n1 mathematics november 2016 memorandum · title: microsoft word - n1 mathematics november 2016...
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NATIONAL CERTIFICATE
NOVEMBER EXAMINATION
MATHEMATICS N1
21 NOVEMBER 2016
This marking guideline consists of 7 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T850(E)(N21)T MATHEMATICS N1
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QUESTION 1 1.1 1.1.1 3 1.1.2 -2 1.1.3 x 1.1.4 7 1.1.5 Constant
(5 × 1) (5) 1.2 1.2.1 243ü (1) 1.2.2 3ü (1) 1.2.3 5ü (1) 1.2.4 35 = 243üü (2) [10] QUESTION 2 2.1 2.1.1
üü
ü
ü
(4)
2.1.2
ü
ü ü
(3)
2.2
ü ü ü
ü
(3)
55
15320 32)(6
bbba ´-
51
5
1556 2)(6 ÷÷
ø
öççè
æ´-=
bbb
bbb3
6 26 ´-=
26 26 bb ´-=812b-=
23
31
-
úúû
ù
êêë
é÷øö
çèæ
2
271 -
úûù
êëé=
[ ]227=729=
[ ])(22)(2 yxxyx -+--]222[22 yxxyx -+--=
]24[22 yxyx ---=yxyx 2422 +--=
x2-=
MARKING GUIDELINE -3- T850(E)(N21)T MATHEMATICS N1
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2.3
ü
ü ü
ü
(4)
2.4
ü
ü ü
ü
(4)
[18] QUESTION 3 3.1 üüü
ü
ü ü
5 ü remainder 5
(7)
3.2
(-) üüü
(3)
3.3 3.3.1
üüüü
(4) 3.3.2
üü ü
üü
(5)
)4log25(log16loglog8 10102 +-+ee
)425(log2log4log218 102 ´-+•= ee
100log2log4log4 102 -+= ee10log22log4log4 102 -+= ee
)1(2)1(4)1(4 -+=6=
55.047.038,0 ´
=x
55,047,038,0
loglog´
=x
55,0log47,0log2138,0log -+=
)259,0()164,0(420,0 ---+-=325,0log -=x
473,0=x
522 ++ xx
50 23 -++ xxx2-x 23 2xx -
xx +22xx 42 2 -
55 -x105 -x
)52)(2( 2 ++-\ xxx
qrbcpd 706487 --qrbcpd 944768 ++-qrbcpd 164111155 --
232243 81624 xyzyxzyx --)123(8 2222 --= xyzzyxxy
yxxyx 22 23 +--)2()2( 23 yxyxx +-+-=
)2()2(2 ---= xyxx)2)(( 2 +-= xyx
MARKING GUIDELINE -4- T850(E)(N21)T MATHEMATICS N1
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3.4 ü
ü ü
(3)
3.4.1
üü
(2)
3.4.2 üü (2) [26] QUESTION 4 4.1
üü ü
ü ü
(5)
4.2
ü
ü
ü
ü
(4)
4.3 ü
ü
ü The number is 13
(3)
[12]
236236 332236 zyxzyx ´´´=zyxzyx 2222 75270 ´´=3434 52220 yzxyzx ´´=
336753322 zyx´´´´´3361260 zyx
yzx 22
)7(35)3(4 -=--- xx2135124 -=-+-= xx
72134 --=-- xx287 -=- x
4=x
gpT p2=
gpT
=p2
gpT
=÷øö
çèæ
2
2p
gpT
=2
2
4p224 gTp =p
2
2
4pgTp =\
8318 -=+ xx8183 --=- xx
262 -=- x13=x
MARKING GUIDELINE -5- T850(E)(N21)T MATHEMATICS N1
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QUESTION 5 5.1 5.1.1 Straight line 5.1.2 Negative 5.1.3 Rectangular hyperbola 5.1.4 No y-intercept 5.1.5 Second and fourth
(5 × 1) (5) 5.2
-2 -1 0 1 2 3 4 5 4 3 2 1 0 -1
(Half a mark each) (5) [10] QUESTION 6 6.1 Sum of interior angle of a triangle = 180°ü
AB = BC isosceles triangles ü
ü
ü
(4)
0
1
2
3
4
5
6
-3 -2 -1 0 1 2 3 4
Y-Values
00 18068 =Ð++ ACBx00 18068 =++ xx
00 180268 =+ x00 681802 -=x
2112
22 0
=x
056=\ x
xy
MARKING GUIDELINE -6- T850(E)(N21)T MATHEMATICS N1
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6.2
ü
ü
as the sides are in the same rationü
(3)
6.3
ü
or 16,6ü
(2)
[9] QUESTION 7 7.1
üü
üü
ü
ü
(6)
7.2 7.2.1 Perimeter = AC2 +BC+ABü
AD2 = AC2 – DC2 = 25 – 9 =16 cm2ü AD = 4 cm If AD = 4 cm
BD = 10 - 3 = 7 cm AB2 = AD2 + DB2 = (4)2 + (7)2 = 16 + 49 = 65 cm2 ü AB = 8,062 cm ü Perimeter = 5 +10 + 8,062 = 23,062 cmü
(5)
DFBC
EFAC
EDAB
==
2114
1812
2416
==
32
=
EDFABC DD\ ///
( ) ( ) 222 2026 x+=222 )20()26( -=\ x
400676 -=276=x692=x
( ) DAA tan.3tansin2 22-•
( ) 0002260tan.345tan45sin2 -•=
( )133
11
212
22
•-•÷÷ø
öççè
æ•=
31212 -••=
31-=2-=
ADBD
MARKING GUIDELINE -7- T850(E)(N21)T MATHEMATICS N1
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7.2.2 Area ✓
✓✓
✓
(4)
[15]
TOTAL: 100
bh21
=
4)10(21
´=
220 cm=