Practice Problems Worksheet

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B
M
C
C
OROUGH OF
ANHATTAN
OMMUNITY
OLLEGE
D
M
EPARTMENT OF
ATHEMATICS
Practice Problems for the MAT 056 Departmental Final
Form Q
The actual final exam will have 20 questions. Please do not assume that the content or difficulty level of these
practice questions are exactly the same as the actual examination. We suggest you study the range of topics
described on the syllabus as well as the types of problems on this sample test.
1. Simplify:
2
S
pr
prs
2. Solve for p:
3. Solve the following equation:
4. Solve for
a)
b)
c)
5. Solve the following absolute value inequality and graph your solution set:
a)
2
2
x
5
14
b)
Write solution in interval notation.
6. Solve the following equation be sure to check the solutions:
7. Solve for :
8. Write down a quadratic equation that has roots: {
}
 y
9. Find the
and
intercepts of the line
5
x
4
20
, then graph the line.
10. What is the equation of the line that passes through the point (1 , 1) and is perpendicular to the
 y
line
?
2
x
3
6
, 4  and is parallel to the line
11. What is the equation of the line that passes through the point
1
 y
?
5
x
4
5
x
y
 1
12. What is the slope of the line expressed by the equation
2
8
13. Subtract the following complex numbers. Then, write the answer in standard form:
a 
bi
3 (
4
i
)
2 (
i
)
(Hint: leave answer in
form)
14. Multiply the complex numbers and then write the answer in standard form:
(4+2i)(5–3i)
15. Simplify. Express the following as a single fraction in simplified form:
1
1
1
1 
2
2
x  2
ab
x
y
a)
b)
c)
3
y
x
1
1
1 –
x  2
b
a
x
y
16. Solve for x. Express the answer in simplified radical form if possible:
 x
2
a)
15
x
11
6
0
b)
17. Simplify the following. Express your answer using only positive exponents.
2
3
4
2
3
2
3
p
q
6 (
x
y
)
 
 
a)
b)
2
5
1
2
3
p
q
2 (
x
y
)
18. Solve the inequality – (a+1)–4 < 2a –8. Graph solution on the number line.
–6x – 10y  20
19. Solve the system of equations
3x  5y  25
Revised: 10/28/13
1

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