Math253
Practice Exam #03
1. Determine the domain of each function and then write down the domain using interval notation.
a)
f ( x=
)
x −8
b) g ( x
=
)
x+3
c) h ( x=
)
3
3 − 2x
2. Write down an equivalent expression using exponential notation.
b)
(
)
14
7
xy
b)
(
5
a 2b 4
)
15
5
c)
m
3. Multiply and simplify each radical expression.
a)
5 ⋅ 10
b) 3 2 x5 ⋅ 4 10 x 2
c)
3
3a 2b3 ⋅ 3 9a 7b 2
4.
Multiply and simplify each radical expression.
a)
(3 +
)(
11 3 − 11
)
(
)(
b) 4 − 7 4 − 7
)
5. Rationalize the denominators.
a)
3
5
b)
2
3
2x 2
c)
3
3+ 5
6. Solve each equation.
a)
3 x + 4=
4x + 3
c)
4x − 3 = 2 + 2x − 5
b)
x+5 −4 =
1
7. Find the distance and the midpoint between the two points.
Recall: d=
a)
( x2 − x1 ) + ( y2 − y1 )
( −2, 5) and (8, 3)
2
2
 1 7
 2 11 
b)  − ,  and  , 
 5 5
5 5 
8. Simplify each expression by writing it in a + bi form.
a)
10
3+i
b)
2i
5 + 3i
9. Solve each quadratic equation.
a) x − 2 x − 6 =
0
b) x 4 + 5 x 2 + 4 =
0
10. A business invests $10,000 in a savings account for 2 years. At the beginning of the second
year, an additional $3,500 is invested. If a total of $16,000 is in the account after the second
year, what is the annual interest rate? Round your final answer to the nearest percent.
Use the equation A = P1 (1 + r ) + P2 (1 + r ) to solve this problem.
2