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Formulas for the Algebra Questions on the GRE® Quantitative Reasoning Test

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!

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 sample problems, flashcards, and study guide 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:

Arithmetic

Geometry

Data Analysis

Category Formula Symbols Comment
Algebra \(x+ a = b \rightarrow x= b - a\)
\(x-a = b \rightarrow x = b+a\)
\(x\cdot a = b \rightarrow x = b \div a\)
\(x \div a = b \rightarrow x = b \cdot a\)
\(x^a = b \rightarrow x = \sqrt[a]{b}\)
\(\sqrt[a]{x} = b \rightarrow x = b^a\)
\(a^x = b \rightarrow \dfrac{\log{b}}{\log{a}}\)
a,b = constants
x = variable
 
Algebra \(x^a \cdot x^b = x^{a+b}\) a,b,x = any real number  
Algebra \(\dfrac{x^a}{x^b} = x^{a-b}\) 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
Slope-Intercept
Form. Try to convert
any given linear
equation to this
format.
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 rearranged
version 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
Point slope form
Quadratic
Equations
\(x = \frac{-b\pm\sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}\) a, b = constants
c = constant (y-axis 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
\(a^2 - b^2 = (a+b)\cdot (a-b)\) 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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