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)

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!

You can also check out our free sample problems, flashcards, and study guide if you want to dig deeper.

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