If you are preparing for the algebra questions on the GRE Quantitative Reasoning Test, chances are that you are overwhelmed by the huge amount of content you need to cover. But you don’t need to feel that way!
The algebra questions cover topics such as linear and quadratic equations, factoring, simplifying algebraic expressions, exponents, and setting up equations to solve word problems.
Algebra 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.
You can also check out our free practice tests, flashcards, and study guides if you want to dig deeper.
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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