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 of Addition
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
Quadratic 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)	Quadratic Formula for equation in the form \(ax^2+bx+c=0\)
Quadratic 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
Quadratic Equations	\(a^2 - b^2 = (a+b)(a-b)\)	a, b = constants or variables	Difference of squares
Percents	\(a \cdot b\%=a \cdot \dfrac{b}{100}\)	a = any real number b% = any percent	Remember to simplify if possible
Percents	\(\% = \dfrac{\vert b-a \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\)	% = % increase or decrease a = new value b = original value c = amount of change