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College Algebra
Algebra Review

1
The Real Number System

Problem  1
practice icon

What property does each of the following equations illustrate?

  1. 4+6=6+4

  2. 3(58)=3(5)3(8)

  3. 2(35)=(23)5

  4. 41=4

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  2

Let A={2,1,1,4,5}, B={3,2,4,7,9} and C={3,0,2,7}. Find the following:

  1. BC

  2. AB

  3. AC

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Julieta cc
Julieta
Mr. Galletti cc
Mr. Galletti
Julieta cc espanol spanish
Julieta
Problem  3

Graph each of the following intervals on the number line and give a verbal description.

  1. (2,4]

  2. (,4]

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  4

Give the corresponding interval notation for the graph of an inequality.

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  5

Find the indicated set, and graph.

  1. (1,4)[2,5]

  2. (1,4)[2,5]

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Julieta cc
Julieta
Mr. Galletti cc
Mr. Galletti
Julieta cc espanol spanish
Julieta
Problem  6
practice icon

Evaluate the following.

  1. |3|

  2. 4|4.5|

  3. |4+9|+3

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  7

Find the distance between 6 and 4 on the real number line.

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  8
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Simplify each expression.

  1. 32+2(3+7)

  2. 32+147

  3. 6+3(5(32+2))

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Mr. Hampton cc
Mr. Hampton
Gordon cc
Gordon
Saba cc
Saba
Problem  9
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Evaluate the following expression on your calculator. Check the calculator output with a hand calculation.

  1. 4+10÷5+2

  2. 4+105+2

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  10
practice icon

Write each of the following in symbols:

The sum of x and 5 is less than 2.
The product of 3 and x is 21.
The quotient of y and 6 is 4.
Twice the difference of b and 7 is greater than 5.
The difference of twice b and 7 is greater than 5.

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Gordon cc
Gordon
Cynthia espanol spanish
Cynthia
Problem  11
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Simplify: 5+3(2+4)

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Aaron cc
Aaron
Lauren
Lauren
Anthony espanol spanish
Anthony
Problem  12
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Simplify: 4020÷5+8

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Katrina cc
Katrina
Brooke cc
Brooke
Logan cc
Logan
Anthony espanol spanish
Anthony
Problem  13
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Simplify (23)(59)

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Preston cc
Preston
Stefanie cc
Stefanie
Anthony espanol spanish
Anthony
Problem  14
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Simplify 25(74)6

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Preston cc
Preston
Stefanie cc
Stefanie
Winston cc
Winston
Julieta espanol spanish
Julieta
Problem  15
practice icon

Simplify 2(47)3+(23)2

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Preston cc
Preston
Stefanie cc
Stefanie
Anthony espanol spanish
Anthony
Problem  16
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Simplify: 8853

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Mr. McKeague cc
Mr. McKeague
Ana
Ana
Matt cc
Matt
Anthony cc
Anthony
Problem  17
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Simplify: 5(4)+2(3)2(1)5

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Mr. McKeague cc
Mr. McKeague
Ana
Ana
Anthony cc
Anthony
Anthony espanol spanish
Anthony
Problem  18
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Find the value of the expression 3x+4y+5 when x is 6 and y is 7

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Ana
Ana
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  19

Locate the numbers 4.5, 0.75, 12, 2, π, and 4.1 on the real number line.

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  20
practice icon

Write |5| without absolute value symbols.

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Ana
Ana
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  21
practice icon

Write |2| without absolute value symbols

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Ana
Ana
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  22
practice icon

Write |3| without absolute value symbols

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Ana
Ana
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  23
practice icon

Simplify 5(4x) by using the associative property.

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Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  24
practice icon

Simplify 14(4a) by using the associative property.

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Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  25
practice icon

Apply the distributive property to 12(3x+6) and then simplify the result.

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Julieta cc
Julieta
Betsy cc
Betsy
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  26
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Simplify: 2(3y+4)+2

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Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  27
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Apply the distributive property to a(1+1a) and then simplify the result.

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Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  28
practice icon

Apply the distributive property to 3(13x+5) and then simplify the result.

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Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  29
practice icon

Apply the distributive property to 6(13x+12y) and then simplify the result.

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Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  30
practice icon

Use the distributive property to combine similar terms for the expression 3x+5x.

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Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  31
practice icon

Use the distributive property to combine similar terms for the expression 3y+y

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  32
practice icon

Simplify: 7x+4+6x+3

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Stefanie cc
Stefanie
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  33
practice icon

Simplify: 4+3(2y+5)+8y

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Stefanie cc
Stefanie
Katrina cc
Katrina
Cynthia espanol spanish
Cynthia
Edwin espanol spanish
Edwin
Problem  34
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Simplify: 3(2y1)+y

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Stefanie cc
Stefanie
Katrina cc
Katrina
Keith cc
Keith
Anthony espanol spanish
Anthony
Problem  35
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Simplify: 83(4x2)+5x

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Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Anthony cc
Anthony
David espanol spanish
David
Problem  36
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Simplify: 5(2a+3)(6a4)

Choose instructor to watch:
Stefanie cc
Stefanie
Katrina cc
Katrina
Keith cc
Keith
Anthony espanol spanish
Anthony
Problem  37
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AB.

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Suhas
Suhas
Katrina cc
Katrina
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  38
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AB.

Choose instructor to watch:
Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  39
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AC.

Choose instructor to watch:
Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  40
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find BC.

Choose instructor to watch:
Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  41
practice icon

For the set {5,3.5,0,34,3,5,9}, list:

  1. whole numbers

  2. integers

  3. rational numbers

  4. irrational numbers

  5. real numbers

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Graham
Graham
Edwin espanol spanish
Edwin

2
Integer Exponents and Scientific Notation

Problem  1
practice icon

Write each expression using positive exponents.

  1. 42

  2. 1.453

  3. x4y5, y0

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  2
practice icon

Simplify each expression and write it using positive exponents. Assume that variables represent nonzero real numbers.

  1. 16x10y44x10y8

  2. (3x2)3x5

  3. (54s2t36zt)2

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  3
practice icon

Express each of the following numbers in scientific notation.

  1. 328.5

  2. 4.69

  3. 0.00712

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  4
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Write the following numbers in decimal form.

  1. 2.1×105

  2. 3.47×103

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  5
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In 2012, Japan had a population os 1.27×108 and a land area of 3.64×105 square kilometers. What is the population density of Japan, that is, the number of people per square kilometer of land? Express your answer in scientific notation.

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio

3
Roots, Radicals, and Rational Exponents

Problem  1
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Determine 364, 464, and 532.

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  2
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Rationalize the denominator of each expression.

  1. 185

  2. 31033

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  3
practice icon

Simplify the following.

  1. 75

  2. 3125108

  3. x5y7, x,y>0

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  4
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Rationalize the denominator.
542

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  5
practice icon

Simplify the following radical expressions. Assume x0.

  1. 48+2712

  2. (3+x)(42x)

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  6
practice icon

Evaluate the following.

  1. 2713

  2. 3612

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  7
practice icon

Evaluate the following expressions without using a calculator.

  1. (4)12

  2. (13)2

  3. (23.1)0

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  8
practice icon

Simplify and write positive exponents.

  1. (25)12

  2. (16s43t3)32, s,t>0

  3. (x23y3)3y12x2, x,y>0

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Saba cc
Saba

4
Polynomials

Problem  1

Write the following polynomial in descending order and find its degree, terms, coefficients, and constant term. 4x2+3x52x7

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  2
practice icon

Add or subtract each of the following.

  1. (3x3+2x25x+7)+(x3x2+5x2)

  2. (s4+34s2)(s4s2)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  3
practice icon

Multiply (2x2)(4x7)

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Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  4
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Multiply (3x+2)(2x3)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  5
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Multiply (7x+4)(5x1)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  6
practice icon

Multiply (4y33y+1)(y2)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Molly S. cc
Molly S.
Gordon cc
Gordon
Saba cc
Saba
Problem  7

Multiply each of the following:

  1. (3y+4)2

  2. (4x25)2

  3. (7y+3)(7y3)

Choose instructor to watch:
Julieta cc
Julieta
Mr. Galletti cc
Mr. Galletti
Julieta cc espanol spanish
Julieta

5
Factoring

Problem  1

Factor the greatest common factor from each of the following.

  1. 3x4+9x3+18x2

  2. 8y26y+4

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Saba cc
Saba
Problem  2
practice icon

Factor x3x2+2x2 by grouping.

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Mr. Hampton cc
Mr. Hampton
Shelby cc
Shelby
Gordon cc
Gordon
Saba cc
Saba
Problem  3
practice icon

Factor each of the following

  1. x22x8

  2. 8x310x212x

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Mr. Hampton cc
Mr. Hampton
Shelby cc
Shelby
Gordon cc
Gordon
Saba cc
Saba
Problem  4

Factor 6x33x245x

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  5

Factor using one of the quadratic factoring patterns.

  1. x249

  2. 8x2+32x+32

Choose instructor to watch:
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  6

Factor using one of the cubic factorization patterns.

  1. x3+27

  2. 27x364

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta

6
Rational Expressions

Problem  1
practice icon

For what value of x is the following rational expression defined? x+1(x3)(x5)

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Nathan cc
Nathan
Problem  2
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Simplify: x22x+13x24x+1

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  3

Multiply the following and express your answer in lowest terms. For what values of the variable is the expression meaningful?

  1. 3a8246a3

  2. x2+x6x24(x+2)2(x2+9)

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Saba cc
Saba
Lauren cc
Lauren
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

Divide and simplify:
3x25x2x24x+4÷9x21x+5

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  5

Add or subtract the following and express your answer in lowest terms.

  1. x+43x+6+2x+1x2+7x+10

  2. 3x42xx+5x24

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  6
practice icon

Simplify x242x+1x2+x6x1

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  7
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Simplify 1x+1xy3y2+1y

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta
Julieta