# Formula List for the PERT Mathematics Test

One of the main problems with math is that we tend to forget concepts and skills when we do not regularly put them into practice.

That becomes an issue when taking the PERT Mathematics test because chances are that it’s been a long time since you reviewed the fundamental concepts of math. So, how can you ace the PERT Mathematics test?

That’s where the team at Union Test Prep comes in. We have gathered the essential formulas you’ll need for the PERT Mathematics test and put them together in the following chart. Use it to solve the free sample problems we also have for you. You can find PERT practice questions, as well as flashcards and a study guide on our website. And best of all, it’s free!

## Formulas for the PERT Mathematics Test

Category Formula Symbols Comment
Arithmetic $$a+b=b+a$$

$$a \cdot b = b \cdot a$$
a, b = any constant or variable Commutative
Property
Arithmetic $$a+(b+c)=(a+b)+c$$

$$a \cdot (b \cdot c)=(a \cdot b) \cdot c$$
a, b, c = any constant or variable Associative
Property
Arithmetic $$a \cdot (b+c)=a \cdot b + a \cdot c$$ a, b, c = any constant or variable Distributive
Property
Arithmetic $$a+0=a$$ a = any constant or variable Identity Property
Arithmetic $$a \cdot 1 = a$$ a = any constant or variable Identity Property
of Multiplication
Arithmetic $$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Arithmetic $$\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c)}{(b \cdot d)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Arithmetic $$\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{a \cdot d)}{(b \cdot c)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Arithmetic $$a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}$$ a, b, c = any real number Remember to simplify
the fraction if
possible.
Algebra $$x+a=b \Rightarrow x=b-a$$

$$x-a=b \Rightarrow x=b+a$$

$$x \cdot a=b \Rightarrow x=b \div a$$

$$x \div a=b \Rightarrow x=b \cdot a$$

$$x^a=b \Rightarrow x = \sqrt[a]{b}$$

$$\sqrt[a]{x}= b \Rightarrow x= b^a$$

$$a^x=b \Rightarrow x=\frac{log\ b}{log\ a}$$
a, b = constants
x = variable

Algebra $$x^a \cdot x^b=x^{a+b}$$ a, b, x = any real number
Algebra $$\dfrac{x^a}{x^b}=x^{a-b}$$ a, b, x = any real number
Algebra $$(x^a)^b =a^{a \cdot b}$$ a, b, x = any real number
Algebra $$(x \cdot y)^a = x^a \cdot y^a$$ a, b, y = any real number
Algebra $$x^1=x$$ x = any real number
Algebra $$x^0=1$$ x = any real number
Algebra $$x^{-a} = \dfrac {1}{x^a}$$ a, x = any real number
Algebra $$x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a$$ a, b, x = any real number
Algebra $$\dfrac{x}{\sqrt{y}} \cdot \dfrac {\sqrt{y}}{\sqrt{y}} = \dfrac{x \sqrt{y}}{y}$$ 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
$$m = \dfrac{(y_2 - y_1)}{(x_2 - x_1)}$$ 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
y = dependent variable
x = independent variable
m = slope

y = independent variable

x = dependent variable
Point-Slope Form
Equations
$$x= \dfrac{-b \pm \sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}$$ a, b, c = constants

c = y-axis intercept

x = variable (x intercepts)
equation in the form
$$ax^2+bx+c=0$$
Equations
$$(a \pm b)^2 = (a^2 \pm 2 \cdot a \cdot b+b^2)$$ a, b = constants or variables Square of sum or difference
$$a^2 - b^2 = (a+b)(a-b)$$ a, b = constants or variables Difference of squares
Percents $$a \cdot b\%=a \cdot \dfrac{b}{100}$$ a = any real number
Percents $$\% = \dfrac{\vert b-a \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100$$ % = % increase or decrease