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MARKING GUIDELINE -1- T...(E)(J)T MATHEMATICS N2
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NATIONAL CERTIFICATE
APRIL EXAMINATION
MATHEMATICS N2
APRIL 2016
This marking guideline consists of 11 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T...(E)(A…)T MATHEMATICS N2
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INSTRUCTIONS AND INFORMATION 1. 2. 3. 4. 5. 6. 7. 8.
ü equals 1 mark and . equals ½ mark. Half marks are not allocated, unless indicated otherwise. Where a formula is required, using the wrong formula is a principle error and NO marks are allocated. Students should show ALL formulae and intermediate steps and simplify where possible. ALL final answers must be rounded off to THREE decimal places (unless indicated otherwise). Questions may be answered in any order, but subsections of questions must be kept together. If subsections are separated, the student can be penalised by ONE mark. Where a student copied wrongly from the question paper, and the standard of the question is still the same, the student will be penalised by ONE mark. If the copying error simplifies the question and makes it easier, the student forfeits the marks. Questions must be answered in blue or black ink. Answers in PENCIL are not marked as it is regarded as rough work.
Ö
MARKING GUIDELINE -3- T...(E)(A…)T MATHEMATICS N2
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)2)(2)(4(2)4(8)4(2 22
+--=---xxa
xxa
QUESTION 1 1.1 1.1.1
(4) 1.1.2
(3) 1.2 1.2.1
(3)
1.2.2
(3)
1.2.3
(5) [18]
32882 22 +-- xaax
3 2
2
3 12 93 ( 4 3)3 ( 3)( 1)
x y x y xyxy x xxy x x
- +
= - += - -
2 2
2
2 2 33 2
12 4 96
12 56
x xx
x xxxx
+ -
+ -=
-=
313
3 33
4 33
aa
a aa
aa
--
- +=
-=
22 4 1 12 3 4 12 4 8
2 ( 2) 4( 3) 1( 3)( 1) 1 4 ( 2)
2
ax a xx x x ax a
a x x xx x a x
- +÷ ´
- - - -
- - += ´ ´
- + -
=
ü ü ü ü
ü
ü
ü
ü
ü
ü
ü
ü
ü ü ü
ü
MARKING GUIDELINE -4- T...(E)(A…)T MATHEMATICS N2
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QUESTION 2 2.1
(4)
2.2 2.2.1
(3)
2.2.2
(3) 2.3
(4) [14]
0,786 2,120x or x= = -
2
2
......................( )pqB xKxpqBKxpqxKB
=
\ =
\ =
.................( )
( )
nEI nR nr
IR Inr nEIR nE InrIR n E Ir
IRnE IRIRor n
IR E
=+
+ =\ = -\ = -
\ =--
=-
9 137,81.............(1) 14 198,26............(2)(1) (2) 5 60,45 = 12,09
From (1) 9(12,09) 137,81
cc
c
+ =+ =
- - = -\
+ =
!
!
!
!
137,81 108,81 29
cc
\ = -\ =
ü
ü
ü
ü ü
ü
ü
ü
ü
ü
ü
ü
MARKING GUIDELINE -5- T...(E)(A…)T MATHEMATICS N2
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322823
==
=
x
x
x
QUESTION 3 3.1
(4)
3.2
(3)
3.3 .
Show ALL the steps. Answers only are not acceptable. Without rounding off:
(5)
5 33 18 36
2 4
76 12
73 6
10 5
a b a ba ba a bba a bba b
- ´
= ´
= ´
=
242.3 =x
513,4 265 12,8 54,6
x ´=
´513,4 265log log
12,8 54,6x ´
\ =´
15 2log log13,4 log 265 log12,8 log54,6x\ = - - -
1log 5log13,4 log 265 log12,8 log54,62
x\ = - - -
4,003
log 4,0031010 069,317
xxx
\ =
\ =\ =
4,002744313
log 4,0027443131010 063,390
xxx
=
\ =\ =
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü ü
ü
ü
ü
MARKING GUIDELINE -6- T...(E)(A…)T MATHEMATICS N2
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sradw
w
nw
/519,366
)603500(2
2
=
=
=
p
p
D
D
DnV
=
=
=
995,10
)603500(2015 p
p
3.4
(4)
[16] QUESTION 4 4.1
4.1.1
The angular velocity of the pulley in radians per second.
(3)
4.1.2
(3) 4.2 4.2.1
(3)
log 9 log 81 log 3 5log 2187 7
x x x
x
+ -=
2 4
7
log 9 log 81 log 3log 2187
log 3 log 3 log 3log 3
2log 3 4log 3 log 37 log 3
5log 37 log 357
x x x
x
x x x
x
x x x
x
x
x
LHS
RHS
+ -=
+ -=
+ -=
=
= =
10,955D cm=
o
22,5 where 22,5cm and 24 cm24
0,938 rad or 53,743
sr
s r
q
q
q
=
= = =
=
o
Final round off: 0,9375 rad or 53,715q =
ü
ü
ü
ü
ü
ü
ü
ü
ü
MARKING GUIDELINE -7- T...(E)(A…)T MATHEMATICS N2
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oq
q
q
824,17952,0cos5,134
128cos
=
=
=
4.2.2
(2) 4.3
4.3.1
(2) 4.3.2
Follow up with height of 4.3
(3) 4.4
(4)
[20] QUESTION 5 5.1 5.1.1
*without rounding off :
(3)
2
2
2
12
1 (24) (0,938)2270,144 cm
A r q=
=
=
2
2
or1 (24) (0,9375)2270 cm
=
=
2 2 2
2 2(13,2) (8)110,24
10,5 cm
AD AB BD
AD
= -
= -=
=
2
2
3
13
1 (8) (10,5)3703,717 cm 703,717 m
V r hp
p
=
=
== !
3 or 703,7167544 cm703,7167544 m= !
2
0 0[ 12 13 21 24 23 18] 0,82
88,8cm
A += + + + + + + ´
=2or A 8880mm=
oq 885,17=
ü
ü
ü
ü
ü
ü
ü
ü
ü ü
ü
ü
ü
ü
ü
ü
ü
ü
MARKING GUIDELINE -8- T...(E)(A…)T MATHEMATICS N2
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307,4125,17061285,134
2
222
==
-=
ACACAC
17,41824,17sin.5.1345,134
824.17sin
=
=
o
opp
)812,0549,46(
812,0
552,46726,0sin9,56307,41sin
1
radiansor
radians
==
=
=
=
=
-
bb
b
b
b
b
o
o
565,296435,63360
565,116435,631802tan
]360;0[ ; 073,5tanA
=-=
=-=-=
Î=+
A
AA
A oo
5.1.2
or
or
Or
or
(3)
5.1.3
Or
(3)
5.2
(3)
o
tan128128 tan128 tan17,88541,306 cm
In ABCAC
ACACAC
q
q
D
=
\ =
\ =\ =
o
tan128128 tan128 tan17,82441,155 cm
In ABCAC
ACACAC
q
q
D
=
\ =
\ =\ =
o
sin134,5134,5sin134,5sin17,88541,306 cm
In ABCAC
ACACAC
q
q
D
=
\ =
\ =\ =
o
o
46,3260,808 rad
46,3480,809 rad
or
bb
bb
=\ =
=\ =
ü
ü
ü ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
ü
MARKING GUIDELINE -9- T...(E)(A…)T MATHEMATICS N2
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5.3
(4) [16] QUESTION 6 6.1
shape x-intercepts y-intercept turning points ½ mark(Ö) 60°,300°
½ mark& ½ mark Ö Ö 0,5 ½ mark Ö
(180°,-1,5) ½ markÖ (360°, 0,5) ½ markÖ
6 x ½ marks=3 marks
(3) 6.2 6.2.1
(2)
o
o
tan 5725
25 tan5738,497m
AC
ACAC
=
\ =\ =
1 os for 0 3602
y c x xo o= - £ £
( )
2 4 5 01 ( 5) 01 or 5
x xx xx x
- - =
+ - =
= - =
ü
ü
Ö
Ö
Ö
Ö
Ö=shape
ü ü ü
ü
Ö
ü
MARKING GUIDELINE -10- T...(E)(A…)T MATHEMATICS N2
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6.2.2
(1)
6.2.3
(1)
6.2.4
(2)
TP- ½ mark
x-intercepts(½mark & ½ mark) Y-intercept(½ mark) Shape (1 mark)
(3)
let 05
xy
== -
2( 4)2
2
bxa-
=
- -=
=
2
If 2 then(2) 4(2) 59
therefore, TP is (2; 9)
xy
=
= - -= -
-
ü
ü
ü ü
Ö
Ö Ö
Ö Ö
Ö
Ö
ü shape of parabola
Ö
üshape of straight line
ü
Ö
Ö
Ö ü
Ö
MARKING GUIDELINE -11- T...(E)(J)T MATHEMATICS N2
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6.3
x-intercept ½ mark y-intercept ½ mark shape 1 mark
(2)
6.4
(0;–5) and (5;0) (2) [16]
TOTAL: 100
Ö
Ö ü