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NATIONAL CERTIFICATE
APRIL EXAMINATION
MATHEMATICS N3
1 APRIL 2016
This marking guideline consists of 10 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T950(E)(A1)T MATHEMATICS N3
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QUESTION 1 1.1 1.1.1
(4) 1.1.2
(2) 1.2
(5)
2 2
2 2
(3 2) (3 2)3 2 3 23( ) 2( )3( )( ) 2( )( )[3( ) 2]( )[3 3 2]
x x y yx x y yx y x yx y x y x yx y x yx y x y
- - +
= - - -
= - - += - + - += + - -= + - -
4 2
2 2
4 3 1( 1)(4 1)
p p
p p
n nn n+ -
= + -
3 2
3 2
2
3 2
3 2
2
2
( ) 2 5 2(1) 2(1) (1) 5(1) 2
=2 1 5 2 =0
-1 is a factor of f ( ) 2 3 2
x-1 2 5 22 2
3 5 3 3
f x x x xf
x xx x
x x xx x
x xx x
= + - +
\ = + - ++ - +
\
+ -+ - +
-
-
-
2
- 2 2 -2 2 . .
( ) ( 1)(2 3 2) = ( 1)(2 1)( 2)
xx
f x x x xx x x
++
\ = - + -- - +
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MARKING GUIDELINE -3- T950(E)(A1)T MATHEMATICS N3
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1.3
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= ü
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(6)
[17]
)3)(1(1772
312
11 2
-+--
+--
++-
=xxxx
xx
xx
)3)(1(1772)1)(12()3)(1( 2
-+--++-+--
xxxxxxxx
)3)(1(17721234 222
-+--+-+++-
xxxxxxxx
)3)(1()32(5 2
-+--
=xxxx
MARKING GUIDELINE -4- T950(E)(A1)T MATHEMATICS N3
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QUESTION 2 2.1
(4) 2.2
(4) 2.3 2.3.1
(4) 2.3.2
(4)
[16]
32
32
12
1 32 2
2
12
32 1 322 1 1
2 32 16
xx
xx xxx
x xxx
-
-= ÷
-= ´
-=
0,5
2
2
72
12
2
2
log 128log 128
1log2
log 2log 27 log 21log 27
-
=
=
=-
= -
( )
2
22
2 2
16 3 3 2
16 3 3 2
16 3 3 4.3 412 4.33 3
1TEST : If 1 then LHS=RHS=5
x x
x x
x x x
x
x
xx
+ = +
\ + = +
\ + = + +
\ =
\ =\ =
=
0
2
(log 2) log( 2) 0log 2 0 or log( 2) 0 log 2 2=10 10 2 1 100 3
x xx xx x
x xx x
- ´ - =\ - = - =
\ = -
\ = - =\ = =
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MARKING GUIDELINE -5- T950(E)(A1)T MATHEMATICS N3
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QUESTION 3 3.1
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(4) 3.2
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(4)
bxbxD
-+
=2
MARKING GUIDELINE -6- T950(E)(A1)T MATHEMATICS N3
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3.3
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(3)
3.4 Deposit is
Total price is Total amount for 9 instalments=
Each monthly instalment =
(4) [15]
dsptw
e =log
dseptw
=
dsetpw =
R3xR33x
R30x
\ 30 10R9 3x xR=
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MARKING GUIDELINE -7- T950(E)(A1)T MATHEMATICS N3
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QUESTION 4 4.1 4.1.1
(2) 4.1.2
(4) 4.1.3
(3) 4.1.4
(3)
( ) ( )
( ) ( )
2 22 1 2 1
2 2
AB
= 4 2 5 1
= 4 16
= 20
=2 5
x x y y= - + -
- + -
+
( ) ( )( )
( )
2 2
2
2
BC=2 5
0 4 5 20
16 5 = 20
5 = 4 5 = 2 5 2 5 2 7 3
k
k
kk
k or kk k
\ - + - =
\ + -
\ -
\ - ±\ - = - = -\ = =
5 1 24 27 5 10 4 2
1 therefore CB AB
AB
CB
AB CB
M
M
M M
-\ = =
--
\ = = --
´ = -^
2
1Area of ΔABC = × base × height 2
1 =21 = 20 20 2
=10 units
AB BC´
´
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MARKING GUIDELINE -8- T950(E)(A1)T MATHEMATICS N3
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4.2
(4) 4.3
(5) [21] QUESTION 5 5.1 Y 3 ü -3 0 3 ü X -3 (2)
1 2 1 2coordinates of M ;2 2
2 4 1 7 = ;2 2
=(1;3) Equation =1
x x y y
x
+ +æ ö= ç ÷è ø- + - +æ ö
ç ÷è ø
\
o o
o o o
1 3tan 1 tan =3
=45 =71,565 ˆBAC = = 71,565 45 = 26,565
AB ACM Mq a
q a
a q
= =
\ = \
\ \
- -
2733 22 =+ yx
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MARKING GUIDELINE -9- T950(E)(A1)T MATHEMATICS N3
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5.2.1 5.2.2
(5)
(3) 5.3
(4) [14]
3 2
2
2
2
3 2
3 2
6 9
3 12 9
Let 0 3 12 9 0
3( 4 3) 0( 1)( 3) 0
1 or 3( 1) ( 1) 6( 1) 9( 1) 4( 3) ( 3) 6( 3) 9( 3) 0
Turningpoints ( 3;0) and ( 1;4)
y x x xdy x xdxyx x
x xx xx xff
= + +
= + +
=
\ + + + =
+ + =+ + == - = -
- = - - - - - - =
- = - - - - - - =- -
11 2
12 2
2
1 2
2
2(0,5)
1 1
y xx
y x x
dy x xdxdydx x x
-
--
= +
= +
= - +
= - +
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MARKING GUIDELINE -10- T950(E)(A1)T MATHEMATICS N3
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QUESTION 6 6.1
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(4) 6.2
(5) 6.3 6.3.1
6.3.2
(3)
(3)
2
2
2
o o
o
sin 1 cossin sinsin sin 0sin (sin 1) 0sin 0 or sin 1
0 or 90or 180
q q
q q
q qq qq q
q q
q
= -
\ =
\ - =\ - =\ = =
\ = =
=
o o
o
o
o
o
o
:30
sin 70 sin 4530sin 70sin 45
39,868
:
cos 25
cos 2539,868 cos 2536,133
In ABCAB
AB
m
In ABDADABAD AB
m
D
=
\ =
=
D
=
\ =
= ´=
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MARKING GUIDELINE -11- T950(E)(A1)T MATHEMATICS N3
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6.4
(2) [17]
TOTAL: 100
22
ap==
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