n1 mathematics april 2016 memorandum - future …...title microsoft word - n1 mathematics april 2016...
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NATIONAL CERTIFICATE
APRIL EXAMINATION
MATHEMATICS N1
1 APRIL 2016
This marking guideline consists of 8 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T930(E)(A1)T MATHEMATICS N1
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QUESTION 1 1.1 1ü 1.2 ü
1.3 10ü 1.4 66,667ü 1.5 R1,30 ü 1.6 -5ü 1.7 Hypotenuseü 1.8 ü
1.9 Isoscelesü 1.10 4ü
(10 x 1)
[10] QUESTION 2 2.1 2.1.1
ü ü
✓
(3)
2.1.2
ü
ü
ü
(3)
yx
xyDD
( ) ( ) cbcb aa +-´ 43
cbcb aa 4433 +- ´=ccbba 4343 +-+=
cba += 7
32
21
-
úúû
ù
êêë
é÷øö
çèæ
3
41 -
úûù
êëé=
3
14úûù
êëé=
34=64=
MARKING GUIDELINE -3- T930(E)(A1)T MATHEMATICS N1
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2.1.3
ü
ü
ü
ü
(4)
2.2
ü ü ü ü ü ü
(6)
2.3
üüü
(3)
2.4
ü ü
ü ü
(4)
[23]
343
0
729272
bbaab ´
31
6
433
33)1(2 ÷÷
ø
öççè
æ´=
bbaa
( )31
1436332 --´= baa
( )31
33332 baa´=aba 32 ´=
ba 26
( )
065,2312
364,3log
921,0124,2319,0
921,0124,2319,0
12,0log133log48,0log
12,013348,0loglog
12,013348,0
=
=
++=
--+-=
-+=
÷ø
öçè
æ ´=\
´=
x
x
x
x
xyxyyx 7416 22 -+
xyxyyx 4610 22 -+-xyxyyx 11106 22 -+
)]2(3[8 --+- xxx]63[8 ---= xxx638 ++-= xxx
610 += x)35(2 +x
MARKING GUIDELINE -4- T930(E)(A1)T MATHEMATICS N1
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QUESTION 3 3.1 üüü
ü ü ü ü ( )( remainder -28
(7)
3.2 3.2.1 ü
ü ü
(3) 3.2.2
= üü
(2)
3.2.3 üü (2) 3.3 3.3.1
ü üü üü
(5)
3.3.2
üüüü ONE mark each term
(4)
3.4
üü ONE mark for multiplication sign, factorise
ü
ü
(4) [27]
17126 2 +- xx
6706 23 +-+ xxx2+x 23 126 xx +
6712 2 +-- xxxx 2412 2 --617 +x3417 +x28-
2+x )17126 2 +- xx
24332 zyx 24352 zyx=33548 zyx 3354 32 zyx´=45270 zyx 452752 zyx´´
4555 7532 zyx´´´=4553360 zyx
2322 zyx
( ) ( )( ) ( )
( )( )xaybxayxabxyaybxab
aybxxyab
24242842
428
+-=+-+=--++=
-+-
222
41
41
21 yxxyx +-
( )2241 xyyxx +-=
xx
xxx
3530
5424 2 -
÷-
( )( )1653
5164
-´
-=
xx
xxx
53
54
´=x
2512x
=
MARKING GUIDELINE -5- T930(E)(A1)T MATHEMATICS N1
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QUESTION 4 4.1
üü ü ü
ü
(5)
4.2 üü
ü ü
(4)
4.3
ü
ü
ü
(3) [12]
)4(26)3(4 +=-- yyy826124 +=-- yyy
82122 +=-- yy12822 +=-- yy
420
44
=- y
5-=\ y
2444 =-x4244 +=x
284 =x7=\ x
2
31 gtp =
23 gtp =23 t
gp=
gpt 3
=\
MARKING GUIDELINE -6- T930(E)(A1)T MATHEMATICS N1
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QUESTION 5 5.1 -4 -3 -2 -1 0 1 2 3 4
1 1,33 2 4 ∞ -4 -2 -1,33 -1 y-axis 4 3
2 1 x-axis -4 -3 -2 -1 1 2 3 4 -1
-2
-3
-4
Scale: 1 cm = 1 unit ONE mark for correct scale in both axis One mark for indicating y-axis and x-axis
(8)
5.2 Rectangular hyperbolaü (1) 5.3 No y-interceptü (1) 5.4 2 and 4ü (1)
[11]
xy
MARKING GUIDELINE -7- T930(E)(A1)T MATHEMATICS N1
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QUESTION 6 6.1 ü
ü
ü
6.2 ü
ü
ü
6.3
ü ü
ü
(3 x 3)
[9]
QUESTION 7 7.1 7.1.1
ü
ü
(2)
7.1.2
ü
ü
(2)
7.2 Perimeter = 4L
= 4(6 cm) ü =24 cmü
(2)
0180264 =++ xxx
12180
1212 0
=x
15=x
00 18080 =++ xx00 801802 -=x
01002 =x050=x
( ) 222 1520 x+=222 )15()20( -=\ x
2254002 -=x175=x229,13=x
!! 60cos330sin2 +
÷øö
çèæ+÷
øö
çèæ=
213
212
2111+=
212=
25
=
( )000 45cos)45(sin30cos4
÷ø
öçè
æ÷ø
öçè
æ÷÷ø
öççè
æ=
21
21
234
÷øö
çèæ÷÷ø
öççè
æ=
21
132
3=
MARKING GUIDELINE -8- T930(E)(A1)T MATHEMATICS N1
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7.3 V = L × b × h
= 200 × 125 × 90ü = 2 250 000 m3 = 2 250 cm3 ü
(2) [8]
TOTAL: 100