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# Algebra and Function Formulas for the TSIA2

Have you ever wondered if you have “what it takes” to succeed at math in college? Well, the TSIA2 is designed to help you answer that question! However, there is an issue. Sometimes the question is not whether or not you have the calculating skills, but if you remember the specific equations needed to solve the problems. That’s where Union Test Prep comes to the rescue! In the following chart, you will find the essential Algebra and Function Formulas you should know if you want to ace the TSIA2.

You’ll also want to check out our other two math formula charts for this test:

Formulas for Geometry and Measurement

Formulas for Data Analysis, Statistics, and Probability

And to practice using these formulas and others, check out all of our free TSIA2 test prep.

## Algebra and Function Formulas

Category Formula Symbols Comment
Equations
and
Expressions
$$x+a=b \Rightarrow x=b-a$$
$$x-a=b \Rightarrow x=b+a$$
$$x \cdot a=b \Rightarrow x=b \div a$$
$$x \div a=b \Rightarrow x=b \cdot a$$
$$x^a=b \Rightarrow x = \sqrt[a]{b}$$
$$\sqrt[a]{x}= b \Rightarrow x= b^a$$
$$a^x=b \Rightarrow x=\frac{log\ b}{log\ a}$$
a, b = constants
x = variable

Equations
and
Expressions
$$x^a \cdot x^b = x^{a+b}$$ a, b, x = any real number
Equations
and
Expressions
$$\frac{x^a}{x^b}=x^{a-b}$$ a, b, x = any real number
Equations
and
Expressions
$$(x^a)^b = x^{a \cdot b}$$ a, b, x = any real number
Equations
and
Expressions
$$(x \cdot y)^a = x^a \cdot y^a$$ a, b, x = any real number
Equations
and
Expressions
$$x^1 = x$$ x = any real number
Equations
and
Expressions
$$x^0 = 1$$ x = any real number
Equations
and
Expressions
$$x^{-a} = \frac {1}{x^a}$$ a, x = any real number
Equations
and
Expressions
$$x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a$$ a, b, x = any real number
Equations
and
Expressions
$$\frac{x}{\sqrt{y}} \cdot \frac {\sqrt{y}}{\sqrt{y}} = \frac{x \sqrt{y}}{y}$$ x, y = any real number
Linear
Equations
$$A \cdot x + B \cdot y = C$$ A, B, C = any real number
y = dependent variable
x = independent variable
Standard form
Linear
Equations
$$y = m \cdot x + b$$ y = dependent variable
m = slope
x = independent variable
b = y axis intercept
Slope-intercept form
Try to convert any linear
equation to this form.
Linear
Equations
$$m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$$ m = slope
$$y_n$$ = independent variable (point n)
$$x_n$$ = dependent variable (point n)
This is a rearrangement of the
point-slope form.
Linear
Equations
$$y-y_1 = m(x-x_1)$$ $$(x_1,y_1)$$ = point on the line
m = slope
y = independent variable
x = dependent variable
Point-slope form
$$x= \frac{-b \pm \sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}$$ a, b, c = constants
in the form $$ax^2+bx+C=0$$