Sample Final Exam for MAT 123
1)
Evaluate sin
π
6
Answer (2 points)
2)
If tan x =
10
and x is in quadrant III, find sin x
11
Answer (3 points)
3)
A2 B 4
Expand completely: log 5 4
C D
Answer (3 points)
1
Sample Final Exam for MAT 123
4)
Solve for x: log8 64
= 2 x + 1.
Answer (3 points)
5)
Solve for x: ln ( e x −2 ) + e
ln ( 3 x +3)
=
11
Answer (2 points)
6)
Find the domain of f ( x ) =
x−3
. You do NOT need to use interval
x−5
notation.
Answer (2 points)
2
Sample Final Exam for MAT 123
7)
If f ( x ) =
1
and g =
( x)
2x − 3
6 x + 1 , find f ( g ( 4 ) )
Answer (3 points)
8)
If f ( x ) = −5 x 2 , find f ( x + h ) − f ( x ) . Simplify your answer as much as
possible.
Answer (2 points)
3
Sample Final Exam for MAT 123
9) Given a non-right triangle ABC where ∠A =
45 , ∠B =
75 , and side
a = 12cm . Find the length of side c. (In the triangle, angle A is opposite side a,
angle B is opposite side b, and angle C is opposite side c.).
Answer (8 points)
5π
Given a non-right triangle ABC where ∠C = , side a = 8cm and side
6
b = 6cm . Find the length of side c. (In the triangle, angle A is opposite side a,
angle B is opposite side b, and angle C is opposite side c.)
10)
Answer (8 points)
4
Sample Final Exam for MAT 123
13) Initially, you have 6 pounds of yeast brewing in a container growing
exponentially. Four hours later, you have 18 pounds. How long will it take until
you have 60 pounds? (Please leave your answer in terms of logarithms.)
Answer (8 points)
5
Sample Final Exam for MAT 123
4 ( x2 − x − 2)
14)
Given the function f ( x ) =
(a)
(b)
(c)
(d)
Give the equations(s), if any, of the vertical asymptote(s).
Give the equations(s), if any, of the horizontal asymptote(s).
What are the coordinates, if any, of the x-intercept(s)?
What are the coordinates, if any, of the y-intercept(s)?
3 ( x 2 − x − 20 )
Answer (10 points)
a)
b)
c)
d)
6
Sample Final Exam for MAT 123
15)
If sin A = −
2
5
and cos B = , with A in quadrant III and B in quadrant IV,
5
9
find:
(a)
sin ( A − B )
Answer (4 points)
(b)
cos 2A
Answer (4 points)
7
Sample Final Exam for MAT 123
π 
16) Given the equation
=
y 2sin  x  + 1 :
5 
(a) What is the amplitude?
(b)
What is the period?
(c)
What is the vertical shift?
(d)
Graph one cycle of the equation on appropriately labeled axes.
Answer (12 points)
a)
b)
c)
8
Sample Final Exam for MAT 123
6
17a) If cos −1   = x , find tan x
7
Answer (4 points)
17b) Find x if 5 x+3 = 13x
Answer (6 points)
9