GRE Resources

### GRE - Brainfuse Quick Guide

A Sample GRE Live Help Session

View a sample study session on Brainfuse to see how you can use Live Help and The Writing Lab to prepare for the exam.

Develop a Game Plan for Taking the Test

These strategies will help you maximize the number of points that you'll earn while taking the test.

A Preview of the Test

This video shows you each section of the revised GRE and includes sample questions. (Make sure to press pause and work on them before you see the answers.)

### GRE Simplified - Your Step-by-Step Guide

01. An Inside Look at the Revised GRE

This is a breakdown of the revised GRE along with a comparison between the computer-based and paper-based exams.

02. Make Your Appointment @ the Test Center

Make sure that you register at an ideal time and in an ideal place.

03. Your Brainfuse GRE Study Plan

How can you use Brainfuse to work toward (or surpass) the score you'd like to earn?

04. Pacing Your Prep for the GRE

Here is a menu of customized study plans that will help you stay on track during the months, weeks, and days leading up to your exam.

05. Beat the Revised Scoring System

Understand the new scoring system and use it to maximize your score.

06. What Score Should I Aim For?

Set a goal and work toward that goal as you study.

07. Mimic Test-Taking Conditions

Rehearse for the test by taking practice exams in a "test-centerish" setting.

08. View and Review Your Answers

In order to learn from a test, you need to review how to answer every difficult and incorrect question.

09. The Analytical Writing Section: Question Types & Strategies

Get to know the 2 types of writing prompts and the best ways to respond to them.

10. GRE Analytical Writing Checklist

What will the human grader and robot grader look for when they read your essay?

11. Sample Plan for the "Analyze an Issue" Essay

Here is a sample of a plan that a writer used as a guide when responding to the "Analyze an Issue" prompt.

12. Sample "Analyze an Issue" Essay

This is an example of an "Analyze an Issue" essay that would earn a "6" on the GRE.

13. Sample Plan for the "Analyze an Argument" Essay

Here is a sample of a plan that a writer used as a guide when responding to the "Analyze an Argument" prompt.

14. Sample "Analyze an Argument" Essay

This is an example of an "Analyze an Argument" essay that would earn a score of "6" on the GRE.

15. Feedback from the Brainfuse Writing Lab

Submit your analytical writing essays to the Writing Lab in order to receive a score based on the GRE rubric and advice on improving your writing.

16. The Verbal Reasoning Section: Question Types & Strategies

This is an overview of each question on the GRE's verbal reasoning section. It includes sample questions, tips for solving them, and cautions to bear in mind as you choose each answer.

17. Upgrade Your GRE Vocabulary

How to study, use, and enjoy knowing so many new words ...

18. Quantitative Reasoning: Question Types & Strategies

Take a look at the 4 question types on the quantitative reasoning section and experiment with test-taking strategies that will help you solve each kind of question.

19. Host Group Study Sessions on MEET

Make studying less solitary by hosting group sessions.

20. The GRE Becomes Kinder As It Ages

Most changes to the GRE actually help the test taker maximize the score that is sent to grad programs.

21. The Day of the Test

What to do, what to bring, and what to leave at home ...

22. After the Test: Settle Your Score With ETS

You cannot only use strategies while taking the test, but ETS now lets you choose the best way to present your scores to grad schools and potential employers.

23. When to Avoid the Answer Choices: A Test-Taking Strategy

Test makers need to create answer choices that will tempt test takers who are in a rush. Here's a lesson on when and how you can avoid them ...

24. When to Use the Answer Choices: A Test-Taking Strategy

There are also times when you can use the answer choices to solve a problem. Here's a lesson on when and how to do that ...

25. The Work-GRE Balance

How can you manage a full-time job and GRE test prep?

26. Working Parents and The GRE -- Can It Happen?

Yes. This resource includes some strategies that can help you follow your study plan and care for children.

### GRE Analytical Writing Lessons

Video - GRE Analytical Writing: Analyze an Argument, Part I

A checklist with 4 key terms helps this test taker analyze an argument.

Video - GRE Analytical Writing: Analyze an Argument, Part II

A checklist with 4 key terms helps this test taker analyze an argument.

Video - GRE Analytical Writing: Analyze an Issue

This test taker plans her response to an essay prompt on the GRE.

Sample Plan - "Analyze an Argument"

A sample of a plan used to respond to one "Analyze an Argument" prompt

Sample Essay - "Analyze an Argument" Response

A sample response to an "Analyze an Argument" writing prompt on the GRE

Sample Plan - "Analyze an Issue"

This writer used an outline to plan her response.

Sample Essay - "Analyze an Issue" Sample Response

A sample response to an "Analyze the Issue" writing prompt on the GRE

Lesson - Preparing for Analytical Writing Tasks

How can you prepare for the analytical writing tasks?

Lesson - Tips for Analyzing an Argument

How can you respond to the "Analyze an Argument" prompt?

Lesson - Tips for Analyzing an Issue

How can you respond to the "Analyze an Issue" prompt?

Lesson - Logical Flaws

Be able to identify and refute these common problems with logical arguments.

Practice - Sample Argument Topics

Practice responding to these argument topics.

Practice - Sample Issue Topics

Practice responding to these issue topics.

Lesson - More Practice With the "Analyze an Argument" Task

Use 4 key terms to analyze an argument.

### GRE Verbal Reasoning Video Lessons

Video - GRE Sentence Equivalence

How can you find 2 synonyms that will complete this sentence?

Video - GRE Critical Reading: Vocabulary and Phrases In Context

How can you figure out the meaning of an unfamiliar word or phrase?

Video - GRE Critical Reading: Author's Tone

How can you determine a writer's attitude toward a topic?

Video - GRE Text Completion

What strategies can you use to complete these sentences?

Video - GRE Critical Reading: Sentence In Passage

Can you describe what the writer is doing in each sentence?

Video - GRE Critical Reading: Evaluating Support

Is this argument logically sound?

Video - GRE Critical Reading: Making Inferences

What could possibly be true in this passage?

Video - GRE Critical Reading: Author's Purpose

Can you tell why an author wrote a certain passage, paragraph, sentence, or phrase?

Video - GRE Critical Reading: Main Idea Questions

What is the author saying about this topic?

Video - GRE Critical Reading: Detail Questions

Double check major and minor details in a passage.

### GRE Verbal Reasoning Lessons

Lesson - Critical Reading Skill: Detail Questions

Anticipate test makers' tricks and practice using strategies that will help you find the correct answer.

Lesson - Critical Reading Skill: Vocabulary in Context

Be able to identify the meanings of words and phrases by using the context of the passage.

Lesson - Critical Reading Skill: Evaluating Support

Be able to evaluate the support provided for an argument.

Lesson - Critical Reading Skill: Identifying Tone

Be able to identify the author's tone in a passage.

Lesson - Critical Reading Skill: Author's Purpose

Be able to identify why the author chose to write a passage or any part of that passage.

Lesson - Critical Reading Skill: Making Inferences

Be able to infer the author's meaning in a passage.

Lesson - Critical Reading Skill: Organizational Patterns and Signal Words

Be able to identify the textual structure and organization of a passage.

Lesson - Critical Reading Skill: Main Idea

Be able to identify the main idea in a passage.

Lesson - Developing Critical Reading Skills

What skills are involved with critical reading?

Lesson - Critical Reading Sample Questions

Read the passage and answer the questions.

Lesson - Sentence Equivalence Sample Questions

Practice these questions and understand the reasoning for the correct responses.

Lesson - Preparing for Sentence Equivalence Questions

What tips can help you answer sentence equivalence questions?

Lesson - Text Completion Sample Questions

Practice these questions and understand the reasoning for the correct answers.

Lesson - Preparing for Text Completion Questions

How should you address Text Completion questions?

Lesson - Preparing for Critical Reading Questions

What can you expect to see in the critical reading sections?

### GRE Video Math Lessons

Types of Real Numbers (Video)

Review the different number types included in the real number system.

Prime vs. Composite Numbers

Compare the qualities of prime and composite numbers.

Commutative Property of Addition

What happen to an addition problem when you change the order of the addends?

Associative Property of Addition (Video)

What happens to an addition problem when you change the grouped numbers?

Commutative Property of Multiplication (Video)

What happens to a multiplication problem when you change the order of the factors?

Associative Property of Multiplication

What happens to a multiplication problem when you change how the factors are grouped?

Mean, Median, and Mode

Practice analyzing data sets in 3 different ways.

Signed Number Multiplication and Division

Review how to multiply and divide signed numbers

Add Integers

How can you add single-digit, double-digit, and triple-digit numbers?

Multiply Integers

Review how to read and solve problems that deal with the multiplication of integers.

Greatest Common Factor

Review how to calculate the GCF of several values.

Prime Factorization [CC]

Review how to rewrite a number as the product of its prime factors.

Signed Number Addition and Subtraction [CC]

How can you add and subtract signed numbers?

Subtract Integers

How can you find the difference between 2 integers?

Subtraction Application Problems [CC]

When do you actually use subtraction?

Order of Operations [CC]

Review the steps to follow when you need to use more than one operation.

Order of Operations Application Problems

Review how to set up and solve problems that involve more than one operation.

Division Application Problems [CC]

Review key words used in division problems and some common situations that call for division.

Place Value

Review how to read whole numbers according to the place value of their digits.

Convert Mixed Numbers to Improper Fractions

How can you convert a mixed number into an improper fraction?

Convert Improper Fractions to Mixed Numbers

How can you convert an improper fraction into a mixed number?

Equivalent Fractions

How can you identify equivalent fractions?

Understanding Fractions

Review the components of a fraction and understand what they mean.

Simplify Fractions

How can you reduce a fraction to its simplest form?

Compare Fractions [CC]

5/7 vs 6/7. Which value is greater?

Add Fractions

Why do you need a common denominator to add fractions?

Subtract Fractions

Why do you need a common denominator to subtract fractions?

Subtract Fractions and Mixed Numbers

What are 2 strategies that you can use to subtract fractions and mixed numbers?

Multiply Fractions (Video)

How can you multiply fractions?

Divide Fractions [CC]

Why do we use reciprocals to divide fractions?

Convert Fractions, Decimals, and Percentages

How can you convert decimals to fractions and percentages.

Write Decimals

How can you write decimals out in word form?

Round Decimals

How does rounding decimals differ from rounding whole numbers?

Addition with Decimals

Does the decimal point change the process?

Subtraction with Decimals [CC]

Does the decimal point change the process?

Multiply Decimals [CC]

Why are zeroes are so important in these problems?

Division with Decimals [CC]

How can you use a decimal point to help you divide decimals?

Percent as Proportion [CC]

How can you solve problems by writing a percentage as a proportion?

Percent Equations [CC]

How can you find the percent of a number and understand the different parts of the basic percent equation?

Percent Change [CC]

Review how to find percent increase and decrease through two word problems involving a lamp that will not sell.

Convert Fractions, Decimals, and Percents

How can you convert percentages to decimals or fractions?

Percent Change [CC]

How can you use percent to understand how much a quantity has increased or decreased?

Negative and Rational Exponents

Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CCSS: HS.N-RN.A.2)

Add and Subtract Square Roots

How can you add and subtract square roots?

Rule of Zero [CC]

What is the value of a number with a zero as an exponent?

Cube Roots

Compare cube roots and square roots, and then review how to find the cube root of a negative number.

Simplify Square Roots

How can you search for perfect squares, the factors that allow us to simplify square roots?

Multiply Square Roots [CC]

How can you multiply expressions with square roots?

Quotient of Powers Property

How can you divide and simplify exponential expressions?

Powers and Exponents

How can you use a power's base and exponent to rewrite the value as a product of factors?

Quotient of Powers Property

Review this law of exponents and use it to divide powers.

Power Rule of Exponents

How can you raise one power to another power?

Mean, Median, and Mode [CC]

How can you analyze a data set in 3 different ways?

Scientific Notation [CC]

How can you work with unimaginably large and small numbers?

Weighted Average [CC]

What happens when each quantity in a set has a different value?

Ratios

How can you work with ratios?

Scale

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)

Scale Factor

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)

Rates

Review how to identify rates and use them to set up expressions.

Rates [CC]

How can you use rates to set up expressions?

Proportion

How can you read proportions and simplify expressions?

Write Expressions and Equations [CC]

Do you want to learn how to read word problems and convert them to algebraic expressions?

Simplify Algebraic Expressions [CC]

What steps must be taken when simplifying algebraic expressions?

Absolute Value [CC]

What do -5 and +5 have in common?

Distributive Property [CC]

Use multiplication to distribute a value to each term in an expression.

Evaluate Algebraic Expressions [CC]

How do you evaluate algebraic expressions?

Multiply Monomials [CC]

How do you go about multiplying terms that contain both constants and variables?

Exponential Equations

Can you identify the fundamentals of exponential equations?

Simplify Rational Expressions (Video)

These answers are only right under certain conditions ... Find out what those conditions are by watching this video.

Solve Inequalities (Video)

Review how to solve linear inequalities and graph their solutions.

Domain and Range [CC]

Identify the domain and range of a data set or function.

Interval Notation (Video)

Use parentheses and brackets as a shorthand way to show possible values of x.

Projectile Motion, Part 1: The Launch

Use this equation to analyze the flight of a marshmallow.

Projectile Motion, Part 2: The Drop

Compare the times of 2 marshmallows -- one dropped, one hurled.

Mixture Problems, Part 1

Learn how to work with the concentration of a highly caffeinated solution.

Mixture Problems, Part 2

Not all mixture problems happen in a lab or a kitchen ...

Distance Problems, Part 1

Use the distance formula to solve for distance, rate, and time (in Part 2).

Distance Problems, Part 2

Use the distance formula to solve one final problem ...

Work Rate Problems

You can maximize your efficiency with this formula ...

Simple Interest

Learn how to calculate the simple interest using a given rate on a given amount.

Function Notation [CC]

Learn how to rewrite functions by using functional notation.

Graphing Functions

Learn how to graph a given function.

1-to-1 Functions

Review the characteristics of a 1-to-1 function.

Operations with Functions

Review how to add, subtract, and multiply two functions (e.g. f(x) + g(x)).

Quadratic Formula

Learn how to use the quadratic formula.

Square Root Property

Review a second method for solving quadratic equations.

Completing the Square

This is another strategy that will help you solve a quadratic equation, and it has roots.

Classify Triangles

Review how classify triangles according to their sides and angles.

Quadrilaterals

Classify quadrilaterals and find the missing angle in one of them.

Area and Perimeter of Quadrilaterals [CC]

Review how to use the length and width of a quadrilateral to determine its perimeter and area.

Area of a Triangle

Find the area of any type of triangle.

Perimeter of Triangles

Find the perimeter of 4 kinds of triangles (and shortcuts for 2 of them!).

Pythagorean Theorem

Review how to work with the Pythagorean Theorem.

Volume and Surface Area of a Cylinder [CC]

Learn how to find the volume and surface area of a cylinder.

Volume of a Rectangular Prism

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (CCSS: 7.G.B.6)

Circumference and Area

Review how to find the circumference and area of a circle.

Angle Measures in Polygons

Identify polygons and review how to find their angle measures.

Volume of Cones and Spheres

Review how to calculate the volume of cones and spheres.

Similar Polygons

How can you figure out if two polygons are similar?

Volume of Pyramids

Review how to calculate the volume of pyramids.

Special Right Triangles: 45-45-90 Triangles

Review how to work with the special right triangle with 45-45-90 angles.

Special Right Triangles: 30-60-90 Triangles, Part 1

Review how to work with the special right triangle with 30-60-90 angles.

Special Right Triangles: 30-60-90 Triangles, Part 2

The lesson on 30-60-90 triangles continues ...

Slope-Intercept Form (Video)

Review how to find the slope using the slope-intercept form.

Add and Subtract Polynomials

What are the fundamental aspects of polynomial manipulation?

Expand Polynomials, Part 1

Review how expand polynomials.

Expand Polynomials, Part 2

Review how to expand polynomials by using foil, distributive property, and like terms.

Factor Polynomials [CC]

Review two strategies that you can use to factor polynomials.

Expand Binomials [CC] (Video)

This description will not FOIL the plot of the "Expand Binomials" video.

Divide Polynomials [CC]

Use factoring or long division to divide polynomials.

Metric Conversions

Review how to work with the SI system.

Metric to Customary Conversions: Length, Mass, and Volume

Review how convert between two systems when using length, mass, and volume.

Metric to Customary Conversions: Temperature

Review how to convert values between Celsius and Fahrenheit.

Customary Conversions

Review how to work with customary system units.

Factorials!

Learn how to work with factorials.

Permutations

Learn how to work with permutations.

Combinations

Learn how to work with combinations.

Independent Events [CC]

How can you figure out the probability of independent events?

Dependent Events [CC]

How can you figure out the probability of dependent events?

Interpret a Pie Chart

Practice responding to questions about a pie chart.

### GRE Math Lessons - Numbers and Operations

Properties of Real Numbers

What properties do real numbers share?

Number Types

What are all of the different types of numbers?

Divide Signed Integers

Review how to divide integers.

Multiply Signed Integers

Review how to multiply integers with and without the same signs.

Subtract Signed Integers

Review the subtraction of signed integers.

Add Signed Integers

How can you add negative and positive numbers?

Lesson - Absolute Value and Signed Integers

Review the definitions of absolute value and signed integers.

Subtraction Application Problems

How do you know when a word problem is asking you to subtract?

Greatest Common Factor

Review the different factors of whole numbers: Greatest Common Factors and Prime Factorization.

Lesson - Order of Operations

Review how to proceed when an expression has more than one mathematical operation.

Lesson - Divide Whole Numbers

Review the three different ways to write division problems and practice dividing whole numbers.

Properties of Multiplication

Review the Commutative, Associative, Identity, Distributive, and Zero properties for the product of 2 or more numbers.

Lesson - Multiplication

Review how to estimate the product of two numbers and how to find the least common multiple (LCM.)

Lesson - Subtraction with Borrowing

Review the steps to subtract large numbers.

Subtract Whole Numbers

Review how to subtract whole numbers.

Properties of Addition

What do all addition problems have in common?

Add Whole Numbers

Review how to add whole numbers and recognize key words that call for addition.

Signed Number Arithmetic

How can you add, subtract, multiply, and divide with signed numbers?

Lesson - Place Value

Review how to read whole numbers according to the place value of their digits.

Fractions

Review exactly what fractions are and how to simplify them.

Improper Fractions and Mixed Numbers

How can you convert improper fractions to mixed numbers and vice versa?

Compare Fractions

Review how to compare fractions by finding their common denominator or by converting each fraction into a decimal.

Add Fractions and Mixed Numbers

How can you add a fraction to another fraction, a whole number, or a mixed number?

Subtract Fractions and Mixed Numbers

Review how to subtract a fraction from another fraction, a whole number, or a mixed number.

Multiply Fractions and Mixed Numbers

How can you multiply fractions by other fractions, whole numbers, and mixed numbers?

Divide Fractions and Mixed Numbers

Why do reciprocals help you divide fractions?

Writing Decimals

How can you use your knowledge of place value to write decimals?

Rounding Decimals

How can you round decimals to a given place value?

Comparing Decimals

How can you use place value to compare decimals?

Decimals and Fractions

How can you change decimals into fractions and fractions into decimals?

Addition and Subtraction with Decimals

How can you add and subtract decimals?

Multiplication and Division with Decimals

How can you multiply and divide decimals?

Understanding Percent

What is a percentage?

Percent as a Proportion

How can you solve problems by writing a percentage as a proportion?

Percent Change

How can you use percent to understand how much a quantity has increased or decreased?

Percent Equations

How can you find the percent of a number and understand the different parts of the basic percent equation?

Simplify Square Roots

How can you simplify expressions that contain square roots?

Add and Subtract Square Roots

How can you add and subtract square roots?

Multiply Square Roots

How can you multiply expressions with square roots?

Working with Roots and Radicals

What is a root, and how can you work with it?

Cube Roots

Review the definition of cube roots.

Lesson - Powers and Exponents

Review key terms and evaluate powers.

Lesson - Rules of Exponents

Review the different characteristics of exponential expressions.

The Imaginary Unit i

Define complex number i such that i2=–1, and show that every complex number has the form a+bi where a and b are real numbers. (CCSS: HS.N-CN.A.1)

Weighted Average

How can you find the average of quantities that have different values?

Lesson - Mean, Median, Mode, and Range

Review how to analyze the values in a data set.

Scientific Notation

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (CCSS: 8.EE.A.4)

Ratios

What is a ratio?

Rates

How can you use rates to set up expressions?

Proportional Relationships

Identify and represent proportional relationships between quantities. (CCSS: 7.RP.A.2)

Solve Proportions

How can you read proportions and simplify the expressions?

#### Numbers and Operations

Properties of Real Numbers

What properties do real numbers share?

Number Types

What are all of the different types of numbers?

### GRE Math Lessons - Algebraic Expressions

Algebraic Expressions

What is an algebraic expression and how can it be simplified?

Simplify Algebraic Expressions

What steps must be taken when simplifying algebraic expressions?

Evaluate Algebraic Expressions

How do you evaluate algebraic expressions?

Combine Like Terms

Interpret complicated expressions by viewing one or more of their parts as a single entity. (CCSS: HS.A-SSE.A.1.b)

Distributive Property

Interpret complicated expressions by viewing one or more of their parts as a single entity. (CCSS: HS.A-SSE.A.1.b)

Lesson - Translate Phrases to Mathematical Expressions

Identify key words that will help you choose which operation to use when solving a word problem.

Monomials

What are the fundamental characteristics of monomials?

Multiply Monomials

How do you go about multiplying terms that contain both constants and variables?

### GRE Math Lessons - Linear Equations

Solve Linear Equations with Rational Numbers

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS: HS.A-CED.A.1)

Divide Rational Expressions

How is division of rational expressions carried out?

Solve Equations with a Variable on One Side of the Equation

How can you find the value of a variable when it appears on one side of an equation?

Solve Linear Equations with Variables on Both Sides of the Equation

How can you find the value of variables when they appear on both sides of an equation?

Quadratic or Rational Inequalities

Review the steps for solving quadratic or rational inequalities.

Absolute Value

What do -5 and +5 have in common?

Linear Inequalities

How are linear inequalities interpreted?

Graphing Relations, Domain, and Range

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (CCSS: HS.F-IF.B.5)

Slope-Intercept Form

How are equations written in slope-intercept form?

Equations with Radicals

What role do radicals play within equations?

Solve Radical Equations

How are radical equations solved?

Rule for Exponents

Review what happens to exponents when operations are performed on them ...

Exponential Equations

Can you identify the fundamentals of exponential equations?

Linear Equations

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS: HS.A-CED.A.1)

Solve Linear Systems

What are the most common methods used when solving linear systems?

Direct and Inverse Variation

Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CCSS: HS.A-CED.A.2)

Systems for Expressing Sets

Review how to write and work with data sets defined by set-builder notation, roster notation, interval notation, and graphical notation.

### GRE Math Lessons - Quadratic Equations

Quadratic & Polynomial Equations

Review how to rewrite and factor polynomials.

Solving Quadratic Equations by Factoring

Solve quadratic equations in one variable. (CCSS: HS.A-REI.B.4)

Solving Quadratic Equations by Completing the Square

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)^2=q that has the same solutions. Derive the quadratic formula from this form. (CCSS: HS.A-REI.B.4.a)

Solving Quadratic Equations by Square Root Property

Solve quadratic equations (e.g., for x^2=49) by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+bi for real numbers a and b. (CCSS: HS.A-REI.B.4.b)

### GRE Math Lessons - Functions and Graphs

Function Notation

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (CCSS: HS.F-IF.A.2)

Graphing Linear Equations

Review linear equations with two variables and practice graphing them.

Graphing Relations, Domain, and Range

Review the domain and range of a function and perform a simple test to see if a graph represents a function.

Graphing Exponential Functions

Review how to graph an exponential function where we see either growth or decay.

Operations and Evaluations of Functions

Review how to add, subtract, and multiply two functions (e.g. f(x)+ g(x))

1-to-1 Functions

Review the characteristics of a 1-to-1 function.

Slope-Intercept Form

Review how to use the slope-intercept form to graph an equation.

Graphing Linear Inequalities

Understand linear inequalities and practice graphing them on a coordinate system.

Coordinate System (Parallel/Perpendicular/Intercepts)

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (CCSS: HS.A-REI.D.10)

Asymptotes and Graphing Rational Functions

Review how to graph a rational function using asymptotes and intercepts.

Conic Sections

Review the shapes of conic sections and how to graph them.

### GRE Math Lessons - Formulas

Distance and Motion Problems

Write a function that describes a relationship between two quantities. (CCSS: HS.F-BF.A.1)

Simple Interest and Money Problems

Use the properties of exponents to interpret expressions for exponential functions. (CCSS: HS.F-IF.C.8.b)

Mixture Problems

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS: HS.F-IF.C.8)

Quadratic Application: Projectile Motion

Determine an explicit expression, a recursive process, or steps for calculation from a context. (CCSS: HS.F-BF.A.1.a)

Work Rate Problems

Combine standard function types using arithmetic operations. (CCSS: HS.F-BF.A.1.b)

### GRE Math Lessons - Polynomials and Factors

Simplify Rational Expressions

How are rational expressions simplified?

Multiply Binomials

What are the steps in binomial multiplication?

Roots of Polynomial Functions

Review how to use 2 given roots to write a polynomial equation.

Factor and Solve Polynomial Equations

How can polynomials be factored and solved?

Polynomial Division

How are polynomials divided?

Expand Polynomials

Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CCSS: HS.A-APR.A.1)

Factor Polynomials

Factor a quadratic expression to reveal the zeros of the function it defines. (CCSS: HS.A-SSE.B.3.a)

Add, Subtract, and Multiply Polynomials

What are the fundamental aspects of polynomial manipulation?

### GRE Math Lessons - Systems of Equations and Matrix

Solving Systems of Equations with Three Variables

Review how to solve systems of equations that have three variables.

Determinants of Matrices

Review how to perform operations with matrices and identify each matrix's determinant.

Applications of Systems of Equations with Three Variables

Review how to solve systems of equations with 3 variables.

Solving System of Nonlinear Equations

Review how to solve nonlinear equations by using substitution and elimination.

Adding and Subracting Matrices

Review the different properties of matrix operations.

Multiplying Two Matrices

Review how to find the product of two matrices.

Inverse Matrix

Review how to find the inverse of a matrix and how to multiply inverses.

Applications of Systems of Equations in Two Variables

Review the strategies you can use to solve systems of equations in word problems.

Solving Systems of Equations

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (CCSS: HS.A-REI.C.5)

### GRE Math Lessons - Logarithms

Graphing Functions and Logarithms

Practice problems on graphing functions that include logarithms.

Solving Logarithmic Equations

Review the properties of logarithmic functions and how to solve equations that involve them.

Logarithmic Functions

Review the definition and how to solve logarithmic functions

### GRE Math Lessons - Geometry

Parts of a Circle

Review the different parts of a circle and how they relate to each other.

Angles in the Plane

Review vertical, right, complementary and supplementary angles, as well as parallel and perpendicular lines.

Transformations: Translations, Rotations, and Reflections

Verify experimentally the properties of rotations, reflections, and translations. (CCSS: 8.G.A.1)

Triangles: The Side-Angle Relationship

Review the relationship between the side and angles in a triangle

The Pythagorean Theorem and its Converse

Explain a proof of the Pythagorean Theorem and its converse. (CCSS: 8.G.B.6)

Perimeter and Area

Review the general formulas of the most common plane figures.

Similarity and Dilations

Review how to identify similar or dilated polygons and how to use them for indirect measurement.

Polygons and Angles

Review polygons, how to identify them and how to measure their angles.

Angle Pairs

Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (CCSS: 7.G.B.5)

Right Triangle Relationships

Review right triangles and their special relationships: 30°-60°-90° and 45°-45°-90°

Lesson - Angles and Triangles

Review the classification of angles by their measurement, also the classification of triangles by their angles and sides.

Quadrilaterals

Review the classification and properties of quadrilaterals.

Surface Area and Volume of Spheres

State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (CCSS: 8.G.C.9)

Volume of Prisms, Cylinders, Cones, and Pyramids

State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (CCSS: 8.G.C.9)

### GRE Math Lessons - Measurement

Scale Drawing

Review how to understand the diagram of an object in which the dimensions are proportional to the original object.

The Imperial System

Review the imperial system and its units.

The Metric System/ SI-Units

Review the metric/SI system and convert between two metric units.

Converting Between Systems of Measurement: Imperial and SI-Units

Review how to convert between the SI and customary systems of measurements.

### GRE Math Lessons - Probability

Series

Review the characteristics of a series.

Sequences

Review the characteristics and how to work with sequences.

Permutations and Factorials

Review the definition of permutations and how to count with them.

Combinations

Review the characteristics of combinations and compare them to permutations.

Probability

Understand the concept of probability and practice solving problems that are based on it.

### GRE Math Lessons - Data and Statistics

Lesson - Interpret and Create Graphs

Review how to interpret and create a bar graph, histogram, and frequency table.

Interpret and Create Venn Diagrams

Apply the Addition Rule, P(A or B)=P(A)+P(B)–P(A and B), and interpret the answer in terms of the model. (CCSS: HS.S-CP.B.7)

Boxplots & the Five-Number Summary

Review the anatomy of a boxplot and construct one by using the five-number summary.

Representative Sampling

Review how to work with a representative sample for a given data set.

Graphs and Charts

Review how to read and work with histograms, dotplots, stem-and-leaf diagrams, bar graohs, and pie charts.

### External Links

ETS GRE Home

Register for the test and try more practice problems on the ETS Website.

Free Additional Practice Questions and Test Prep

You can never have too many practice tests! This website gives you the chance to take more sample GRE exams for free.

Information on the GRE and Grad Schools from U.S. News & World Report

Review key GRE study tips and research top grad school programs.

A Wall Street Journal Article: "More Business Schools to Accept GRE Scores"

Journalist Melissa Korn reports on many business schools' decisions to accept GRE scores.

Resource with a GRE Vocabulary List

This link includes a comprehensive list of GRE vocabulary words and their basic definitions. Make sure to look up secondary definitions as well.

GRE Digital Flashcard Creator

Create a set of flashcards that you can share with fellow test takers, or use a pre-made set if you are pressed for time. Some smartphone apps are also linked to this program.