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GRE Math - Quantitative Reasoning

Need some free GRE Math help?
This is a series of free lessons that will cover the mathematics topics required for the Quantitative Reasoning Measure of the GRE revised General Test. It is based on the Math Review text from ETS - the organization that conducts the examinations.

The topics covered are arithmetic, algebra, coordinate geometry, geometry, data analysis and tips for the GRE Examinations.

GRE Math Practice Test Questions and Solutions

These videos will give you a quick revision for some common GRE exam style questions. Scroll down the page if you need more in-depth explanations and examples.


Integers Adding, Subtracting, Multiplying and Dividing Integers, Even and Odd Integers, Factors and Multiples, Least Common Multiple, Greatest Common Factor, Prime Numbers, Prime Factorization Fractions Equivalent Fractions, Reducing Fractions, Mixed Numbers, Adding and Subtracting Fractions, Multiplying and Dividing Fractions
Exponents and Roots Exponents, Zero and Negative Exponents, Square Roots, Rules for Square Roots, Roots of Higher Order Decimals Decimals, Decimal Place Value, Expanding Decimals, Convert Decimals to Fractions, Convert Fractions to Decimals, Repeating Decimals, Rational and Irrational Numbers
Real Numbers Rational and Irrational Numbers, Real Numbers, Inequalities, Absolute Value,Properties of Real Numbers Ratio Ratios and Proportions
Percent Percent, Percents, Fractions, and Decimals, Percent Problems, Using Percent Equation, Using Percent Proportion, Percent Application Problems, Percent Change  


Operations with Algebraic Expressions Algebraic Expressions, Simplifying Algebraic Expressions, Combine Like Terms, Distributive Property, Factor out the GCF, Multiplying Expressions, Expanding, Perfect Square Trinomials, Difference of Two Squares, Simplifying Rational Expressions Rules of Exponents Rules of Exponent, Zero Exponents, Product Rule, Quotient Rule, Power Rule, Negative Exponent, Same Exponent
Solving Linear Equations Equivalent Equations, Solving Linear Equations, Isolate the Variables, Examples with Single Step, Examples with Multiple Steps, Examples using Combining Like Terms, Examples using Distributive Property Solving Linear Equations in Two Variables Linear Equations in Two Variables, Solving Simultaneous Equations, Using the Substitution Method, Using the Elimination Method
Solving Quadratic Equations Quadratic Equations, Solve Quadratic Equations using the Quadratic Formula, Using the Discriminant to find the number of Solutions, Solve Quadratic Equations by Factoring Solving Linear Inequalities Examples on how to solve linear inequalities.
FunctionsFunctions as equations, Domain of Functions Applications Applications of Algebra, Translating Words to Algebra, Examples of using Algebra to solve Word Problems, Average Word Problems, Mixture Word Problems, Distance, Rate, Time Word Problems, Work Word Problems, Word Problems that involve Simultaneous Equations, Word Problems that involve Inequalities
Interest Applications Simple Interest Word Problems, Compound Interest Word Problems  

Coordinate Geometry

Coordinate Plane xy-coordinate system, four quadrants, ordered pair, plot points on the coordinate plane, reflection of points about the x-axis, y-axis and origin Distance Formula
Equations of Lines Equations of Parallel Lines and Perpendicular Lines
Solving Systems of Equations using the Graphical Method Solving Stems of Inequalities using the Graphical Method
Quadratic Graphs Equations of Circles
Graphs of Functions how to graph some basic functions, how to graph piece-wise defined functions, reflection of graphs in the x-axis or y-axis, horizontal and vertical graph transformations, vertical stretching and shrinking graphs, graphs of inverse functions, how to find the inverse function using algebra  


Lines and Angles points, lines and planes, angles, parallel lines and angles Polygons polygons, interior and exterior angles of regular polygons
Triangles angles and sides of triangles, types of triangles, Pythagorean Theorem, special right triangles, area of a triangle, congruent triangles, similar triangles Quadrilaterals quadrilaterals; squares, rectangles, parallelograms, trapezoids, area of quadrilaterals
Circles circumference of a circle, arc length, area of a circle, area of sector, tangent of a circle, inscribed and circumscribed polygons Three-Dimensional Figures rectangular solids and right circular cylinders.

Data Analysis

The goal of data analysis is to understand data well enough to describe past and present trends, predict future events with some certainty, and thereby make better decisions. In this limited review of data analysis, we begin with tools for describing data; follow with tools for understanding counting and probability; review the concepts of distributions of data, random variables, and probability distributions; and end with examples of interpreting data.

Graphical Methods for Describing Data Numerical Methods for Describing Data
Counting Methods Probability
Distributions of Data, Random Variables, and Probability Distributions  

Tips for the GRE exam

Learn all about the structure of the test and the new question types, get resources for additional practice and information on the new GRE, and hear advice on how to study and prepare for the exam. The following video provides an overview of the GRE and explains how to make the most of your study time. The following video gives a GRE test review. It explains what you should know about the GRE before you get going with GRE prep.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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