ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra

This is a complete, sequenced, free course. It has unlimited, randomly-generated exercises and worksheets. It can be used for a year-long high school course, or a one-semester college course.

You're about to learn that $\,x\,$ is to mathematics as ‘cat’ is to English. Next time you see ‘$\,x\,$’, I hope you think One Mathematical Cat, Please! and laugh a bit $\ldots\,$ making mathematics a little less stressful, and a little more fun.

Sections with the light green background are from the original ‘cat’ book (cat-on-swing). It was filled out to become this First Course in Algebra (which is also available as the cat-in-hammock book).

Section 1:
The Language of Mathematics
Read Section 1
1. Expressions Versus Sentences
Section 2:
Brushing Up On Basic Arithmetic Skills
Read Section 2
2. Basic Addition Practice
3. Multiplication
4. Divisibility
5. Basic Properties of Zero and One
6. Mixed Basic Add/Subtract/Multiply/Divide Practice
Section 3:
The Real Numbers
Read Section 3
7. Deciding if a Number is a Whole Number, an Integer, etc.
Section 4:
Addition of Signed Numbers
Read Section 4
8. Addition of Signed Numbers
Section 5:
Subtraction of Signed Numbers
Read Section 5
9. Subtraction of Signed Numbers
10. Mixed Addition and Subtraction of Signed Numbers
Section 6:
Average
Read Section 6
11. Writing Fractions with a Denominator of 2 in Decimal Form
12. Average of Two Signed Numbers
12.5  Application of Averaging Concepts: Factoring a Quadratic   (optional; for more advanced readers)
13. Average of Signed Numbers
Section 7:
The Base Ten Number System
Read Section 7
14. Identifying Place Values
15. Multiplying by Powers of Ten
Section 8:
Decimals
Read Section 8
16. Changing Decimals to Fractions
17.  Multiplying and Dividing Decimals by Powers of Ten
18. Changing Decimals to Percents
19. Changing Percents to Decimals
Section 9:
Mathematicians are Fond of Collections
Read Section 9
20. Introduction to Sets
21. Interval and List Notation
Section 10:
Holding This, Holding That
Read Section 10
22. Introduction to Variables
23. Reading Set Notation
24. Going from a Sequence of Operations to an Expression
25. Going from an Expression to a Sequence of Operations
26. Solving Simple Sentences by Inspection
27. Using Mathematical Conventions
Section 10.5:
Solving For A Particular Variable
(important for science classes)
28. ‘Undoing’ a Sequence of Operations
29. Solving for a Particular Variable
30. Getting Bigger? Getting Smaller?
Section 10.7:
Scientific Notation and Significant Figures
(important for science classes)
31. Scientific Notation
32. Significant Figures and Related Concepts
32.5 (optional)
A Conundrum: When is Equal, not Equal? Or, not Equal, Equal?
Section 11:
Introduction to Fractions
Read Section 11
33. Rewriting Fractions as a Whole Number Plus a Fraction
34. Locating Fractions on a Number Line
35. Fractions Involving Zero
Section 12:
Multiplying Fractions
Read Section 12
36. Finding Reciprocals
37. Determining if a Product is Positive or Negative
38. Multiplying and Dividing Fractions
39. Practice with the Form $\,a\cdot\frac{b}{c}\,$
40. More Practice with the Form $\,a\cdot\frac{b}{c}\,$
41. Renaming Fractional Expressions
Section 13:
Adding Fractions
Read Section 13
42. Practice with Multiples
43. Finding Least Common Multiples
44. Renaming Fractions with a Specified Denominator
45. Practice with Factors
46. Adding and Subtracting Fractions
47. Adding and Subtracting Simple Fractions with Variables
48. Divisibility Equivalences
Section 13.5:
Prime Numbers and Related Concepts
(Short on time? Section 13.5 can be skipped without any loss of continuity.)
48a. Prime Numbers
48b. The Prime Factorization Theorem
48c. Relatively Prime Numbers and Related Concepts
Section 14:
I Live Two Blocks West Of You
Read Section 14
49. Identifying Inequalities as True or False
50. Bigger, Smaller, Greater, Lesser
51. Practice with the Phrases ‘At Least’ and ‘At Most’
52. Identifying Inequalities with Variables as True or False
53. Solving Equations of the Form $\,xy = 0\,$
Section 15:
Numbers Have Lots of Different Names!
Read Section 15
54. Recognizing Zero and One
Section 16:
Exact versus Approximate
Read Section 16
55. Writing Fractions in Simplest Form
56. Deciding if a Fraction is a Finite or Infinite Repeating Decimal
57. Deciding if Numbers are Equal or Approximately Equal
Section 17:
Rounding
Read Section 17
58. Rounding Decimals to a Specified Number of places
Section 18:
Unit Conversion
Read Section 18
59. Tables of Unit Conversion Information 60. Classifying Units as Length, Time, Volume, Weight/Mass 61. Practice with Unit Abbreviations 62. Practice with Unit Names 63. Practice with Unit Conversion Information 64. One-Step Conversions
Section 19:
More Unit Conversion
Read Section 19
65. Multi-Step Conversions
66. Rate Problems
67a Work Problems: Basic Concepts
67b Work Problems: Quick-and-Easy Estimates
67c Work Problems: Guided Practice
Section 20:
Exponent Notation
Read Section 20
68. Practice with Exponents
69. Practice with Order of Operations
69.3 (optional) Laurel, Yanny, Cookies, Bananas, and Clocks
69.5 Taking PEMDAS too Literally: Don't Make This Mistake!
70. Basic Exponent Practice with Fractions
Section 21:
Exponent Laws
Read Section 21
71. Practice with $\,x^mx^n = x^{m+n}\,$
72. Practice with $\,(x^m)^n = x^{mn}\,$
73. Practice with $\,x^m/x^n = x^{m-n}$
74. Practice with $\,x^{-p} = 1/x^p$
75. One-Step Exponent Law Practice
76. Multi-Step Exponent Law Practice
Section 22:
Radicals
Read Section 22
77. Practice with Radicals
78. Approximating Radicals
78.5 Renaming Square Roots
Section 23:
Rational Exponents
Read Section 23
79. Writing Radicals in Rational Exponent Form
80. Writing Rational Exponents as Radicals
81. Practice with Rational Exponents
Section 24:
The Distributive Law
Read Section 24
82. Practice with  x  and  -x
83. Practice with Products of Signed Variables
84. Practice with the Distributive Law
85. Mental Math: Addition
86. Don't Mix Up $\,3x\,$ Versus $\,x^3\,$!
Section 25:
Revisiting Exponents
Read Section 25
87. Equal or Opposites?
88. Recognizing the Patterns $\,x^n\,$ and $\,(-x)^n\,$
89. Writing Expressions in the Form $\,kx^n$
90. Writing More Complicated Expressions in the Form $\,kx^n$
91. Writing Quite Complicated Expressions in the Form $\,kx^n$
Section 26:
FOIL and More
Read Section 26
92. Identifying Variable Parts and Coefficients of Terms
93. Combining Like Terms
94. Simplifying Expressions Like $\,-a(3b-2c-d)\,$
95. Basic FOIL
96. More Complicated FOIL
97. Simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$
98.  Simplifying Expressions Like $\,(a-b)(c+d-e)\,$
98.5 Dividing More Than One Term by a Single Term
Section 27:
These Sentences Certainly Look Different!
Read Section 27
99. Practice with the Mathematical Words And, Or, and Is Equivalent To
Section 28:
Introduction to Factoring
Read Section 28
100. Recognizing Products and Sums; Identifying Factors and Terms
101. Identifying Common Factors
102. Factoring Simple Expressions
Section 29:
Greatest Common Factor
Read Section 29
103. Listing All the Factors of a Whole Number
104. Finding the Greatest Common Factor of 2 or 3 Numbers
105. Finding the Greatest Common Factor of Variable Expressions
106. Factoring out the Greatest Common Factor
Section 30:
Transforming Tool #1
(the Addition Property of Equality)
Read Section 30
107. The Addition Property of Equality
Section 31:
Transforming Tool #2
(the Multiplication Property of Equality)
Read Section 31
108. The Multiplication Property of Equality
Section 32:
Solving Linear Equations in One Variable
Read Section 32
109. Solving Simple Linear Equations with Integer Coefficients
110. Solving More Complicated Linear Equations with Integer Coefficients
111. Solving Linear Equations Involving Fractions
112. Solving Linear Equations, All Mixed Up
Section 32.5:
Applications and More
113. Simple Word Problems Resulting in Linear Equations
Section 33:
Solving Linear Inequalities in One Variable
Read Section 33
114. Solving Simple Linear Inequalities with Integer Coefficients
115. Solving Linear Inequalities with Integer Coefficients
116. Solving Linear Inequalities Involving Fractions
117. Solving Linear Inequalities, All Mixed up
Section 34:
Introduction to Absolute Value
Read Section 34
118. Simplifying Basic Absolute Value Expressions
119. Determining the Sign (Positive or Negative) of Absolute Value Expressions
120. Solving Simple Absolute Value Sentences
121. Solving Sentences Involving ‘Plus or Minus’
Section 35:
Solving Absolute Value Equations
Read Section 35
122. Solving Absolute Value Equations
Section 36:
Solving Absolute Value Inequalities Involving ‘Less Than’
Read Section 36
123. Solving Absolute Value Inequalities Involving ‘Less Than’
Section 37:
Finishing Up Absolute Value Sentences
Read Section 37
124. Solving Absolute Value Inequalities Involving ‘Greater Than’
125. Solving Absolute Value Sentences (All Types)
Section 38:
Factoring a Difference of Squares
126. Identifying Perfect Squares
127. Writing Expressions in the Form $\,A^2\,$
128. Factoring a Difference of Squares
Section 39:
Solving Equations Involving Perfect Squares
129. Solving Simple Equations Involving Perfect Squares
130. Solving More Complicated Equations Involving Perfect Squares
131. Translating Simple Mathematical Phrases
132. Word Problems Involving Perfect Squares
Section 40:
Factoring Trinomials
133. Basic Concepts Involved in Factoring Trinomials
134. Factoring $\,x^2 + bx + c\,$,   $\,c \gt 0\,$
135. Factoring $\,x^2 + bx + c\,$,   $\,c \lt 0\,$
136. Factoring Trinomials, All Mixed Up
Section 41:
Solving Quadratic Equations by Factoring
137. Identifying Quadratic Equations
138. Writing Quadratic Equations in Standard Form
139. Solving Simple Quadratic Equations by Factoring
Section 42:
More on Quadratic Equations
140. Factoring $\,ax^2 + bx + c\,$
141. Solving More Complicated Quadratic Equations by Factoring
Section 42.5:
Arithmetic with Fractions Involving Variables
142. Multiplying and Dividing Fractions with Variables
143. Adding and Subtracting Fractions with Variables
Section 43:
Percent Increase and Decrease
144. Writing Expressions Involving Percent Increase and Decrease
145. Calculating Percent Increase and Decrease
146. Problems Involving Percent Increase and Decrease
147. More Problems Involving Percent Increase and Decrease
Section 44:
Introduction to the Coordinate Plane
148.  Locating Points in Quadrants and on Axes
149. Practice with Points
150. The Pythagorean Theorem
151. The Distance Formula
152. The Midpoint Formula
153. Introduction to Equations and Inequalities in Two Variables
Section 45:
Lines
154. Introduction to the Slope of a Line
155. Practice with Slope
156. Graphing Lines
157. Finding Equations of Lines
Section 46:
More On Lines
158. Point-Slope Form
159. Horizontal and Vertical Lines
160. Parallel and Perpendicular Lines
160.5 Linear Inequalities in Two Variables
Section 47:
Functions
161. Introduction to Functions
162. Introduction to Function Notation
163. More Practice with Function Notation
164. Domain and Range of a Function