Mastering Basic Math Principles for the GRE
The GRE Quantitative Reasoning section tests your ability to understand, interpret, and analyze quantitative information. While it covers a range of topics, a strong foundation in basic math principles and formulas is crucial for success. This module will refresh your understanding of these fundamental concepts, equipping you to tackle more complex problems.
Arithmetic Fundamentals
Arithmetic forms the bedrock of quantitative reasoning. Understanding operations, number properties, and their applications is essential. We'll cover integers, fractions, decimals, percentages, ratios, and proportions.
Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Working with fractions and decimals requires careful attention to detail. Converting between them and performing operations accurately will save you time and prevent errors.
Remember that percentages are simply fractions out of 100. For example, 25% is equivalent to 25/100 or 0.25.
Algebraic Concepts
Algebra allows us to generalize mathematical relationships and solve for unknown quantities. Key concepts include variables, expressions, equations, and inequalities.
Geometry Essentials
Geometry deals with shapes, sizes, positions of figures, and properties of space. Understanding basic geometric formulas for area, perimeter, volume, and angles is vital.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is represented by the formula a² + b² = c², where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse. This theorem is fundamental for solving problems involving right triangles, distances, and coordinate geometry.
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Familiarize yourself with formulas for common shapes like triangles, rectangles, circles, and their 3D counterparts (cubes, cylinders, spheres).
Data Analysis and Statistics
The GRE often includes questions related to interpreting data presented in tables, charts, and graphs. Understanding basic statistical measures like mean, median, mode, and range is key.
| Measure | Definition | Example |
|---|---|---|
| Mean | The average of a set of numbers. | For {2, 4, 6}, the mean is (2+4+6)/3 = 4. |
| Median | The middle value in a sorted set of numbers. | For {2, 4, 6}, the median is 4. For {2, 4, 6, 8}, the median is (4+6)/2 = 5. |
| Mode | The value that appears most frequently in a set of numbers. | For {2, 4, 4, 6}, the mode is 4. |
| Range | The difference between the highest and lowest values in a set. | For {2, 4, 6, 8}, the range is 8 - 2 = 6. |
Key Formulas to Memorize
Having a ready recall of essential formulas will significantly speed up your problem-solving. Focus on mastering these common ones:
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Regular practice and review are key to solidifying these principles. The more you use them, the more intuitive they will become.
Learning Resources
The official GRE Math Review from ETS provides a comprehensive overview of the math topics covered on the test, including arithmetic, algebra, geometry, and data analysis.
Khan Academy offers free, in-depth video lessons and practice exercises covering all GRE math topics, broken down into manageable sections.
This blog post from Magoosh provides a curated list of essential GRE math formulas and key concepts, perfect for quick review and memorization.
Kaplan offers a helpful overview of critical GRE math formulas, explaining their application and importance for test-takers.
GregMat+ provides accessible video lessons on fundamental math concepts essential for the GRE, presented in an easy-to-understand manner.
Manhattan Prep's blog features articles on GRE math strategies, including essential formulas and how to apply them effectively during the exam.
While not GRE-specific, Math is Fun offers clear explanations and interactive tools for fundamental math concepts that are directly applicable to GRE preparation.
Search for 'GRE Math Formulas Explained' on YouTube for numerous videos from various educators breaking down key formulas and problem-solving techniques.
Quizlet offers user-created flashcards and study sets for GRE math formulas, allowing for interactive memorization and practice.
This comprehensive Wikipedia page lists a vast array of mathematical formulas, useful for referencing and understanding the origins and applications of various mathematical principles.