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!
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  \(x+a=b \Rightarrow x=ba\) \(xa=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\) 
a, b = constants x = variable 

Algebra  \(x^a \cdot x^b=x^{a+b}\)  a, b, x = any real number  
Algebra  \(\dfrac{x^a}{x^b}=x^{ab}\)  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 = yaxis intercept 
Slopeintercept 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 pointslope form. 
Linear Equations 
\(yy_1 = m(xx_1)\)  \((x_1,y_1)\) = point on the line y = dependent variable x = independent variable m = slope y = independent variable x = dependent variable 
PointSlope Form 
Quadratic Equations 
\(x= \dfrac{b \pm \sqrt{b^24 \cdot a \cdot c}}{2 \cdot a}\)  a, b, c = constants c = yaxis 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 
\(a^2  b^2 = (a+b)(ab)\)  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  \(\% = \dfrac{\vert ba \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\)  % = % increase or decrease a = new value b = original value c = amount of change 
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