GRE Math Formulas: The Only Cheat Sheet You Need

Okay, so you’re gearing up to conquer the GRE, and let’s be real—the math section can feel like climbing Mount Everest! ETS designs the GRE exam to test your reasoning, but a solid grasp of foundational concepts is a must, and knowing your way around GRE math formulas is half the battle. Manhattan Prep offers fantastic courses that drill these concepts, but sometimes you just need a quick reference. Our comprehensive cheat sheet compiles all the essential GRE math formulas you’ll need, saving you precious time and brainpower, so you can focus on acing those tricky Quantitative Comparison questions!

Conquer the GRE Quant: Your Formula Survival Guide is Here!

Hey future grad students! Feeling intimidated by the GRE Quant section? Don’t sweat it! You’re absolutely capable of acing it, and we’re here to help.

This guide is your secret weapon – a carefully curated collection of the formulas you’ll need to tackle those tricky quantitative problems.

Think of it as your quick-reference cheat sheet, designed to be your go to. It’s designed to help you remember those critical formulas.

It will help you quickly recall the formulas you need, saving you precious time and boosting your confidence.

What This Cheat Sheet Is (and Isn’t)

Let’s be crystal clear: this cheat sheet isn’t a magic bullet. It won’t replace a solid understanding of the underlying math concepts.

You still need to learn the material.

But it is a powerful tool to have in your arsenal.

Think of it as the ultimate memory jogger, designed to help you recall those essential formulas when you need them most.

Unlock Your GRE Potential

Why is formula memorization so important? Simply put, knowing your formulas cold is a game-changer.

It allows you to quickly identify the problem type and immediately apply the correct formula. This saves you valuable time on the exam, allowing you to tackle more questions and increase your chances of scoring higher.

That efficiency translates directly into a better score.

On the GRE, every second counts!

How Formulas Translate to a Higher Score

Acing the GRE Quant is a strategic game. It’s not just about knowing what to do; it’s about knowing how to do it quickly and accurately.

Knowing your formulas instantly eliminates the mental block of trying to recall them.

This frees up your cognitive energy to focus on the nuances of the problem, allowing you to solve it more efficiently and accurately.

Ultimately, that speed and accuracy translate to more correct answers, and that’s what drives your score up!

Let’s get started and unlock your GRE potential!

Core Math Areas: Building Your Foundation for GRE Success

Now that we’ve established the ground rules, let’s dive into the heart of the GRE Quant section: the core math areas!

Think of these areas as the pillars that support your entire GRE performance. Mastering them is crucial for building a strong foundation and confidently tackling a wide range of questions. We will focus on high-yield topics and common GRE problem types to ensure you’re spending your study time wisely.

Arithmetic: Essential Number Concepts and Operations

Arithmetic is the bedrock of all mathematical understanding. Don’t underestimate its importance on the GRE!

Fractions, Decimals, Percentages: Master the Conversions

These three concepts are intricately linked. You need to be able to convert fluently between them.

For example:

• Fraction to Decimal: Divide the numerator by the denominator (e.g., 1/4 = 0.25).
• Decimal to Percentage: Multiply by 100 (e.g., 0.25 = 25%).
• Percentage to Fraction: Divide by 100 and simplify (e.g., 75% = 75/100 = 3/4).

Knowing these conversions inside and out will save you valuable time on test day!

Ratios and Proportions: Setting Up for Success

Ratios compare quantities, while proportions state that two ratios are equal.

The key is to set up your proportions correctly. If you have a ratio of 2:3 for apples to oranges, make sure the apples are always in the same position (numerator or denominator) in both ratios.

Cross-multiplication is your best friend for solving proportions.

Integers, Exponents, Roots: Taming the Numbers

Understand the rules for operating with exponents (especially negative exponents!).

For instance: x^-n = 1/xⁿ.

Also, remember the properties of roots, like √a √b = √(ab).

Be comfortable simplifying radicals – it comes up more often than you might think.

Algebra: Mastering Equations and Functions

Algebra is all about manipulating variables and relationships. Brush up on these key concepts.

Solving Equations: Linear and Quadratic Power

Linear equations are straightforward, but quadratic equations can be a bit trickier.

• Memorize the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a.

Practice factoring quadratics as well; it’s often faster than the quadratic formula.

Inequalities: Handling the Flip

Remember the golden rule: when multiplying or dividing an inequality by a negative number, you must flip the inequality sign.

Also, understand how inequalities are represented on a number line.

Functions: Understanding the Notation

Familiarize yourself with function notation (e.g., f(x) = 3x + 2).

Practice evaluating functions for given inputs, and be prepared to solve problems involving function composition (e.g., f(g(x))).

Geometry: Navigating Shapes and Spaces

Geometry questions can seem intimidating, but with the right formulas and strategies, you can conquer them.

Lines and Angles: Know Your Relationships

Understand the definitions of angle types (acute, obtuse, right, straight) and angle relationships (supplementary, complementary, vertical angles).

Remember that the angles in a triangle always add up to 180 degrees.

Triangles: The Area and the Theorem

The area of a triangle is 1/2 base height.

The Pythagorean theorem (a² + b² = c²) is essential for right triangles.

Memorize the side ratios for 30-60-90 and 45-45-90 triangles, as they are often shortcuts.

Circles: Area, Circumference and Sectors

Area = πr². Circumference = 2πr.

Understand how to calculate the area of a sector (a slice of the circle) based on the central angle.

3D Shapes: Volume and Surface Area

Know the volume and surface area formulas for common solids like cubes, cylinders, and rectangular prisms.

Pay attention to the units!

Data Analysis: Interpreting and Analyzing Data

Data analysis questions test your ability to interpret and draw conclusions from data.

Statistics: Mean, Median, Mode, and Standard Deviation

Know the formulas for mean (average), median (middle value), mode (most frequent value), and standard deviation (measure of spread).

Understand when to use each measure and how outliers can affect them.

Probability: Calculating the Odds

Probability is the number of favorable outcomes divided by the total number of possible outcomes.

Understand combinations and permutations formulas for calculating the number of ways to choose items from a set, considering order (permutations) or not (combinations).

Data Interpretation: Reading Between the Lines

Practice reading and interpreting graphs and charts effectively. Pay attention to labels, scales, and trends. Be wary of misleading graphs!

Formula Application & Problem-Solving: Putting Knowledge into Practice

Alright, you’ve got a solid arsenal of formulas. Now comes the fun part: putting them to work!

This section is all about bridging the gap between knowing what to do and knowing how to do it efficiently on the GRE. Let’s transform those formulas from abstract concepts into powerful problem-solving tools.

We’ll dissect key strategies, master time management, and even explore the calculator’s role in your quest for a killer Quant score. Let’s jump in!

Problem-Solving Strategies: Techniques for Tackling Quant Questions

The GRE Quant section isn’t just about raw calculation. It’s about strategic thinking. Let’s arm you with some essential techniques.

Breaking Down Word Problems: Keyword Identification & Equation Setup

Word problems can seem daunting, but they become manageable when approached systematically.

The key is to translate the English into math. Start by identifying keywords that signal mathematical operations:

• "Of" often means multiplication.
• "Is," "was," or "were" usually indicates equals.
• "Per" signifies division.

Underline or highlight these keywords as you read. Then, represent the unknowns with variables and build your equations step-by-step. With practice, this process will become second nature.

Working Backwards: A Strategic Approach

Sometimes, the fastest route to the answer is to start from the choices.

Working backward is particularly effective when the problem involves complex calculations or multiple steps.

• Plug each answer choice into the problem’s conditions until you find the one that satisfies all requirements.* This can often save you precious time compared to solving for the variable directly.

Plugging in Numbers: Making the Abstract Concrete

Feeling lost in a sea of variables? Plug in your own numbers! This strategy is fantastic for problems involving variables in the answer choices or abstract concepts.

Choose simple, easy-to-work-with numbers (avoid 0, 1, and numbers already in the problem). Solve the problem using your chosen numbers and then plug those same numbers into the answer choices. The choice that matches your result is the correct answer.

Time Management: Strategies for Efficiency

Time is your most valuable resource on the GRE. Effective time management can significantly boost your score.

Quickly Identifying the Problem Type & Selecting the Appropriate Formula

The faster you recognize the problem type, the quicker you can access the right formula.

Practice identifying common patterns and associating them with specific formulas.

For example, if you see a problem involving combined work rates, immediately think of the relevant formula.

This recognition comes with practice, so dedicate time to reviewing a wide range of problem types.

Prioritizing Questions: Tackling Easier Questions First to Build Confidence

Don’t get bogged down by a challenging question early on. Start with the questions you know you can solve quickly and accurately.

This builds momentum and confidence, freeing up mental energy to tackle tougher problems later.

Knowing When to Guess Strategically & Move On

It’s okay to guess! The GRE doesn’t penalize you for incorrect answers.

If you’ve spent a reasonable amount of time on a question (say, 2-3 minutes) and are still stuck, make an educated guess and move on. Don’t leave any questions unanswered!

Eliminate obviously wrong answers to increase your odds of guessing correctly.

Calculator Usage: Enhancing Your Calculation Power

The GRE provides an on-screen calculator, but it’s not a magic bullet. Use it strategically.

The calculator is most helpful for complex calculations, especially those involving decimals or large numbers.

However, don’t rely on it for simple arithmetic or problems that can be solved more efficiently by hand.

Over-reliance on the calculator can actually slow you down. Practice using it effectively during your preparation.

Remember to double-check your inputs to avoid careless errors. A wrong number entered into the calculator can lead to a wrong answer, even if you understand the underlying concepts.

Practice Makes Perfect: Mastering the GRE Quant Section

Alright, you’ve got a solid arsenal of formulas. Now comes the fun part: putting them to work! This section is all about bridging the gap between knowing what to do and knowing how to do it efficiently on the GRE. Let’s transform those formulas from abstract concepts into powerful tools!

The real secret sauce to GRE Quant mastery isn’t just memorizing formulas (though that’s important!). It’s all about consistent, strategic practice. Let’s explore how to make the most of practice tests, questions, and other resources.

Utilizing GRE Practice Tests: Simulating the Real Exam

Think of practice tests as dress rehearsals for the main event. They’re absolutely essential for familiarizing yourself with the GRE’s unique format.

Familiarization with the Test Format

First, the timer ticking away relentlessly. Second, question types. Third, the sheer mental endurance required. Practice tests expose you to all of this in a low-stakes environment. You get to experiment with pacing strategies, learn to manage your anxiety, and build your overall test-taking stamina.

Analyzing Your Results: Digging for Gold

But the real magic happens after you finish a practice test. This is where you become a detective, carefully analyzing your results. What question types consistently trip you up? Which formulas need more love?

Take a hard look at every question, not just the ones you missed. Understanding why you got something right is just as important as understanding why you got something wrong.

Pro Tip: Create a spreadsheet to track your performance on each practice test. Identify patterns and focus your study efforts accordingly.

Making the Most of GRE Math Practice Questions: Strengthening Formula Application

Practice questions are like targeted training drills. They’re your opportunity to hone specific skills and solidify your understanding of individual formulas.

Targeted Practice for Specific Formula Application

Don’t just randomly blast through questions! Identify your weak areas (based on your practice test analysis) and focus your efforts there. For example, if you’re struggling with geometry, dedicate a few days to practicing geometry problems exclusively.

This targeted approach is far more effective than general, unfocused practice.

Reviewing Solutions: Learning from Mistakes

Never skip reviewing the solutions to practice questions! Even if you got the answer right, the solution might offer a more efficient or elegant approach. And if you got it wrong, the solution is your roadmap to understanding where you went astray.

Pay close attention to the reasoning behind each step. Ask yourself: Could I have solved this problem more quickly? What concept did I misunderstand?

Leveraging GRE Prep Books and Materials: Additional Learning Resources

There’s a wealth of GRE prep books and materials available, both online and in print. Finding the right resources can make a huge difference in your study experience.

Where to Find All the Information You Need to Study

Look for resources that align with your learning style and budget. Official ETS materials are always a good starting point, as they provide authentic GRE questions. But don’t be afraid to explore other options as well.

Consider prep books from reputable companies like Manhattan Prep, Kaplan, and The Princeton Review. Online resources like Khan Academy and GRE-focused websites can also be valuable.

Benefits of Math Tutors and GRE Prep Instructors

Sometimes, you need a little extra help to reach your full potential. A math tutor or GRE prep instructor can provide personalized guidance, answer your questions, and keep you motivated.

A good tutor can identify your specific weaknesses and tailor a study plan to address them. They can also offer test-taking strategies and help you build your confidence. Think of them as your personal GRE Sherpa, guiding you to the summit!

Understanding Quantitative Reasoning

Remember, the GRE Quant section isn’t just about memorizing formulas. It’s about quantitative reasoning – your ability to think critically and solve problems using mathematical concepts.

As you practice, focus on developing your problem-solving skills. Learn to break down complex problems into smaller, more manageable steps. Practice identifying patterns, making connections, and thinking outside the box. The more you develop your quantitative reasoning skills, the better you’ll perform on the GRE.

And lastly, remember to celebrate every small victory and enjoy the journey!

[Practice Makes Perfect: Mastering the GRE Quant Section
Alright, you’ve got a solid arsenal of formulas. Now comes the fun part: putting them to work! This section is all about bridging the gap between knowing what to do and knowing how to do it efficiently on the GRE. Let’s transform those formulas from abstract concepts into powerful tools!
The road to GRE Quant mastery isn’t just about memorization, it’s about application under pressure. And that pressure is never more real than on test day. Let’s arm you with some crucial test-day tips and tricks to maximize your performance and minimize those pesky test-day jitters.]

Test Day Tips & Tricks: Maximizing Your Performance

Test day is your day to shine!

You’ve put in the work, now it’s time to execute.

But even the best preparation can be undermined by avoidable mistakes or a lack of strategic thinking on the big day.

Let’s fine-tune your approach so you can confidently tackle the GRE Quant section.

Know the GRE Test Format: Your Roadmap to Success

Walking into the GRE without a clear understanding of the test format is like navigating a maze blindfolded.

Don’t do it!

Familiarize yourself with the structure: the number of sections, the types of questions you’ll encounter, and, most importantly, the time allotted for each section.

Question Types and Timing

The GRE Quant section primarily consists of Quantitative Comparison and Problem Solving questions. Understand the nuances of each type.

Quantitative Comparison requires you to compare two quantities. Problem Solving offers multiple-choice options.

Knowing the difference helps you approach each question strategically.

Timing is everything.

Practice allocating your time wisely.

A good rule of thumb is to aim for approximately 1 minute 45 seconds per question.

However, some questions will naturally take longer than others.

The Importance of Pacing Yourself

Pacing isn’t just about speed; it’s about strategic allocation of your cognitive resources.

Don’t get bogged down on a single, overly challenging question.

If you’ve spent more than 2-3 minutes on a problem without making significant progress, make an educated guess and move on.

You can always revisit it later if you have time.

Remember, every question is worth the same number of points. Don’t sacrifice easier questions for the sake of struggling with a difficult one.

Using Scratch Paper Effectively: Your Secret Weapon

Scratch paper is your best friend on the GRE.

But it’s only useful if you know how to wield it effectively.

Think of it as an extension of your brain, a space to externalize your thought processes and keep your work organized.

Don’t underestimate its power.

Organization is Key

Develop a system for organizing your scratch paper.

Divide it into sections, label each section with the question number, and clearly separate your work for each problem.

This prevents confusion and makes it easier to review your calculations if needed.

Neatness counts.

Strategic Note-Taking

Use your scratch paper to jot down key information, formulas, and intermediate steps.

When tackling word problems, translate the text into mathematical equations and diagrams.

Visualizing the problem can often lead to a breakthrough.

Don’t be afraid to use abbreviations or symbols to save time, as long as they’re clear to you.

Quick Formula Review: Priming Your Brain

Before you enter the testing room, dedicate some time to a final, quick review of key formulas.

This isn’t about cramming new information.

It’s about priming your brain and solidifying the knowledge you already possess.

Think of it as a mental warm-up.

Focus on High-Yield Formulas

Prioritize the formulas you know you’ll need: area and volume formulas, special right triangle ratios, the quadratic formula, and basic statistical formulas.

These are the bread and butter of the GRE Quant section.

Don’t try to memorize everything. Focus on the essentials.

Mental Rehearsal

As you review each formula, visualize how you would apply it to a typical GRE problem.

This active recall helps strengthen your memory and improves your ability to recognize when a formula is needed during the test.

Take a deep breath, remind yourself of all the hard work you’ve put in, and walk into that testing room with confidence.

You’ve got this!

So, there you have it! Keep this list of GRE math formulas handy as you study, practice those problems, and remember that mastering these formulas is a huge step towards acing the quant section. Good luck, you’ve got this!