# 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
Section 2:
Brushing Up On Basic Arithmetic Skills
Section 3:
The Real Numbers
Section 4:
Section 5:
Subtraction of Signed Numbers
Section 6:
Average
Section 7:
The Base Ten Number System
Section 8:
Decimals
Section 9:
Mathematicians are Fond of Collections
Section 10:
Holding This, Holding That
Section 10.5:
Solving For A Particular Variable
(important for science classes)
Section 10.7:
Scientific Notation and Significant Figures
(important for science classes)
Section 11:
Introduction to Fractions
Section 12:
Multiplying Fractions
39. Practice with the Form $\,a\cdot\frac{b}{c}\,$
40. More Practice with the Form $\,a\cdot\frac{b}{c}\,$
Section 13:
Section 13.5:
Prime Numbers and Related Concepts
(Short on time? Section 13.5 can be skipped without any loss of continuity.)
Section 14:
I Live Two Blocks West Of You
Section 15:
Numbers Have Lots of Different Names!
Section 16:
Exact versus Approximate
Section 17:
Rounding
Section 18:
Unit Conversion
Section 19:
More Unit Conversion
Section 20:
Exponent Notation
Section 21:
Exponent Laws
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 $\,x^{-p} = 1/x^p$
Section 22:
Section 23:
Rational Exponents
Section 24:
The Distributive Law
86. Don't Mix Up $\,3x\,$ Versus $\,x^3\,$!
Section 25:
Revisiting Exponents
88. Recognizing the Patterns $\,x^n\,$ and $\,(-x)^n\,$
89. Writing Expressions in the Form $\,kx^n$
Section 26:
FOIL and More
94. Simplifying Expressions Like $\,-a(3b-2c-d)\,$
95. Basic FOIL
97. Simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$
98.  Simplifying Expressions Like $\,(a-b)(c+d-e)\,$
Section 27:
These Sentences Certainly Look Different!
Section 28:
Introduction to Factoring
Section 29:
Greatest Common Factor
Section 30:
Transforming Tool #1
Section 31:
Transforming Tool #2
(the Multiplication Property of Equality)
Section 32:
Solving Linear Equations in One Variable
Section 32.5:
Applications and More
Section 33:
Solving Linear Inequalities in One Variable
Section 34:
Introduction to Absolute Value
Section 35:
Solving Absolute Value Equations
Section 36:
Solving Absolute Value Inequalities Involving ‘Less Than’
Section 37:
Finishing Up Absolute Value Sentences
Section 38:
Factoring a Difference of Squares
Section 39:
Solving Equations Involving Perfect Squares
Section 40:
Factoring Trinomials
134. Factoring $\,x^2 + bx + c\,,$   $\,c \gt 0\,$
135. Factoring $\,x^2 + bx + c\,,$   $\,c \lt 0\,$
Section 41:
Section 42:
140. Factoring $\,ax^2 + bx + c\,$