Post on 30-Dec-2021
Web
site
: w
ww
.eku
rhu
len
ite
ch.c
o.z
a
Emai
l: in
fo@
eku
rhu
len
itec
h.c
o.z
a
MA
TH
EM
AT
IC
S N
1
Ty
pic
al ex
am
q
uest
io
ns
EKU
RH
ULE
NI T
ECH
CO
LLEG
E.
No
. 3 M
oga
le S
qu
are
, Kru
gers
do
rp.
Web
site
: w
ww
. eku
rhu
len
itec
h.c
o.z
a Em
ail:
info
@ek
urh
ule
nit
ech
.co
.za
TEL:
01
1 0
40
73
43
CEL
L: 0
73
77
0 3
02
8/0
60
71
5 4
52
9
Copyright reserved Please turn over
T850(E)(N21)T
NOVEMBER EXAMINATION
NATIONAL CERTIFICATE
MATHEMATICS N1
(16030121)
21 November 2016 (X-Paper)
09:00–12:00
REQUIREMENTS: Graph paper
Scientific calculators may be used.
This question paper consists of 6 pages and a formula sheet of 2 pages.
(16030121) -2- T850(E)(N21)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE
MATHEMATICS N1
TIME: 3 HOURS
MARKS: 100
INSTRUCTIONS AND INFORMATION
1.
2.
3.
4.
Answer ALL the questions.
Read ALL the questions carefully.
Number the answers according to the numbering system used in this question paper.
Write neatly and legibly.
(16030121) -3- T850(E)(N21)T
Copyright reserved Please turn over
QUESTION 1
1.1 Given: 457 2 xx
Use the above equation to complete the following sentences:
1.1.1 The expression has ... terms.
1.1.2 … is the highest exponent of x.
1.1.3 ... is the variable.
1.1.4 … is the coefficient of 2x
1.1.5 4 is the ... term
(5 × 1) (5)
1.2 Given: 5243log3
Answer the following questions using the above expression:
1.2.1 ... is the number. (1)
1.2.2 … is the base. (1)
1.2.3 ... is the logarithm. (1)
1.3 Write the expression in QUESTION 1.2 in exponential form. (2)
[10]
QUESTION 2
2.1 Simplify the following by making use only of exponential laws.
2.1.1 5
5
15320 32
)(6b
bba
(4)
2.1.2 23
3
1
(3)
2.2 Remove the brackets and simplify:
)(22)(2 yxxyx
(3)
(16030121) -4- T850(E)(N21)T
Copyright reserved Please turn over
2.3 Simplify the following logarithms without the use of a calculator:
)4log25(log16loglog8 10102 ee
(4)
2.4 Use logarithms with base 10 to determine the value of x. Show ALL the calculations.
55.0
47.038,0 x
(4)
[18]
QUESTION 3
3.1 Divide 53 xx by 2x (7)
3.2 Subtract qrpdbc 946847 from qrbcpd 706487 (3)
3.3 Fully factorise the following expressions:
3.3.1 232243 81624 xyzyxzyx (4)
3.3.2 yxxyx 22 23 (5)
3.4 Given: 23636 zyx ; zyx 2270 and 3420 yzx
By making use of prime factors, determine the following:
3.4.1 The LCM
3.4.2 The HCF
(7)
[26]
QUESTION 4
4.1 Solve for x.
)7(35)3(4 xx
(5)
4.2 Manipulate the formula to make p the subject of the formula if
g
pT 2
(4)
4.3 A certain number increased by 18 is three times the original number diminished
(decreased) by 8.
Find the number.
(3)
[12]
(16030121) -5- T850(E)(N21)T
Copyright reserved Please turn over
QUESTION 5
5.1 Given: 3)( xxg and x
xf4
)(
5.1.1 What type of graph is y = –x + 3?
5.1.2 Is the graph of g(x) positive or negative?
5.1.3 Give the name of f (x).
5.1.4 Give the y-intercept of f (x).
5.1.5 In which quadrant(s) will the graph of f (x) be?
(5 × 1) (5)
5.2 Use the following value of x to sketch the graph of g(x):
[-2 ; -1 ; 0 ; 1 ; 2 ; 3 ; 4 ]
(5)
[10]
QUESTION 6
6.1 Calculate, with a reason, the magnitude of x in the following triangle:
A
x
C
680
B
(4)
6.2 Show that the following triangles are similar:
B
D
24 21
16 14
A C E F
12 18
(3)
(16030121) -6- T850(E)(N21)T
Copyright reserved
6.3 Calculate the value of x in the following triangle:
x
P B
20
26
Y (2)
[9]
QUESTION 7
7.1
Simplify the following expressions by making use of the special angles. DO NOT
USE A CALCULATOR.
DAASin tan.3tan2 22
D
B
600
2 1
2 1
F 300 E
450
A C 3
1
(6)
7.2 A
5cm
B
D 3cm C
10cm
Use the shape above to determine the following:
7.2.1 Perimeter of triangle ABC (5)
7.2.2 Area of triangle ABC (4)
[15]
TOTAL: 100
(16030121) -1- T850(E)(N21)T
Copyright reserved
MATHEMATICS N1
FORMULA SHEET
Rectangle: Perimeter = 2(l + b)
Area = l × b
Reghoek: Omtrek = 2(l + b)
Area = l × b
Square: Perimeter = 4a
Area = a2
Vierkant: Omtrek = 4a
Area = a2
Triangle: Perimeter = a + b + c
Area = ½b × h
Driehoek: Omtrek = a + b + c
Area = ½b × h
Rectangular prism:
Volume = l × b × h
Reghoekige prisma:
Volume = l × b × h
Right triangular prism:
Volume = ½b × h × l
Regte driehoekige prisma:
Volume = ½b × h × l
Cube: Volume = a3 Kubus: Volume = a
3
Right pyramid:
Volume = 31 (base area × h)
Regte piramide:
Volume = 31 (basisarea × h)
Ellipse:
Area = 4
π(major axis × minor axis)
Ellips:
Area = 4
π(hoofas × neweas)
Circle: Circumference = D or 2r
Area = 4
πD2
or r2
Sirkel: Omtrek = D of 2r
Area = 4
πD2
of r2
Cylinder: Volume = h4
πD2
or r2h Silinder: Volume = h
4
πD2
of r2h
Cone: Volume = 3
h
4
πD2
or 3
hπr 2
Keël: Volume = 3
h
4
πD2
of 3
hπr 2
Annulus: A = 22 rR Annulus: A = 22 rR
(16030121) -2- T850(E)(N21)T
Copyright reserved
The right-angled triangle: Die reghoekige driehoek:
c
B
a
A θ C
b
The theorem of Pythagoras:
c2 = a
2 + b
2
Die stelling van Pythagoras:
c2 = a
2 + b
2
Ratios of angle θ : Verhoudings vir hoek θ :
c
aθsin
c
bθcos
b
aθtan
Copyright reserved Please turn over
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
Copyright reserved Please turn over
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 1.2.1 243 (1)
1.2.2 3 (1)
1.2.3 5 (1)
1.2.4 35
= 243 (2)
[10]
QUESTION 2
2.1 2.1.1 5
5
15320 32
)(6b
bba
5
1
5
1556 2)(6
b
bb
b
bb
36 2
6
26 26 bb 812b
(4)
2.1.2 23
3
1
2
27
1
227
729
(3)
2.2 )(22)(2 yxxyx
]222[22 yxxyx
]24[22 yxyx
yxyx 2422
x2
(3)
MARKING GUIDELINE -3- T850(E)(N21)T
MATHEMATICS N1
Copyright reserved Please turn over
2.3 )4log25(log16loglog8 10102 ee
)425(log2log4log2
18 102 ee
100log2log4log4 102 ee
10log22log4log4 102 ee
)1(2)1(4)1(4
6
(4)
2.4
55.0
47.038,0 x
55,0
47,038,0loglog
x
55,0log47,0log2
138,0log
)259,0()164,0(420,0
325,0log x
473,0x
(4)
[18]
QUESTION 3
3.1 522 xx
50 23 xxx
2x23 2xx
xx 22
xx 42 2
55 x
105 x
5
)52)(2( 2 xxx remainder 5
(7)
3.2 qrbcpd 706487
(-) qrbcpd 944768
qrbcpd 164111155
(3)
3.3 3.3.1 232243 81624 xyzyxzyx
)123(8 2222 xyzzyxxy
(4)
3.3.2 yxxyx 22 23
)2()2( 23 yxyxx
)2()2(2 xyxx
)2)(( 2 xyx
(5)
MARKING GUIDELINE -4- T850(E)(N21)T
MATHEMATICS N1
Copyright reserved Please turn over
3.4 236236 332236 zyxzyx
zyxzyx 2222 75270 3434 52220 yzxyzx
(3)
3.4.1 336753322 zyx 3361260 zyx
(2)
3.4.2 yzx 22 (2)
[26]
QUESTION 4
4.1 )7(35)3(4 xx
2135124 xx
72134 xx
287 x
4x
(5)
4.2
g
pT 2
g
pT
2
g
pT
2
2
g
pT
2
2
4
224 gTp
2
2
4
gTp
(4)
4.3 8318 xx
8183 xx
262 x
13x
The number is 13
(3)
[12]
MARKING GUIDELINE -5- T850(E)(N21)T
MATHEMATICS N1
Copyright reserved Please turn over
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
0
1
2
3
4
5
6
-3 -2 -1 0 1 2 3 4
Y-Values
x -2 -1 0 1 2 3 4 y 5 4 3 2 1 0 -1
(Half a mark each) (5)
[10]
QUESTION 6
6.1 00 18068 ACBx Sum of interior angle of a triangle = 180° 00 18068 xx AB = BC isosceles triangles
00 180268 x 00 681802 x
2
112
2
2 0
x
056 x
(4)
MARKING GUIDELINE -6- T850(E)(N21)T
MATHEMATICS N1
Copyright reserved Please turn over
6.2
DF
BC
EF
AC
ED
AB
21
14
18
12
24
16
3
2
EDFABC /// as the sides are in the same ration
(3)
6.3 2222026 x
222 )20()26( x
400676
276x
692x or 16,6
(2)
[9]
QUESTION 7
7.1
DAA tan.3tansin2 2
2
00022
60tan.345tan45sin2
1
33
1
1
2
12
22
312
12
31
2
(6)
7.2 7.2.1 Perimeter = AC2 +BC+AB
AD2 = AC
2 – DC
2
= 25 – 9
=16 cm2
AD = 4 cm
If AD = 4 cm
ADB BD = 10 - 3 = 7 cm
AB2 = AD
2 + DB
2
= (4)2 + (7)
2
= 16 + 49
= 65 cm2
AB = 8,062 cm
Perimeter = 5 +10 + 8,062
= 23,062 cm
(5)
MARKING GUIDELINE -7- T850(E)(N21)T
MATHEMATICS N1
Copyright reserved
7.2.2 Area bh
2
1 ✓
4)10(2
1 ✓✓
220 cm ✓
(4)
[15]
TOTAL: 100
Copyright reserved Please turn over
T930(E)(A1)T
APRIL EXAMINATION
NATIONAL CERTIFICATE
MATHEMATICS N1
(16030121)
1 April 2016 (X-Paper)
09:00–12:00
Nonprogrammable scientific calculators and graph paper may be used.
This question paper consists of 7 pages and 1 formula sheet of 2 pages.
(16030121) -2- T930(E)(A1)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE
MATHEMATICS N1
TIME: 3 HOURS
MARKS: 100
INSTRUCTIONS AND INFORMATION
1.
2.
3.
4.
Answer ALL the questions.
Read ALL the questions carefully.
Number the answers according to the numbering system used in this question paper.
Write neatly and legibly.
(16030121) -3- T930(E)(A1)T
Copyright reserved Please turn over
QUESTION 1
Choose the correct word(s) from those given in brackets. Write only the word(s) next to the
question number (1.1–1.10) in the ANSWER BOOK.
1.1 Natural numbers start at (-2; -1; 0; 1; 2 ).
1.2 The ratio of x to y is
yxyx
y
xxy ;;; .
1.3 The coefficient of 4x in the term of 410x is (40 ; x ; 10 ; -10 ; 10 x).
1.4 240 km/h equals to (864; 66,667; 0,067; 667) m/s.
1.5 Calculate the new price if the price of chocolate is R1,20 c and it is increased by 8%.
(R1,25; R1,30; R1,10; R1,50)
1.6 The y-intercept of 52 xy
5;5;
5
2;2 .
1.7 The side opposite the 90° is called (adjacent; hypotenuse; pythagoras; angle).
1.8 The formula to calculate gradient is
x
mx
y
x
a
y
x
;
;; .
1.9 (Equilateral; Scalene; Isosceles; Right-angled) triangle has two equal sides and two
equal angles.
1.10 Solve for x if 34
3
x ; Then x =
4
3;4;12;3 .
(10 x 1)
[10]
(16030121) -4- T930(E)(A1)T
Copyright reserved Please turn over
QUESTION 2
2.1 Simplify the following expressions by only using exponential and log laws:
2.1.1 cbcbaa
43 (3)
2.1.2 32
2
1
(3)
2.1.3 3
430
729
272
b
baab
(4)
2.2 Use logarithm base 10 to determine the value of x . Show ALL the calculations.
12,0
13348,0 x
(6)
2.3 Add the following terms: xyxyyx 7416 22 and .1046 22 yxxyxy (3)
2.4 Remove the brackets and simplify:
)]2(3[8 xxx
(4)
[23]
QUESTION 3
3.1 Divide: 676 3 xx by .2x (7)
3.2 Use 24332 zyx ; 33548 zyx and 45270 zyx to answer the questions.
3.2.1 Show the prime factors of each of the terms. (3)
3.2. 2 Determine the LCM. (2)
3.2.3 Determine the HCF. (2)
3.3 Fully factorise the following :
3.3.1 aybxxyab 428 (5)
3.3.2 222
4
1
4
1
2
1yxxyx
(4)
(16030121) -5- T930(E)(A1)T
Copyright reserved Please turn over
3.4 Simplify:
x
x
x
xx
3
530
5
424 2
(4)
[27]
QUESTION 4
4.1 Solve for :y
)4(26)3(4 yyy
(5)
4.2 Solve the number:
Four less than four times a number is equal to 24.
(4)
4.3 Make t the subject of the formula:
2
3
1gtp
(3)
[12]
QUESTION 5
Given the function :4
xy
5.1 Use the table method to sketch the graph of x
y4
for the domain
{-4;-3; -2; -1; 0; 1; 2; 3; 4}.
(8)
5.2 Give the name of the graph. (1)
5.3 What is the y-intercept? (1)
5.4 In which quadrants is the graph drawn? (1)
[11]
(16030121) -6- T930(E)(A1)T
Copyright reserved Please turn over
QUESTION 6
Calculate the magnitude of x in the following diagram:
6.1
6 x
4 x 2 x
6.2 Adjust the sketch to show that the sides are equal.
x
800
6.3 x
B A
15 20
C
(3 x 3)
[9]
(16030121) -7- T…(E)(A1)T
Copyright reserved
QUESTION 7
7.1
2 60°
2 1 1
30°
45°
1 3
Simplify the following expressions by making use of the special angle. Do not use a
calculator.
7.1.1 60cos330sin2 (2)
7.1.2 45cos)45(sin30cos4 (2)
7.2 Find the perimeter of the following square:
L = 60 cm
(2)
7.2 Determine the volume in cubic centimetre if the dimensions of the rectangular prism
are: length 200 mm; breadth 125 mm and height 90 mm.
(2)
[8]
TOTAL: 100
(16030121) -1- T930(E)(A1)T
Copyright reserved Please turn over
MATHEMATICS N1
FORMULA SHEET
Rectangle: Perimeter = 2(l + b)
Area = l × b
Square: Perimeter = 4a
Area = a2
Triangle: Perimeter = a + b + c
Area = ½b × h
Rectangular prism:
Volume = l × b × h
Right triangular prism:
Volume = ½b × h × l
Cube: Volume = a3
Right pyramid:
Volume = 31 (base area × h)
Ellipse:
Area = 4
π(major axis × minor axis)
Circle: Circumference = D or 2r
Area = 4
πD2
or r2
Cylinder: Volume = h4
πD2
or r2h
Cone: Volume = 3
h
4
πD2
or 3
hπr 2
Annulus: A = 22 rR
(16030121) -2- T930(E)(A1)T
Copyright reserved
The right-angled triangle:
c
B
a
A θ C
b
The theorem of Pythagoras:
c2 = a
2 + b
2
Ratios of angle θ :
c
aθsin
c
bθcos
b
aθtan
Copyright reserved Please turn over
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
Copyright reserved Please turn over
QUESTION 1
1.1 1
1.2
y
x
1.3 10
1.4 66,667
1.5 R1,30
1.6 -5
1.7 Hypotenuse
1.8
x
y
1.9 Isosceles
1.10 4
(10 x 1)
[10]
QUESTION 2
2.1 2.1.1 cbcbaa
43
cbcb aa 4433 ccbba 4343
cba 7 ✓
(3)
2.1.2 32
2
1
3
4
1
3
1
4
34 64
(3)
MARKING GUIDELINE -3- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved Please turn over
2.1.3 3
430
729
272
b
baab
3
1
6
433
3
3)1(2
b
baa
31
1436332 baa
31
33332 baa
aba 32
ba 26
(4)
2.2
065,2312
364,3log
921,0124,2319,0
921,0124,2319,0
12,0log133log48,0log
12,0
13348,0loglog
12,0
13348,0
x
x
x
x
(6)
2.3 xyxyyx 7416 22
xyxyyx 4610 22
xyxyyx 11106 22
(3)
2.4 )]2(3[8 xxx
]63[8 xxx
638 xxx
610 x
)35(2 x
(4)
[23]
MARKING GUIDELINE -4- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 3
3.1 17126 2 xx
6706 23 xxx
2x 23 126 xx
6712 2 xx
xx 2412 2
617 x
3417 x
28
( 2x )( )17126 2 xx remainder -28
(7)
3.2 3.2.1 24332 zyx24352 zyx
33548 zyx3354 32 zyx
45270 zyx452752 zyx
(3)
3.2.2 4555 7532 zyx
=4553360 zyx
(2)
3.2.3 2322 zyx (2)
3.3 3.3.1
xayb
xayxab
xyaybxab
aybxxyab
24
242
842
428
(5)
3.3.2 222
4
1
4
1
2
1yxxyx
224
1xyyxx ONE mark each term
(4)
3.4
x
x
x
xx
3
530
5
424 2
165
3
5
164
x
x
x
xx ONE mark for multiplication sign, factorise
5
3
5
4
x
25
12x
(4)
[27]
MARKING GUIDELINE -5- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 4
4.1 )4(26)3(4 yyy
826124 yyy
82122 yy
12822 yy
4
20
4
4
y
5 y
(5)
4.2 2444 x
4244 x
284 x
7x
(4)
4.3 2
3
1gtp
23 gtp
23t
g
p
g
pt
3
(3)
[12]
MARKING GUIDELINE -6- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 5
5.1 x -4 -3 -2 -1 0 1 2 3 4 y 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 hyperbola (1)
5.3 No y-intercept (1)
5.4 2 and 4 (1)
[11]
MARKING GUIDELINE -7- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 6
6.1 0180264 xxx
12
180
12
12 0
x
15x
6.2 00 18080 xx 00 801802 x
01002 x 050x
6.3 2221520 x
222 )15()20( x
2254002 x
175x
229,13x
(3 x 3)
[9]
QUESTION 7
7.1 7.1.1 60cos330sin2
2
13
2
12
2
111
2
12
2
5
(2)
7.1.2 000 45cos)45(sin30cos4
2
1
2
1
2
34
2
1
1
32
3
(2)
7.2 Perimeter = 4L
= 4(6 cm)
=24 cm
(2)
MARKING GUIDELINE -8- T930(E)(A1)T
MATHEMATICS N1
Copyright reserved
7.3 V = L × b × h
= 200 × 125 × 90
= 2 250 000 m3
= 2 250 cm3
(2)
[8]
TOTAL: 100
Copyright reserved Please turn over
T930(E)(A6)T
AUGUST EXAMINATION
NATIONAL CERTIFICATE
MATHEMATICS N1
(16030121)
6 August 2015 (Y-Paper)
13:00–16:00
REQUIREMENT: Graph paper
Scientific calculators may be used.
This question paper consists of 7 pages and 1 formula sheet of 2 pages.
(16030121) -2- T930(E)(A6)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE
MATHEMATICS N1
TIME: 3 HOURS
MARKS: 100
INSTRUCTIONS AND INFORMATION
1.
2.
3.
4.
5.
Answer ALL the questions.
Read ALL the questions carefully.
Number the answers according to the numbering system used in this question paper.
Round answers off to three decimal numbers (where applicable).
Write neatly and legibly.
(16030121) -3- T930(E)(A6)T
Copyright reserved Please turn over
QUESTION 1
1.1 1.1.1 250 km /h equals … m/s. (2)
1.1.2 The reciprocal of 20 is … (1)
1.1.3 Express 370 mm as a percentage of 1,225 m. (2)
1.2 Given: 747 3 xx
1.2.1 … is the exponent of x.
1.2.2 7 is the … of x-3
.
1.2.3 … is the variable.
1.2.4 … is the constant term.
1.2.5 The number of terms is …
(5 x 1)
(5)
[10]
QUESTION 2
2.1 Simplify the following by only making use of exponential laws:
55
15800 243
)(5a
aba
(4)
2.2 Subtract cba 82414 from .10412 cab (3)
2.3 Simplify: 426 1648 aaa (3)
2.4 Divide 51412 23 ddd by .1d
Then indicate the quotient and remainder.
(7)
2.5 Remove the brackets and simplify the following :
)103)(3( 2 yyy
(5)
[22]
(16030121) -4- T930(E)(A6)T
Copyright reserved Please turn over
QUESTION 3
3.1 Show the prime factors of each of the following expressions:
cab
bca
bca
2
2
3
81
30
12
Now determine the highest common factor (HCF) and the lowest common multiple
(LCM) of the expressions.
(7)
3.2 Simplify the following logarithms without the use of a calculator. Show ALL the
steps.
32log9log100log325log 23105
(5)
3.3 Simplify the fraction:
abba 5
8
2
1
3
42
(4)
3.4 Simplify the following:
20
4422 xy
xy
yxxy
(4)
[20]
QUESTION 4
4.1 Solve for x:
)10(65511 xx
(4)
4.2 The sum of THREE successive uneven numbers is 21. Determine the THREE
numbers.
Let the first number be x.
(5)
4.3 hrV 2
2
1 is the formula used to calculate the volume of a cone .
Manipulate the formula to make r the subject of the formula.
(3)
4.4 Calculate the value of r in QUESTION 4.3 if V = 9 and h = 5. (2)
[14]
(16030121) -5- T930(E)(A6)T
Copyright reserved Please turn over
QUESTION 5
5.1 Sketch the graph [( x ; y ) ( )]12 xy by using a table of values.
Use values of x ranging from -2 to 1
Use a scale of 1 cm = 1 unit on both axis. Indicate the x and y axis.
(6)
5.2 Give the name of the graph you have sketched in QUESTION 5.1. (1)
5.3 Given : The graph of cmxy
Y
X
-3
-3
5.3.1 Give the coordinate of the y-intercept of the graph.
5.3.2 Give the slope of the graph.
5.3.3 Does this graph have a positive of a negative slope?
(3 x 1)
(3)
[10]
QUESTION 6
6.1 Determine the size of the interior angle x if the exterior angle .130
C
A
860
B x 1300 D
C
(2)
(16030121) -6- T930(E)(A6)T
Copyright reserved Please turn over
6.2 In the given figure below 90
A ; cmEA 5,22 ; .33 cmEF
F
33 cm
A E
22,5 cm
6.2.1 Calculate the length of side AF. (4)
6.2.2 Give the value of ))(sin(cos . (3)
6.3 Prove that 4
360sin45cos2
200 by making use of special angles. Do NOT use
a calculator.
HINT:
2 600
2
1 1
300
450
3 1
(4)
[13]
(16030121) -7- T930(E)(A6)T
Copyright reserved
QUESTION 7
7.1 A floor has to be covered with tiles.
7.1.1 Calculate the area in metres of a tile with dimensions 415 mm × 390 mm.
7.1.2 Calculate the area of the floor measuring 4,5 m by 5,5 m.
7.1.3 Hence, calculate how many tiles you will need to tile the floor.
(3 x 2)
(6)
7.2 The price of Sasko bread is R7,80c and it is increased by 8%. Calculate the new
price.
(3)
7.3 Calculate the area of the following:
10 mm
18 mm
(2)
[11]
TOTAL: 100
(16030121) -1- T930(E)(A6)T
Copyright reserved
MATHEMATICS N1
FORMULA SHEET
This sheet must accompany the question paper.
Rectangle: Perimeter = 2(l + b)
Area = l × b
Square: Perimeter = 4a
Area = a2
Triangle: Perimeter = a + b + c
Area = ½b × h
Rectangular prism:
Volume = l × b × h
Right triangular prism:
Volume = ½b × h × l
Cube: Volume = a3
Right pyramid:
Volume = 31 (base area × h)
Ellipse:
Area = 4
π(major axis × minor axis)
Circle: Circumference = D or 2r
Area = 4
πD2
or r2
Cylinder: Volume = h4
πD2
or r2h
Cone: Volume = 3
h
4
πD2
or 3
hπr 2
Annulus: A = 22 rR
(16030121) -2- T930(E)(A6)T
Copyright reserved
The right-angled triangle:
c
B
a
A θ C
b
The theorem of Pythagoras:
c2 = a
2 + b
2
Ratios of angle θ :
c
aθsin
c
bθcos
b
aθtan
Copyright reserved Please turn over
NATIONAL CERTIFICATE
AUGUST EXAMINATION
MATHEMATICS N1
6 AUGUST 2015
This marking guideline consists of 7 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 1
1.1 1.1.1 69,444 m/s ✓✓ (2)
1.1.2
20
1
✓
(1)
1.1.3 30,204% ✓✓ (2)
1.2 1.2.1 1 ; -3 ✓ any one exponent
1.2.2 Coefficient ✓
1.2.3 x ✓
1.2.4 -7 ✓
1.2.5 3 ✓
(5 x 1)
(5)
[10]
QUESTION 2
2.1 5
5
15800 243
)(5a
aba
51
51558 3)1(5 a ✓✓ 235 a ✓
215a ✓
(4)
2.2 12b – 4a – 10c
(-)-24b + 14a + 8c
36b – 18a – 18c ✓✓✓ ( ONE mark per term )
(3)
2.3 426 1648 aaa = 48 1632 aa ✓
= 4)(82 a ✓
= 122a ✓
(3)
MARKING GUIDELINE -3- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved Please turn over
2.4 3112 dd ✓✓✓ ( ONE mark per term)
1d 51412 23 ddd
23 dd ✓
dd 1411 2
dd 1111 2 ✓
53 d
33 d ✓
2 ✓
Quotient: ( 3112 dd )
Remainder: 2 ✓
(7)
2.5 )103)(3( 2 yyy 3093103 223 yyyyy √√√√√√ (half mark per term)
306 23 yyy √√√√ ( half mark per term)
(5)
[22]
QUESTION 3
3.1
cababc
bcabca
bcabca
24
22
323
381
53230
2312
✓✓✓ ( ONE mark per term )
cba
LCM
23
24
1620
523
✓✓ ONE mark for the value, one mark for the variables
abcHCF 3 ✓✓ ONE mark for the value, one mark for the variables
(7)
3.2 32log9log100log325log 23105
5
2
2
3
2
10
2
5 2log3log10log35log √√√√ ( half mark per term) 5)1(2)1)(2(3)1(2 ✓
5262 ✓ 1 ✓
(5)
3.3
abba 5
8
2
1
3
42
2
2
30
481540
ab
bab ✓✓✓✓ONE mark for each term of the numerator
ONE mark for the LCD
(4)
MARKING GUIDELINE -4- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved Please turn over
3.4
20
4422 xy
xy
yxxy
xyxy
yxxy
44
2022
✓ division becomes multiplication & fraction turns
)1(4
20)1(
xyxy
xyxy
✓✓ for the factors
5 ✓
(4)
[20]
QUESTION 4
4.1 )10(65511 xx xx 660516 ✓
166065 xx ✓
11
44
11
11
x✓
4x ✓
(4)
4.2 2142 xxx ✓✓ ONE mark for the uneven numbers / 2163 x ONE mark for the addition sign and equal to 21 6213 x
153 x ✓ 5x ✓
The three numbers are:
5, 7 and 9 ✓ If only the three numbers are given, give one mark only
(5)
4.3 hrV 2
2
1
hrV 22 ✓ 22
rh
V
✓
h
Vr
2 ✓
(3)
4.4
h
Vr
2
)5(
92
r ✓
071.1 ✓
(2)
[14]
MARKING GUIDELINE -5- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 5
5.1 x -2 -1 0 1
y -3 -1 1 3
y-axis√
7 12 xy
6
5√scale ✓for sketching a straight line
4
3
2
√scale 1 ✓for the y-intercept
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x-axis√
-1
- 2
-3
-4
√√√√ Half mark for calculating and plotting each of the coordinates correctly
√√ Half mark for labelling of each of the axes
√√ marks for correct scale on each of the axes
✓ONE mark for straight line graph
✓ONE mark for 1 as y intercept
(6)
5.2 Straight line ✓ (1)
5.3 5.3.1 (0;-3)✓
5.3.2 m = -1✓
5.3.3 Negative slope✓
(3 x 1)
(3)
[10]
MARKING GUIDELINE -6- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved Please turn over
14,24
75,582
335,22
2
222
222
AF
AF
AF
EFAEAF
QUESTION 6
6.1
0130
BA 00 13086 x ✓ 00 86130 x
044 ✓
(2)
6.2
6.2.1
✓✓
✓ ✓
(4)
6.2.2
1089
15,543
)33
14,24)(
33
5,22(
✓✓✓
(3)
6.3 4
360sin45cos2
200
2)2
3(
2
12 LHS ✓✓
4
3
4
3.1
✓✓
(4)
[13]
MARKING GUIDELINE -7- T930(E)(A6)T
MATHEMATICS N1
Copyright reserved
QUESTION 7
7.1 7.1.1 Area of one tile = 0,415 × 0,390✓
= 0,162 m2✓
7.1.2 Floor area = 4,5 × 5,5 ✓
= 24,75 m2✓
7.1.3 Number of tiles required =
162,0
75,24
= 152,9✓
Need 153 tiles✓
(3 x 2)
(6)
7.2 8% of R7,80c
= 0,08 × R7,80 ✓
= 0,62✓
Therefore R7,80c + 0,62
The new price is R8,42c✓
(3)
7.3 A = l × b
= 18 × 10 ✓
= 180 mm2 ✓
(2)
[11]
TOTAL: 100
Copyright reserved Please turn over
T920(E)(N14)T
NOVEMBER EXAMINATION
NATIONAL CERTIFICATE
MATHEMATICS N1
(16030121)
14 November 2014 (Y-Paper)
13:00–16:00
REQUIREMENTS: Graph paper
A scientific calculator may be used.
This question paper consists of 6 pages, a answer sheet (graph paper) and
a formula sheet of 2 pages.
(16030121) -2- T920(E)(N14)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE
MATHEMATICS N1
TIME: 3 HOURS
MARKS: 100
INSTRUCTIONS AND INFORMATION
1.
2.
3.
4.
5.
6.
7.
8.
Answer ALL the questions.
Read ALL the questions carefully.
Number the answers according to the numbering system used in this question paper.
Start each question on a NEW page.
Use a pencil for drawings.
The answers of ALL calculations must be approximated to THREE decimals.
Rough calculations may be done at the back of the ANSWER BOOK.
Write neatly and legibly.
(16030121) -3- T920(E)(N14)T
Copyright reserved Please turn over
QUESTION 1
Choose the correct answer from those given in brackets. Write only the answer next to the
question number (1.1–1.10) in the ANSWER BOOK.
1.1 Simplify the following: 25 22
= [ 2
7 ; 8 ; 128 ; 4
7 ; 11 ]
1.2 How many terms does the following expression have?
baba 46)(4 2
= [ 1; 2; 3; 4; 5]
1.3 270 km/h equals … m/s
[16; 6; 75; 216; 120; 972]
1.4 The ratio of x to y is represented by:
xy[ ; y
x ;
yx ;
]yx
1.5
The graph of x
y3
must be drawn in the following quadrant (s):
[ 2 & 3 ; 1 & 2 ; 2 & 4 ; 1 & 3 ]
1.6 If tan C = 26 , then the value of angle C is …
[ 0,4880 ; 54
0 ; 87,8
0 ; 68, 96
0 ]
1.7 … is the symbol of similar triangles.
( ; ||| ; = ; )
1.8 An integer is …
3
2[
; 1,2 ; -2 ; 2,5 ; 3
2
]
1.9 The graph of 63 xy has the y-intercept of :
[3 ; -2 ; -6 ; 6 ]
1.10 Solve for x if 3
ax= 3 ; then x = [ 9a ; a ; a
1
; a
9
]
(10 x 1)
.
[10]
(16030121) -4- T920(E)(N14)T
Copyright reserved Please turn over
QUESTION 2
2.1 Simplify the following expressions by only using exponent and log laws.
Leave answers with positive exponents.
2.1.1 cbcbaa
65
(4)
2.1.2 3
10
5
1
278243
(4)
2.1.3
3
3log DD
(2)
2.2 Simplify the following without a calculator:
2 logee3 + log216 – log 100
(4)
2.3 Calculate the product of: 3234 aa
(3)
2.4 Divide 144 23 aaa by 1a (6)
2.5 Remove the brackets and simplify the following:
236 aaa
(3)
[26]
QUESTION 3
3.1 Factorise the following expressions:
3.1.1 3224 162440 xyyxyx
(2)
3.1.2 anamnm 3
(2)
3.2 Determine the lowest common multiple (LCM) and the highest common factor (HCF)
of the following: (Use prime factors)
46440 cba 23490 cba
35260 cba
(5)
3.3 Solve for y
1023
5
yy
(3)
(16030121) -5- T920(E)(N14)T
Copyright reserved Please turn over
3.4 Simplify the following:
aba
cba
ba
cba
1515
555
44
2222
(5)
[17]
QUESTION 4
4.1 The total resistance of resistors connected in parallel in a circuit is given by
21
111
RRRT
Make R2 the subject of the formula
(4)
4.2 Determine the velocity of a point on the circumference of a shaft if the shaft has a
diameter of 40 mm and rotates at 50 revolutions per minute. Give the answer in m/s.
HINT: V = 2πrm
(5)
[9]
QUESTION 5
5.1 Complete the TABLE below in the ANSWER BOOK. Use the graph paper supplied
to draw the graph of xy sin
x
00
300
600
900
1200
1500
1800
2100
2400
2700
3000
3300
3600
y
[13]
QUESTION 6
6.1 Given :
A
y
370
B C
6.1.1 What is the name of the above triangle? Give a reason for your answer. (2)
6.1.2 Determine the value of y of the triangle in QUESTION 6.1.1. (4)
(16030121) -6- T920(E)(N14)T
Copyright reserved Please turn over
6.2 Simplify the following expression by making use of the special angles. Do not use a
calculator.
0
000
30tan
60tan60cos30sin4
600
2 1
300
3
(5)
6.3 Determine the value of B if B = tan 60028’ (2)
[13]
QUESTION 7
7.1 Determine the length of the hypotenuse of a right angle triangle, if the length of the
two adjacent sides of the triangle are 14 mm and 16 mm respectively.
(3)
7.2 A builder needs 12 000 bricks to complete a building. How many bricks must he
order if he anticipate that 6% of the bricks will break.
(3)
7.3 Calculate the area of the following figure:
40 mm
12 mm
HINT: The top is a semicircle. (6)
[12] TOTAL: 100
(16030121) -7- T920(E)(N14)T
Copyright reserved Please turn over
EXAMINATION NUMBER:
CENTRE NUMBER:
(16030121) -8- T920(E)(N14)T
Copyright reserved Please turn over
MATHEMATICS N1
FORMULA SHEET
Rectangle: Perimeter = 2(l + b)
Area = l × b
Reghoek: Omtrek = 2(l + b)
Area = l × b
Square: Perimeter = 4a
Area = a2
Vierkant: Omtrek = 4a
Area = a2
Triangle: Perimeter = a + b + c
Area = ½b × h
Driehoek: Omtrek = a + b + c
Area = ½b × h
Rectangular prism:
Volume = l × b × h
Reghoekige prisma:
Volume = l × b × h
Right triangular prism:
Volume = ½b × h × l
Regte driehoekige prisma:
Volume = ½b × h × l
Cube: Volume = a3 Kubus: Volume = a
3
Right pyramid:
Volume = 31 (base area × h)
Regte piramide:
Volume = 31 (basis area × h)
Ellipse:
Area = 4
π(major axis × minor axis)
Ellips:
Area = 4
π(hoofas × newe as)
Circle: Circumference = D or 2r
Area = 4
πD2
or r2
Sirkel: Omtrek = D of 2r
Area = 4
πD2
of r2
Cylinder: Volume = h4
πD2
or r2h Silinder: Volume = h
4
πD2
of r2h
Cone: Volume = 3
h
4
πD2
or 3
hπr 2
Keël: Volume = 3
h
4
πD2
of 3
hπr 2
Annulus: A = 22 rR Annulus: A = 22 rR
-1-
(16030121) -9- T920(E)(N14)T
Copyright reserved Please turn over
The right-angled triangle: Die reghoekige driehoek:
c
B
a
A θ C
b
The theorem of Pythagoras:
c2 = a
2 + b
2
Die stelling van Pythagoras:
c2 = a
2 + b
2
Ratios of angle θ : Verhoudings vir hoek θ :
c
aθsin
c
bθcos
b
aθtan
-2-
Copyright reserved Please turn over
NATIONAL CERTIFICATE
NOVEMBER EXAMINATION
MATHEMATICS N1
14 NOVEMBER 2014
This marking guideline consists of 8 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 1
1.1 8
1.2 2
1.3 75
1.4
y
x
1.5 2 & 4
1.6 87,80
1.7 |||
1.8 -2
1.9 -6
1.10
a
9
(10 x 1)
[10]
QUESTION 2
2.1 2.1.1 cbcbaa
65
cbcb ba 6655 ✓
ccbb ba 6565 . ✓
cb ba .11 ✓
c
b
a
a11
✓
(4)
2.1.2 3
10
5
1
278243
31
35
1
5 31)3( ✓ ✓
313 ✓
7 ✓
(4)
2.1.3
3
3log DD
3log. 3DD ✓
)1.(D
D ✓
(2)
2.2 2 logee3 + log2 16 – log 100
= 2 10log22log4log3 2 eoe ✓ ✓ ✓
= 6 + 4 – 2
= 8✓
(4)
MARKING GUIDELINE -3- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
2.3 3234 aa
32 2716 aa ✓ ✓
5432 a ✓
(3)
2.4 132 aa ✓ ✓ ✓
1a 144 23 aaa
23 aa ✓
aa
aa
33
43
2
2
✓
1a ✓
1a 0
)13)(1( 2 aaa
(6)
2.5 236 aaa
636 aaa ✓
646 aa ✓
62 a ✓
(3)
[26]
QUESTION 3
3.1
3.1.1 3224 162440 xyyxyx
23 2358 yxyxxy ✓ ✓
(2)
3.1.2 anamnm 3
nmanm 3 ✓
anm 3 ✓
(2)
3.2 464464 522240 cbacba ✓
234234 533290 cbacba ✓
352352 532260 cbacba ✓
464
46423
360
532
cba
cbaLCM
✓
232
232
10
52
cba
cbaHCF
✓
(5)
MARKING GUIDELINE -4- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
3.3 10
23
5
yy
106
)(3)5(2
yy✓
603210 yy ✓ 106032 yy
505 y
10y ✓
(3)
3.4
aba
cba
ba
cba
1515
555
44
2222
)(5
)(15
)(4
)(2
cba
baa
ba
cba
✓ ✓ ✓ 1 mark for multiplication, 2 marks for common f
5
15
4
2 a ✓
1
3
2
1 a
2
3a ✓
(5)
[17]
QUESTION 4
4.1
21
111
RRRT
21
111
RRRT
✓
21
1 1
RRR
RR
T
T
✓
112 RRRRR TT ✓
1
12
RR
RRR
T
T
✓
(4)
MARKING GUIDELINE -5- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
4.2 rnv 2
50)20(2 ✓ 202
40
2
Dr ✓
min/185,6283 mm ✓
1000
185,6283/ sm
min/283,6 m ✓
60
283,6
sm /105,0 ✓
(5)
[9]
QUESTION 5
5.1
y
00
300
600
900
1200
1500
1800
2100
2400
2700
3000
3300
3600
x
0 0,5
√
0,9
√
1
√
0,9
√
0,5
√
0
√
-0,5
√
-0,9
√
-1
√
-0,9
√
-0,5
√
0√
(6)
MARKING GUIDELINE -6- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
7 marks for graph
(7)
[13]
✓ Shape
✓ Scale; Label; x and y-axes
y = sin x
MARKING GUIDELINE -7- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 6
6.1
6.1.1 Isosceles triangle ✓
because two sides are equal in length ✓
OR
AB=AC✓
(Any 1 reason)
(2)
6.1.2
CB
CBA 0180✓ Isosceles triangles
000 1803737 y ✓
00 74180 y ✓ 0106y ✓
(4)
6.2 0
000
30tan
60tan60cos30sin4
3
11
3
2
1
2
14
✓ ✓ ✓
3
11
3
1
1
1
3
1
31 ✓
3 ✓
(5)
6.3 '02860tanB 0467,60tan ✓
765,1B ✓
(2)
[13]
MARKING GUIDELINE -8- T910(E)(N14)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 7 7.1 222 1614 x ✓
256196 ✓
452
260,21 ✓
(3)
7.2 Extra brick required 00012100
6 ✓ =720✓
Total no of bricks = 12 000 + 720
= 12 720 ✓
(3)
7.3 Area of the semi-circle
2
2
1r ✓
2402
1 ✓
2274,2513 mm ✓
Area of the triangle bh2
1 ✓
12080
2
1
28004 mm ✓
(6)
[12]
Total area 8004274,5132 2274,3137 mm ✓
TOTAL: 100
Copyright reserved Please turn over
T910(E)(J24)T
AUGUST EXAMINATION
NATIONAL CERTIFICATE
MATHEMATICS N1
(16030121)
24 July 2014 (Y-Paper)
13:00–16:00
Scientific calculators may be used.
This question paper consists of 6 pages, a graph paper and a formula sheet of 2 pages.
(16030121) -2- T910(E)(J24)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE
MATHEMATICS N1
TIME: 3 HOURS
MARKS: 100
INSTRUCTIONS AND INFORMATION
1.
2.
3.
4.
5.
6.
7.
8.
Answer ALL the questions.
Read ALL the questions carefully.
Number the answers according to the numbering system used in this question paper.
The answers of ALL calculations must be approximated to THREE decimals.
Rough calculations may be done at the back of the ANSWER BOOK.
Use a pencil for drawings.
Start each question on a NEW page.
Write neatly and legibly.
(16030121) -3- T910(E)(J24)T
Copyright reserved Please turn over
QUESTION 1 Indicate whether the following statements are TRUE or FALSE. Choose the answer and write
only 'true' or 'false' next to the question number (1.1–1.10) in the ANSWER BOOK.
1.1 24 km/h equals to 667 m/s. 1.2 The graph of 5123 xy has the gradient of 12.
1.3 The coefficient of x4 in the term of
410x is 10.
1.4 Natural numbers start at 1.
1.5
12
11
5
8
7
3
1.6 The following expression has three terms
c
baba
3
8)2(36
42
1.7 is the symbol to indicate congruent triangles.
1.8 320 cm2 is equal to 0,0320 m
2.
1.9 If 20% of an amount of money is R105,25c, then the amount of money is R526,25c 1.10 The exterior angle of a triangle can be obtained when one side of a triangle is
extended.
(10 × 1)
[10] QUESTION 2 2.1 Simplify the following without the use of a calculator:
2.1.1 33
12
93
281
27ba
b
ba
(5)
2.1.2
429
8
164 bbb
(4)
2.1.3 10log3log80001log664log2 e
e
(5)
2.2 Subtract bdpqqr 351156 from bdpqqr 14010815 (3)
2.3 Divide 32
136 234 xxxx by 12 x . Show ALL the steps.
(7)
[24]
(16030121) -4- T910(E)(J24)T
Copyright reserved Please turn over
QUESTION 3
Simplify by factorising fully:
3.1 2
83
17
8551
D
DD
(2)
3.2 q
pp
q
pp
8
62
4
217 232
(4)
3.3 Add: 3
243 2
2
x
xx
x
(4)
3.4 Determine from 222334 15;21 zyxzyx and 427xyz
3.4.1 The LCM (4)
3.4.2 The HCF by using prime factors (1)
3.5 Fully factorise the following expressions:
3.5.1 pqdpqzpq 632745 (2)
3.5.2 axayyx 66 (4)
[21]
QUESTION 4
4.1 Solve for x
)6(3)3(5 xx
(3)
4.2 Change the subject of the formula so that the symbol in brackets becomes the new
subject
2
2QrA ……………………(r)
(3)
4.3 The difference between twice a number and six equals to twelve.
Calculate the number.
Let the number be x.
(4)
[10]
(16030121) -5- T910(E)(J24)T
Copyright reserved Please turn over
QUESTION 5
Given 14 xy and x
y3
Hence answer the following questions
5.1 Give the equation of the straight line graph. (1)
5.2 Is the slope of the straight line graph positive or negative? (1)
5.3 Give the name of the other graph. (1)
5.4 In which quadrant(s) will the other graph be sketched? (1)
5.5 Give the value of the slope value of the straight line graph? (1)
5.6 Give the y-intercept of the straight line graph? (1)
5.7 Use x-values if 2
1; 1; 2; 3; 4 to sketch the graph mentioned in QUESTION 5.3; using
the scale of 1 cm = 1 unit
(4)
[10]
QUESTION 6
6.1 In ABC : BC =5 cm; AC = 7 cm and 090
B
A
7 cm
B 5 cm C
6.1.1 Calculate the magnitude of angle C?
(3)
6.1.2 Calculate AB with the aid of the theorem of Pythagoras (3)
6.2 By means of a line drawing, distinguish between the following:
6.2.1 An obtuse angle
6.2.2 Opposite angles
6.2.3 An acute angle
6.2.4 A right angle
(4 × 2)
(8)
(16030121) -6- T910(E)(J24)T
Copyright reserved Please turn over
6.3 Calculate the value of B in each of the following with the use of a calculator: 6.3.1 775,3tan B (1)
6.3.2 '3662cos'5423sin 00 B (2)
6.4 Simplify the following expression by making use of the special angles. Do not use a
calculator.
2 60°
0
020
30sin
60tan30sin6
1
30°
3
(4)
6.5 Calculate the area of the figure below:
6 cm
10 cm
(4)
[25]
TOTAL: 100
(16030121) -7- T910(E)(J24)T
Copyright reserved Please turn over
DEPARTMENT OF HIGHER EDUCATION AND TRAINING
DEPARTEMENTE VAN HOËR ONDERWYS EN OPLEIDING
GRAPH PAPER. GRAFIEKPAPIER
(Return this sheet with the other answers)
(Lewer hierdie blad in saam met u antwoordboek)
EXAMINATION NUMBER:
EKSAMMENOMMER:
(16030121) -8- T910(E)(J24)T
Copyright reserved Please turn over
MATHEMATICS N1
FORMULA SHEET
This sheet must accompany the question paper.
Rectangle: Perimeter = 2(l + b)
Area = l × b
Square: Perimeter = 4a
Area = a2
Triangle: Perimeter = a + b + c
Area = ½b × h
Rectangular prism:
Volume = l × b × h
Right triangular prism:
Volume = ½b × h × l
Cube: Volume = a3
Right pyramid:
Volume = 31 (base area × h)
Ellipse:
Area = 4
π(major axis × minor axis)
Circle: Circumference = D or 2r
Area = 4
πD2
or r2
Cylinder: Volume = h4
πD2
or r2h
Cone: Volume = 3
h
4
πD2
or 3
hπr 2
Annulus: A = 22 rR
-1-
(16030121) -9- T910(E)(J24)T
Copyright reserved Please turn over
The right-angled triangle:
c
B
a
A θ C
b
The theorem of Pythagoras:
c2 = a
2 + b
2
Ratios of angle θ :
c
aθsin
-2-
Copyright reserved Please turn over
NATIONAL CERTIFICATE
AUGUST EXAMINATION
MATHEMATICS N1
24 JULY 2014
This marking guideline consists of 8 pages.
MARKING GUIDELINE
MARKING GUIDELINE -2- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
False
False
False
True
False
True
True
True
True
True
(10 × 1)
[10]
QUESTION 2 2.1 2.1.1
312
93
312
93
281
27
729
27ba
b
ba
b
ba
333
1
124
933
)1(23
3b
b
ba
✓ ✓
33
31
3
23
bb
a ✓
3
8 3a ✓
(5) 2.1.2
429
8
164 bbb
42
3
96
2
12 bbb ✓
42396 22 bbb ✓
429362 b 332 b ✓
38b ✓
OR
3
47
4
29
8
8
18
b
b
bb
(4)
2.1.3
13
31411816
10log3log810log62log
10log3log80001log664log
2
1
3
2
2
eb
e
e
(5)
MARKING GUIDELINE -3- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
2.2 bdpqqr 14010815
bdpqqr 351156
bdpqqr 17579 ✓ ✓ ✓
(3)
2.3
2
1
2
13 3 xx ✓ ✓ ✓
32
136 234 xxxx
12 x
34 36 xx ✓
xx2
12 ✓
xx2
1)( 2
3x
2
1)( x ✓
2
7 ✓
(7)
[24]
QUESTION 3
3.1
2
83
17
8551
D
DD
5
2
53
5317
5317DD
D
DD
✓
653 DD 553 DD ✓
(2)
3.2
q
pp
q
pp
8
62
4
217 232
2
32
62
8
4
217
pp
q
q
pp
✓
pp
q
q
pp
312
8
4
317 2
✓
p7 ✓
(4)
MARKING GUIDELINE -4- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
3.3
3243 2
2
x
xx
x
2
22 3)24(3
x
xxxx ✓ ✓
2
223 3243
x
xxx ✓
2
23 34
x
xx ✓
(4)
3.4 334334 7321 zyxzyx ✓ 222222 5315 zyxzyx ✓
434 327 xyzxyz ✓
3.4.1
434
4343
945
2573
zyx
yx
✓
(4)
3.4.2 23xyz ✓ (1)
3.5 3.5.1 pqdpqzpq 632745
dzpq 7359 ✓ ✓
(2)
3.5.2 axayyx 66
ayyaxx 66 ✓ ✓
ayax 161 ✓
ayx 16 ✓
OR
ayx
xyayx
axayyx
16
66
66
(4)
[21]
MARKING GUIDELINE -5- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
QUESTION 4
4.1 )6(3)3(5 xx
183155 xx ✓ 181535 xx
332 x ✓
5,16x ✓
(3)
4.2
2
2QrA
22 QrA ✓
22r
Q
A ✓
Q
Ar
2 ✓
(3)
4.3 1262 x ✓
6122 x ✓
182 x ✓
9x ✓
(4)
[10]
QUESTION 5
5.1 14 xy √ (1)
5.2 Positive√ (1)
5.3 Rectangular hyperbola√ (1)
5.4 Second and fourth√ (1)
5.5 4√ (1)
5.6 -1√ (1)
MARKING GUIDELINE -6- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
5.7
x
2
1
1 2 3 4
y -6 -3
2
3
-1
4
3
2 marks for correct table.
√ Scale
√ Graph
Scale 1 cm = 1 unit; 2 marks for correct graph with correct scale
(4)
[10] QUESTION 6
6.1 6.1.1
AC
BCC
cos
7
5 ✓
7
5cos 1
C ✓
0415,44 ✓
(3)
6.1.2
222
BCACAB
22
57 ✓
2549
24AB ✓
cmAB 899,4 ✓
(3)
MARKING GUIDELINE -7- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
6.2 6.2.1
√√
(2)
6.2.2
x
o o √√√√
x
angle marked x and o are opposite
(2)
6.2.3
√√
(2)
6.2.4
(2)
6.3 6.3.1 775,3tan B 775,3tan 1B
0163,75 ✓
(1)
6.3.2 '00 3662cos'5423sin B
460,0405,0 ✓
865,0 ✓
(2)
√√
MARKING GUIDELINE -8- T910E)(J24)T
MATHEMATICS N1
Copyright reserved Please turn over
6.4
0
020
30sin
60tan.30sin6
2
1
1
3
2
1.6
2
✓ ✓
2
1
33 ✓
29 ✓
18 ✓
(4)
6.5 Area of rectangle
106A ✓
260 cm ✓
Area of semi-circle
2
42
1DA
26.
42
1 ✓
92
1
137,14 ✓
Area of a figure
60 – 6,283
= 53,717 cm2
OR
Area of semi-circle
283,6
22
1
2
1
2
2
A
A
A
(4)
[25]
TOTAL: 100