FINAL EXAMINATION
Solution Key, MATH-002
Question 1
(a)
Find the measure of the reference angle for the angle
Solution:
Reference angle
(b)
If sin
and cos
Solution: sin 2
(c)
find sin 2
cos
State the period of the function y = 3 tan
Solution: Here, b=
,
Period=
=
=
(d)
Find the exact radian value of cos
Solution: cos
cos
=
(e)
How many different committees of 4 people can be selected from 10 people?
Solution:
Question 2
(a)
Verify the identity
Solution: L.H.S:
(b) Perform the indicated operation and simplify
Solution:
0
2(c) From a point A on a line from the base of the Washington Monument,
The angle of elevation to the top of the monument is 42
From a point
100 feet away and on the same line, the angle to the top is 37.8
Find the approximate height of the Washington Monument.
Solution:
Let
denotes the distance from point A to the base of the Monument, and
denotes the height of the Monument,
In right triangle DAC,
C
....... (i) eqn.
In right triangle DBC,
B 100
Substituting
from (i) into (ii) eqn.
A
D
Method-II
2(c) From a point A on a line from the base of the Washington Monument,
The angle of elevation to the top of the monument is 42
From a point
100 feet away and on the same line, the angle to the top is 37.8
Find the approximate height of the Washington Monument.
Solution:
Let
denotes the distance from point A to the base of the Monument, and
denotes the height of the Monument,
In triangle ABC, by Sine rule,
=
C
....... (i) eqn.
4.2
In right triangle ADC,
B 100
Substituting equation (i) into (ii)
= 559.7 feet or 560 feet
A
D
Question 3
(a) Solve the equation for the exact solutions in the interval
0
Solution:
(OR)
,
The solutions in the interval,
(b)
0
are
Find the area of the triangle if sides of the triangle are given below:
6 , b = 8 , c = 10
Solution:
Area =
= 24 square unit
(c) Divide the complex numbers
(1) Mark
Write answer in standard form.
Solution:
(1) Mark
)
Mark
(1) Mark
Question 4
3
 2
 2

Given the matrices A =  1 1  and B = 
3
 0  5 
3
 2
 2

AB =  1 1  
3
 0  5  
Solution:
0
, find AB
5  1 
4
0
5  1 
4
AB
AB
(b) Given A =
,
find
Solution:
(1) Mark
(1) Mark
(c) Solve the following system of equations only for
by using Cramer’s rule
3
Solution:
=
(1) Mark
(1) Mark
=
(1) Mark
(1) Mark
By Cramer’s rule,
(1) Mark
Question 5
(a) Insert three arithmetic mean between 7 and 19.
Solution: Let ,
be the three arithmetic means. After inserting the three means,
the sequence will be
7,
, n=5
19=7+4
4
,
The three arithmetic means are
(b) Evaluate the infinite geometric series
Solution:
(c)
=
List the elements in the sample space defined by the following experiment:
Two people are selected from three senators and two representatives.
Solution:
Label three senators as
Then sample space
and two representative as