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Support NowAlgebra can be easily summarized in *a few rules that you need to follow and at Union Test Prep, we have the essential formulas you’ll need for Algebra. You can see them all at a glance, and be prepared to succeed at the GRE® Quantitative Reasoning Test.
Remember that this chart only shows formulas for one part of the test: Algebra. Access our other three formula charts for the GRE® Quantitative Reasoning section, here:
Category  Formula  Symbols  Comment 

Algebra  \(x+ a = b \rightarrow x= b  a\) \(xa = b \rightarrow x = b+a\) \(x\cdot a = b \rightarrow x = b \div a\) \(x \div a = b \rightarrow x = b \cdot a\) \(x^a = b \rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x} = b \rightarrow x = b^a\) \(a^x = b \rightarrow \dfrac{\log{b}}{\log{a}}\) 
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  \((x^a)^b = x^{a\cdot b}\)  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 
\(Ax+By=C\)  A, B, C = any real number y = dependent variable x = independent variable 
Standard form 
Linear Equations 
\(y = mx+b\)  y = dependent variable m = slope x = independent variable b = y axis intercept 
SlopeIntercept Form. Try to convert any given linear equation to this format. 
Linear Equations 
\(m = \dfrac{y_2y_1}{x_2x_1}\)  m = slope \(y_n\) = independent variable (point n) \(x_n\) = dependent variable (point n) 
This is a rearranged version of the pointslope form. 
Linear Equations 
\(y  y_1 = m(xx_1)\)  \((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope 
Point slope form 
Quadratic Equations 
\(x = \frac{b\pm\sqrt{b^24 \cdot a \cdot c}}{2 \cdot a}\)  a, b = constants c = constant (yaxis intercept) x = variable 
Quadratic Formula for equation in form \(ax^2+bx+c=0\) 
Quadratic Equations 
\((a\pm b)^2= a^2 \pm 2ab + b^2\)  a,b = constants or variables  Square of a sum or difference 
Quadratic Equations 
\(a^2  b^2 = (a+b)\cdot (ab)\)  a,b = constants or variables  Difference of squares 
Computing Interest 
\(SI = P \cdot IR \cdot t\)  SI = Simple Interest P = Principal (Amount borrowed) IR = Interest Rate t = time (same units as in IR) 

Computing Interest 
\(A_{SI} = P + SI = P \cdot (1+IR\cdot t)\)  \(A_{SI}\) = Future value to be paid (for SI) P = Principal (Amount borrowed) SI = Simple Interest IR = Interest Rate t = time (same units as in IR) 

Computing Interest 
\(A_{CI} = P \cdot \big{(}1+\dfrac{IR}{n}\big{)}^{n\cdot t}\)  \(A_{CI}\) = Future value to be paid (for CI) P = Principal (Amount borrowed) IR = Interest Rate n = # of times interest is compounded per unit,t t = time (same units as in IR) 
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