SCHOOL OF ELECTRICAL & ELECTRONICS ENGINEERING DIPLOMA IN ELECTRICAL ENGINEERING [ELECTRICAL & ELECTRONICS] E3001 – APPLIED MATHEMATICS 1 RESIT EXAMINATION 2009 STAGE 1 GROUPS: A, B, C & D DATE: 27/07/2009
TIME: 4.00-6.10 PM
VENUE: HOSTEL 103
INSTRUCTIONS:
1.
You are allowed 10 minutes EXTRA as reading time during which you are NOT to write.
2.
Begin each answer on a fresh page and use both sides of the sheet.
3.
Write your candidate number at the top of each attached sheet.
4.
Insert all written foolscap, graph paper, drawing paper, etc. in their correct sequence and secure with string
. 5.
Write clearly the number(s) of the question(s) attempted on the top of each sheet.
6.
Answers to all questions must be written in INK on the Answer Sheet provided.
7.
No programmable calculators are allowed.
8.
Answer all questions.
SECTION A – MULTIPLE CHOICE [20 MARKS] (Choose the best answer)
1)
Find cos30 in surd form.
A. B. C. D.
2)
2 1 3 1 2 1
2
If you covert A. B. C. D.
3)
3
2
from radians to degrees, its equivalent in degrees is:
120° 30° 60° 90°
xdx is equal to
A. B.
x
2
c
2
1
c
x
C. x ln x 1 c 1 1 D. c x x 2 4)
An alternating voltage of frequency 60 Hz has maximum value of 115V. The equation for its instantaneous value is: A. B. C. D.
5)
V V V V
115sin 200 t 115sin 60t 115sin 60 t 115sin120 t
The gradient of the curve y A. B. C. D.
3 2 x
x
2
3 x
4 at
x
3 is:
– 6 25 – 17 – 45
2
6)
The engineering expression
(16 4) 2 (8 2) 4
is equal to
A. 4 -4 B. 2 1 C. 2 2 D. 1 7)
A triangular plot of land ABC has sides a A is equal to:
7.0m and c
6.0m. Angle
46.57 53.13 75.52 86.59
A. B. C. D. 8)
8.0m, b
3
x dx is equal to
A. B.
x 4
4 1 x
c c
C. x ln x 1 c 1 1 D. c x x 2 9)
A sinusoidal voltage is given by v statement is incorrect. A.
R is
C. Frequency =
10)
2
2
s
Hz
, is the angular velocity.
The quadratic equation in x whose roots are 3 and 2 is: A. B. C. D.
11)
) .Which of the following
the average value of the voltage
B. Periodic time =
D.
R sin( t
x 2 x 2 x 2 x 2
x 6 5 x 6 x 6 5 x 6
The equation of a straight line graph is: 2 y line is:
7
6 x .The gradient of the straight
3
A. 7 B. 3 6 C. D. 12)
7 2 °
If you covert 180 from degrees to radians, its equivalent in degrees is: A.
2
B. C. D. 13)
6 3
Solving ln x
4 yields
x
A. e 4 B. 10000 C. e D. 1 14)
An alternating voltage is given by v 240 sin(100 t 0.32) volts. When time [Hint: Use Radians] t 4ms , the voltage v has a value of : A. B. C. D.
15)
193.34 V 3.92 V 1.96 V 120 V
The equation of the line passing through the point 2, 3 with a slope of 2 is: A. y 7 x 2 B. 2 y 14 x 4 C. y 2 x 7 D. y 3 x 4
16)
The period of the function f
cos 2
is:
A. B. 2 C. 2 D. 4 17)
The coordinate
3 , 1 in polar form is:
4
18)
A.
3,30
B.
2,30
C.
3,330
D.
2,330
Secant when referred to a right angled triangle is: A. B. C. D.
19)
hypotenuse hypotenuse adjacant adjacant opposite
adjacant hypotenuse
Which of the following is correct about logarithms? Log AB is same as: A. B. C. D.
20)
opposite
LogA LogB LogA LogB B LogA LogA LogB
The period of the function f
sin
is:
A. B. 2 C. 2 D. 4
SECTION B – LONG ANSWERS [80 MARKS] Attempt all 8 questions Question No.1
A.
By using Kirchhoff’s Laws in a certain electrical network, the current (in Amperes) are related by the equations:
5
0.2 I 1
12
3 I 2
Find the values of the current
I 1
I 1
& I 2
2( I 1 I 2 ) 0.42 I 2
2( I 1
I 2 )
& I 2 that satisfies the above two equations. [6 marks]
5
B.
Find all the values of
in the equation 2 sin
1 in the interval [0 - 2 ] [4 marks]
Question No.2
Resolve the following into partial fractions. A.
B.
11 6 x x
2
5 x
[5 Marks]
6
12 x
2
[5 Marks]
9
Question No.3
A.
Solve for x in the following equations: i. ii.
7 x 7 6 x 3 3 x 5 9 6 x 6
iii. log 10 x iv. log 4 416 B.
[2 marks] [2 marks]
4
[2 marks] x
[2 marks]
Use the quadratic formula to solve 2 x 2
6 x
5
0.
[2 marks]
Question No.4
A.
B.
A sinusoidal waveform is given by v
250 sin(50 t 0.541) Volts.
i.
Find the amplitude, periodic time, frequency, and phase angle, stating whether it is leading or lagging sin(wt ) . [4 marks]
ii.
Sketch the graphical representation of the equation. 1
Prove the trigonometric identity: 1
sin
sec 2
[3 marks] [3 marks]
Question No.5
A.
Sketch the graph of the following showing the intercepts and the asymptotes if any:
6
B.
i.
y
ii.
y
ln( x 3 4
x
3)
[2 marks]
5
[2 marks]
2 Sketch the graph of y x
2 x
3 , showing the intercepts.
[6 marks]
Question No.6
A.
a 5 bc 3
Simplify
2
3
a b c 3
B.
2
4
and evaluate when a
3 2
,b
1 2
and c
1
1
3
[3 marks]
1
x 4 y 3 z 3
Simplify
2
[2 marks]
5
x 2 y 3 z 2
C.
Divide 2 x 2
D.
3 Simplify: 7 x
x
3 by x 1 15 x
4 y 12 z
[3 marks] 12 y
3 7 x
7 x
8 z
[2 marks]
Question No.7
Find the unknown x values. A.
5m 3m
x
[5 marks]
B.
5.5 x
2 2.5
[5 marks]
7
Question No.8
A.
The distance x meters moved by a car in a time t seconds is given by x 3t 3 2t 2 4t 1 . Determine the expressions for: i. Velocity ii. Acceleration iii. And find the velocity and acceleration when t =1s [5 marks]
B.
Differentiate:
4 x 3
2 ln( 4 x)
2(cos3 x
4 sin 4 x)
[3 marks]
4
C.
3 x 2 dx
Evaluate:
[2 marks]
1
THE END
8
SECTION A – MULTIPLE CHOICE [20 MARKS]
Please attach this sheet to the answer booklet 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
