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North Seattle Community College
Math 084
Chapter 1 Review
For the test, be sure to show all work! Turn off cell phones.
Perform the operation.
Perform the operation.
Write the product using exponents.
Perform the operation and simplify the result if possible.
Perform the operation and simplify the result, if possible.
Perform the operation and simplify the result if possible.
Write the fraction as a decimal. If the result is a repeating decimal,
use an overbar.
Add.
Add, then simplify your answer.
Perform the operation.
PAGE 1
Perform the operation.
Translate the verbal model into an equation.
The number of waiters w needed is the quotient of the number of
customers c and 8.
Perform the operation and simplify the result when possible.
Subtract.
Subtract, then simplify your answer.
Perform the operation.
Evaluate the expression.
Evaluate the expression.
Translate the phrase to an algebraic expression.
Twice the sum of 210 and t.
PAGE 2
Translate the phrase to an algebraic expression.
Tickets to a circus cost $3 each. Express how much tickets will
cost for a family of x people if they also pay for two of their
neighbors.
Use the formula to complete the table.
t = 2000 - d
-
Deductions
d
Take-home
pay
t
Perform the operation and simplify the result when possible.
Perform the operation.
Perform the operation.
Please enter your answer as a decimal fraction or integer.
Evaluate the expression, given that x = 3, y = - 2, and z = - 10.
Perform the operation and simplify the result, if possible.
Perform the operation.
PAGE 3
ANSWER KEY
Chapter 1 Review
1.
3.
5.
2.
4.
6.
8.
7.
9.
10.
11.
12.
13.
14.
15.
16.
18.
17.
20.
19.
21.
Deductions
d
Take-home
pay
t
22.
23.
24.
25.
27.
ANSWER KEY - Page 4
26.
North Seattle Community College
For the test, be sure to show your work.
1.
Simplify the expression:
Solve each equation:
2.
3.
2x + 5 = 11
4.
7
 h  15
5
5.
- 3(3y - 3) - 2y = 8
6.
7.
9y - 1 = 5y + 5
8.
9.
10.
8x  22  x   6x  2  10
11. 3(s + 2) + 2 = 2(s + 4) + s
PAGE 1
Beginning Algebra
Chapter 2 Review
Solve the formula for the given variable.
12.
13.
for
h  vt 16t 2
14.
for v
for
Solve each inequality. Write the solution set in interval notation. Graph the solution.
15.
16.
17.
18.
19. Use the distributive property to remove the parentheses:
20. Simplify the expression by combining like terms:
PAGE 2
1.
2.
11. All Real Numbers
s
8
25
12.
3.
13.
4.
14.
5.
15.
6.
16.
7.
y
3
2
17.
8.
18.
9.
19.
10.
20.
PAGE 3
v
h  16t 2
t
or
v
h
 16t
t
Beginning Algebra
Chapter 3-4 Review
For the in class test:
Show all work. Use only pencil. Turn off cell phones.
For problems 1-3, graph the equation. Carefully label the graph.
1.
3x  y  2 (Find your 3 ordered points by using a “t” chart. Show all work!)
2. y  
3.
3
x  2 (Graph the line using the y intercept and the slope.)
4
y  3
Problems:
4.
Write the equation of the line with a
3
slope of
and a y intercept of -4.
5
5.
Find the slope of the line through
(4, -2) and (-7, 8)
Answers:
4._______________________
5 ________________
.
6.
Write the equation of the line passing through 6.
(3, -7) and (-3, 1)
7.
Solve the system by graphing.
4 x  2 y  8

 y  3x  6
________________
8.
Solve the system by the elimination method.
 2 x  5 y  11

7 x  3 y  5
8.
________________
9.
Solve the system by the elimination method.
x  y  1

 x  y  7
9.
_________________
10. Solve the system by the substitution method.
 x  y  2

 y  2 x  10
10.
________________
11. Solve the system by the substitution method.
 y  3x  2

 6 x  2 y  4
11.
________________
12. a. Write the following equation in standard
form of a line.
y
12.
a________________
5
x3
3
b. Is the slope of the line negative or
positive? Why?
c. Find the x and y intercepts of the
equation. Write the answer as ordered pairs.
b_________________
c.____________________
Solve the following problems.
Be sure to set up a system with two variables and use
either the substitution method or elimination method to
solve the system.
13. A total of $14,000 was invested. Part of
the $14,000 was invested at 6% and the rest
invested at 8%. If the interest for one year is
$1060, how much was invested at each rate?
14. The sum of two numbers is 18. If twice
the smaller number is 6 more than the larger,
find the two numbers.
13._________________
14.__________________
North Seattle Community College
For the test, be sure to show all work!
PROBLEMS
Math 084
Chapter 5 Review
ANSWERS
For problems 1-3, simplify. Write the answer with positive
exponents only.
1.
2
1.
3
 
7
2.
1 3 2 
5 6
 a b  3a b
3

3.
y4
y 8
3
4.

2.

3
3.
Write the following in scientific notation.
4.
0.00314
5.
Write the following in expanded form.
5.
3.46  10 7
For problems 6-9, simplify. Write the answer with positive exponents only.
6.
7 x y 5x y 
10 xy 7 x y 
7.
x  x 
x 
8.
21a 10 18a 17

3a 4
6a 11
3
5
2
3
6
9
6 1
3 3
7.
5  4
8.
9  10 5  10 
2
3
9.
6.
6  10
9.
4
10. Subtract.
 7 x
2
10.
 
 2 x  6  8x 2  4 x  7

1
11. Find the value of the following expression when
11.
x is a (-3).
4x 2  2x  1
For problems 13-16, multiply.

12.

12.
5xy 2 3x 3  4 x 2 y  10 xy 2
13.
1 
1

 x   x  
3 
4

13.
14.
a  2a 2  6a  7
14.
15.
a  62
15.
16.
3x  53x  5
16.
For problems17-18, divide.
17.
17.
6 x a  12 x b  6 x c
36 x 2
18.
2 x 2  7 x  12
x2
2
2
2
18.
2
North Seattle Community College
Elementary Algebra
PROBLEMS
Chapter 6 Review
ANSWERS
For problems 1-2, factor out the greatest common factor.
1.
2.
3.
7 x 3  21x
1.
33a 4 b 5  48a 5 b 3  18a 4 b 4
2.
Factor by grouping.
3.
15x 2  10bx  3bx  2b 2
4.
Factor problems 4-11 completely.
4.
4 x 2  21x  20
5.
5 y 2  11y  6
5.
6.
8 y 2  18
6.
7.
81  y 4
7.
1
8.
3m 3  18m 2  21m
8.
9.
4 x 5  20 x 4  11x 3
9.
10.
64 y 3  8
10.
11.
12 x 3  27 xy 2
11.
For problems 12-16, solve the equation by factoring.
12.
m 2  3m  10  0
2
12.
13.
3x 2  7 x  20
13.
14.
98r 2  18  0
14.
15.
5x 2  15x  0
15.
16.
33x 3  42 x 2  6 x 4
16.
3
Chapter 7 Review---Math 085
For the in class test, be sure to show all work!
PROBLEMS:
For problems 1-4, simplify the expression.
3x 2  x  10
1.
x 4  16
2.
x 2  6 x  ax  6a
x 2  7 x  ax  7a
For problems 3 and 4, multiply the rational expression.
6 x  12 3x  3
3.

6 x  12 12 x  24
4.
a
2
 a 8
 5a  24 

 a 3

Divide.
5.
3x 2  2 x  1 3x 2  13x  4

x 2  6 x  8 x 2  8 x  16
For problems 6 and 7, subtract the rational expressions
x2
18 x  81

6.
x9
x9
7.
3a
2

a  8a  15 a  5
14.
A boat travels 48 miles up a river in
the same amount of time it takes to
travel 72 miles down the same river.
If the current of the river is 3 miles
per hour, what is the speed of the
boat in still water?
15.
An inlet pipe can fill a pool in
21 hours, while an outlet pipe can
empty it in 28 hours. If both pipes
are left open, how long will it take
to fill the pool?
16..
y varies directly as x. If y = -20, when x
= 4, find y when x = 7.
2
For problems 8-14, solve the equation.
4
1
8.
3
x
x
9.
a
3

a 3 2
10.
1
11.
7 6

x x2
3
1
8

 2
x  6 x  2 x  4 x  12
For problems 15-16, simplify the complex fraction.
16
1 2
x
12.
2 8
1  2
x x
1
a  5a  6
1
a3
2
13.
2
North Seattle Community College
Math 085
Chapter 8 Review
For full credit on your test, be sure to show all work.
Problems:
Answers:
For problems 1-10, find the roots. Assume all variables represent positive numbers.
100 x 4 y 16
1.
1.
2.
 80b14
2.
3.
15 32m 5 n 7
3.
4.
 x 3 48x11
4.
5.

6.
7
81
144 x 10 y 22
121
5.
6.
2
7.
 7 100
7.
5
50
6
8.
8.
For problem 9 and 10, add or subtract.
7 242  9 32
9.
10.
7.
7 108a 7  a 3 75a
9.
9.
10.
10.
For problems 11-14, multiply.
11.

12.
7
6 2

6  12


w 6 7 w 6

11.
11.
12.
12.
3
For problem 13, rationalize the denominator.
17  8
13.
17  8
13.
For problems 14 –16, solve the equation.
14.
8x  8  2  0
14.
15.
6 x  13  2  5
15.
16.
y2  4 y
16.
For problems 17-18, simplify the expression.
17.
18.
3
 54
36

3
2
17.
18.
North Seattle Community College
Math 085
Chapter 9 REVIEW
For problems 1-2, use the square root property to solve each quadratic equation.
1.
x 2  44
2.
3x  62
 81
For problems 3 & 4, complete the square to solve the equation.
3.
x 2  8x  3  0
4.
5x 2  9 x  2  0
2
For problems 5 & 6, use the quadratic formula to solve the equation.
5.
x 2  4x  7  0
6.
5x 2  10 x  1  0
Write as a complex number.
7.
 98
Combine like terms and simplify.
8.
2  3i   5  2i   5  i 
For problems 9 & 10, multiply and simplify.
9.
7i5  2i 
3
3  4i 5  i 
10.
Divide.
11.
4  5i
4  5i
12. Graph the following quadratic equation. Be sure to answer all questions. Label your
points carefully and be sure to draw the axis of symmetry.
y  x 2  7 x  10
The shape of this graph is a________________________________.
The graph opens________________________________________.
The vertex is______________________.
The axis of symmetry is__________________.
The y intercept is________________________.
The x roots are__________________________.
North Seattle Community College
1.
Solve the equation
Math 085 Final Review
3s  13s  1  8
2.
Solve the system by graphing.
 y  x  3

 y  7 x  21
3.
Use the quadratic formula to solve the equation.
2x 2  4x  9
4.
Solve the equation.
4r 2 4r
 
2
3 r
3
5.
Write the solution in scientific notation.
1.3  10 4.8  10 
4
3
1.2  10 5
6.
Solve the proportion.
2 x  1 14

45
5
7.
Write an equation in slope-intercept form of the line that passes through the points
(7, - 4) and (- 11, 2).
8.
Solve the equation by completing the square.
x 2  14 x  39  0
9.
Use the elimination method to solve the system.
 x  3 y  1

15 x  11y  97
Math 085 Final Review
10.
Simplify the expression, if possible
x 2  16
x 2  3x  4
11.
Simplify the complex fraction.
4
x2
1
1
x2
12.
Use the substitution method to solve the system.
2a  4b  28

a  14  2b
13.
Perform the operation. Simplify, if possible.
y3 y6

y2 2 y
14.
Perform the division.
3x  1 x  5  42x 2
15.
Use the quadratic formula to solve the equation.
x 2  5x  3  0
16.
Multiply and simplify, if possible.
2x 2  11x  5
x4
x 2  6x  8


8x  4
x 2  16
x2  4
17.
It takes a grounds keeper 40 minutes to prepare a softball field for a game. It takes
his assistant 65 minutes to prepare the same field. How long will it take if they work
together to prepare the field?
Math 085 Final Review
18.
Solve the equation.
12 x  42  x   8x  2  12
19.
Find the square root. Assume that the variable represents a nonnegative number.
4k 2
20.
Perform the operation. Simplify, if possible.
2x
x 1

x 1 x  4
21.
Simplify if possible. Assume that
represents a positive number.
9x13
22.
Assume that y varies directly with x . If y  6 when x  3 , find y when x  8 .
23.
Perform the operations.
2x
24.
2
 
 
 2x  3  4x 2  2x  3  2x 2  2x  3

Graph the quadratic equation
y  x 2  6x  9
25.
Assume that r varies inversely with s . If r  70 when s  2 , find r when s  12 .
26.
Simplify the expression. Write the answer without using parentheses or negative
exponents.
 y 4 z -3
  2 4
 3y z
27.



2
Graph the inequality.
2 x  3 y  12
Math 085 Final Review
28.
Use the most convenient method to find all real solutions. If a solution contains a
radical, give the exact solution.
x 2  7 x  11  0
29.
Use the square root property to solve the equation.
x  22
30.
Find the product.
x
31.
2

 4 xy  y 2 4 x  y 
Solve the inequality; write the solution in interval notation.

32.
 175
2 5
1
 x
9 6
3
Divide
4  3i
2i
33.
Solve. Graph the solution. Write the answer in interval notation.
1 
4x  1
5
3
Math 085 Final Review
Answer Key
1.
17.
2.
3.
18.
19.
or
1
22
2
4.
5.
6.
20.
5.2  10 6
21.
22.
7.
23.
8.
9.
24.
25.
10.
26.
11.
27.
12. infinitely many solutions
28.
13.
29.
14.
15.
30.
31.
16.
32.
33.
24
no solution
27.
See below
See below

7
5

2
2
x  2  5 7
2 
2
 - , 
15, 
15 
11 2
 i
5 5
 1 
 2 ,4 
x