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NATIONAL
SENIOR CERTIFICATE
GRADE 10
MATHEMATICS
COMMON TEST
MARCH 2022
MARKING GUIDELINE
MARKS:
75
TIME:
1½ hours
This memorandum consists of 6 pages.
2
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Mathematics
March 2022 Common Test
NSC – Marking Guideline
QUESTION 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
 answer
 answer
 answer
 answer
 answer
 answer
 answer
 answer
 answer
 answer
D
B
C
A
B
C
B
D
A
D
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
[20]
QUESTION 2
2.1
(a  2)(a 2  2a  8)
 a3  2a 2  8a  2a 2  4a  16
 a  4a  16
3
2.2.1


expand
simplification
(2)
x3  y 9
3
  x3   y 3  


 x  y
3
 x
2

x  2y 
 x  xy  4 y 

common factors


common bracket
answer

common factors


common bracket
answer

 xy  y
3
6

3
2
3
6
(2)
2.2.2
f  e 1 e f
 f  1  e  ef
 1( f  1)  e(1  f )
 1( f  1)  e( f  1)
 ( f  1)(1  e)
(3)
OR
f  e 1 e f
 f  ef  e  1
 f (1  e)  (e  1)
 f (1  e)  1(1  e)
 (1  e)( f  1)
(3)
OR
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Mathematics
f  e 1 e f
 f  ef  e  1
 f (1  e)  (e  1)
 f (1  e)  1(1  e)
 (1  e)( f  1)
2.3.1
NSC – Marking Guideline
18m2  6 m  36m 2
22 m  2.33m
(2.32 ) m2  (2.3)  m  (22.32 ) m 2

22 m  2.33m
2m  2.32 m  4.2 m.3 m.22 m  4.32 m  4

22 m  2.33m
2m  2 m  2 m  4 .32 m  4 m  2 m  4

22 m  2.33m
 22 m  2 2 m.33m3m
 22
2.3.2
y2  y  2 y2  2 y
 2
y2  4
y y
( y  2)( y  1) y ( y  2)


( y  2)( y  2) y ( y  1)
1
March 2022 Common Test

common factors


common bracket
answer

prime bases

raising powers

simplification

answer

factors of
trinomial
difference of 2
squares
common factor
answer



(3)
(4)
(4)
2.4
Students do not
need to expand
binomial x binomial
Area  (6 x  3)(4 x  2)
Area  (24 x 2  12 x  12 x  6) units 2
Area  (24 x 2  24 x  6) units 2



(6 x  3)
(4 x  2)
A  lw
(3)
[18]
QUESTION 3
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Mathematics
3.1.1
NSC – Marking Guideline
3
5

2
x2 x4
LCD : ( x  2)( x  4)
RESTR : x  2 or x  4
March 2022 Common Test

LCD

numerator

CA factors

CA

common factor
5 x  625

625
5 5
x  4

answer


4  2 x  12
2  x  6

number line /
notation
3( x  4)  5( x  2)  2( x  2)( x  4)
3x  12  5 x  10  2( x 2  2 x  8)
8 x  2  2 x 2  4 x  16
2 x 2  12 x  14  0
2( x  7)( x  1)  0
 x  7 or x  1
3.1.2
5
x4
(4)
 5  626
x
5 x.54  5 x  626
5 x (54  1)  626
4
5 (5  1)  626
x
x
3.2
3.3
4
6  2 x  2  10
4  2 x  12
2  x  6
4a  b  5
3a  4b  19
Eq 1  4 
Eq 1  Eq 2
(3)
(3)
( Eq 1)
( Eq 2)
16a  4b  20
3a  4b  19
13a
 39
a 3
Sub a  3 in Eq 1 4(3)  b  5
b  7


Eq1  4
Adding eqs

a =3

substitution

b=7
(5)
OR


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b  4a  5
Sub Eq 3  Eq 2
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Mathematics
March 2022 Common Test
NSC – Marking Guideline
4a  b  5
( Eq 1)
3a  4b  19 ( Eq 2)
Eq 1 Eq 3 b  4a  5
Sub Eq 3 in Eq 2:
3a  4(4a  5)  19
3a  16a  20  19
13a  39
a 3
Sub a  3 in Eq 1 4(3)  b  5
b  7


a =3
substitution

b=7
(5)
[15]
Give reasons for your statements in the answers to QUESTIONS 4 and 5.
QUESTION 4
4.1
10 x  78  4 x
6x = 78o
x = 13o
(ext  of ΔSTC)
y = 180o – [78o + 4(13o)] (sum of  s ΔSTC)
y = 50o


S
R

S/R

S/R

S/R
OR
y = 180o – (10  13o)
y = 50o
z = 78o
( sum of  s st . line)
corresp  s; ST //AB 
(4)
4.2
Rhombus
Square
Rectangle
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


answer
answer
answer
(3)
[7]
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Mathematics
March 2022 Common Test
NSC – Marking Guideline
QUESTION 5
5.1
 s opp  sides 
alt  s ; KN // LM 
 s opp  sides 
Mˆ 1  Lˆ 2
but Nˆ 1  Lˆ 2
Nˆ  Kˆ
1
 Mˆ 1  Kˆ
5.2

S/R

S/R
(3)

S/R
(proved above)

S/R
alt s ; KN // LM

S/R
 ∆KLN and ∆MNL (A; A; S)

S/R
KL  NM
KN  ML

S

R

S/R
( sum s of NME )

S/R
(s opp  sides )

S/R
and Eˆ  Mˆ 2
(s opp  sides )
 Mˆ 1  Mˆ 2  Mˆ 1  Mˆ 2  180
2Mˆ  2Mˆ  180

S/R

substitution

simplification
LN is common
Kˆ  Mˆ 1
Nˆ  Lˆ
3.
1
2
( given)
(congruent s proved above)
 KLMN is a parallelogram.
Reason:
2 Pairs of opp sides equal and parallel
5.4
S/R
In ∆KLN and ∆MNL:
1.
2.
5.3

Mˆ 1  Mˆ 2  Lˆ2  Eˆ  180
but Lˆ  Mˆ
2
1
(3)
2
2( Mˆ 1  Mˆ 2 )  180
Mˆ  Mˆ  90
1
1
(4)
2
ˆ  90
 LME
(5)
[15]
TOTAL: 75
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