 3x 5 x 3

3x 5 x 32

factors x 7

(4) [26]

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Mathematics/P1

5 NSC ? Memorandum

DBE/November 2016

QUESTION/VRAAG 2

2.1.1

30 ; 10 ; 10 ....... 3

a 30 r 1 3

Tn ar n1 10 30 1 n1 729 3

1 31n 2187

37 31n 7 1n

n8

OR/OF

1 1 n1 2187 3

1 7

1 n1

3 3

7 n 1

n8

2.1.2

S

1

a

r

30 1 1

3

45

2.2 Sn a (a d) ...... (a n 2d) (a n 1d) 1 Sn (a n 1d) (a n 2d) ......... (a d) a 2

Adding both equations/Tel die twee vergelykings bymekaar:

2Sn 2a n 1d 2a n 1d 2a n 1d ............. n2a n 1d

Sn

n 2a

2

n

1d

OR/OF

Sn a (a d) ...... (a n 2d) Tn

Sn Tn Tn d Tn 2d ......... a

1 2

Adding both equations/Tel die twee vergelykings bymekaar:

2Sn a Tn a Tn a Tn ..... a Tn

Sn

n 2

a

Tn

but Tn a (n 1)d

Sn

n 2a

2

n 1d

r= 1 3

substitution into correct formula

37 31n or

1 3

7

1 3

n1

or

use of logs

n8

(4)

substitution into correct formula

answer (2)

expanding Sn

reverse writing

2Sn n2a n 1d

Sn

n 2

2a

n

1d

(4)

expanding Sn reverse writing

2Sn na Tn

Sn

n 2

2a

n

1d

(4)

[10]

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