Maths Grade 10 2012 examplar Memo

NATIONAL
SENIOR CERTIFICATE

GRADE 10

MATHEMATICS P1
EXEMPLAR 2012
MEMORANDUM
MARKS: 100

This memorandum consists of 7 pages.

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NSC – Grade 10 – Memorandum

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QUESTION 1
1.1.1

(m − 2n )(m 2 − 6mn − n 2 )
= m 3 − 6m 2 n − mn 2 − 2m 2 n + 12mn 2 + 2n 3
3

2

2

= m − 8m n + 11mn + 2n

3

 expansion
 m3 ; + 2n3
 − 8m 2 n + 11mn 2
(3)

1.1.2

3

x +1 x2 − x +1

=

−

2

4 x − 3x − 1
4x + 1

(

( x + 1) ( x 2 − x + 1) ( 4 x + 1)( x − 1)
−
4x +1

x2 − x + 1

= x + 1 − ( x − 1)
1.2.1

)

 ( x + 1) x 2 − x + 1
 (4 x + 1)(x − 1)
 x + 1 − ( x − 1)
answer

=2
6 x 2 − 7 x − 20

(5)
 (3 x + 4 )
 (2 x − 5)

= (3 x + 4 )(2 x − 5)

(2)
1.2.2

2

a + a − 2ab − 2b
= a (a + 1) − 2b(a + 1)
= (a + 1)(a − 2b)

grouping
 (1 + a)
 (a − 2b )
(3)

1.3

1.4

Since 7 = 49 and 8 = 64 and
49 < 51 < 64 ,
7 < 51 < 8
i.e. 51 lies between 7 and 8

Let x = 0,245

Then 1000 x = 245,245
i.e.
999 x = 245
245
i.e. x= 999
Therefore x is a rational number.

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2

2

 49 < 51 < 64
 answer
(2)
 introduce variable

 1000 x = 245,245
 999 x = 245
245
x=
999
(4)
[19]

Please turn over

Mathematics/P1

3
NSC – Grade 10 – Memorandum

DBE/2012

QUESTION 2
2.1.1

x 2 − 4 x = 21 x 2 − 4 x − 21 = 0
(x + 3)(x − 7 ) = 0 x+3= 0

or

 standard form
 factors x−7 = 0

x = −3

x=7

 answers
(3)

2.1.2
96

5
= 3x 4

32 =

 32 = x

5 x4 5
4

 x = (32 ) 5

4

x = (32 ) 5

4

( )

= 25

4
5

= 24
= 16

 answer
(3)

2.1.3

R=

2 x
3S

3RS
= x
2
9R 2 S 2 x= 4

2.2

 Multiply by 3S and divide by 2
 Squaring both sides
(2)

6q + 7 p = 3......................Equation 1
2q + p = 5......................Equation 2
6q + 7 p =
3......................Equation 1
14q + 7 p =