21 Most Difficult GRE Math Formulas for 2024

Feeling intimidated by the GRE math section? While the GRE emphasises critical thinking and problem-solving, a solid foundation in key formulas can be helpful. This blog will be your one-stop shop for mastering the essential math formulas you need to ace the GRE math section. We’ll break down the most important formulas across various areas like algebra, geometry, and statistics, explain their applications with clear examples, and even offer tips on how to effectively memorise and use them on test day.

Should You Memorise GRE Math Formulas?

The answer is yes, you should memorise GRE math formulas. But why? Because knowing precisely when and how to apply these formulas translates to faster and more accurate answers. Without them, you might struggle to find the solution altogether, potentially leading to incorrect answers. The more incorrect guesses you accumulate, the lower your overall quant score will be.

What Kind of Math Should You Expect on the GRE?

The good news is that the GRE Quantitative Reasoning section focuses on core mathematical concepts you likely come across in high school, specifically during your 10th or 12th grade. Thankfully, it doesn’t include advanced areas like trigonometry, calculus, or complex geometry proofs. However, it does revisit topics you might have forgotten, such as properties of shapes, integer rules, exponent laws, and most importantly, word problems.

The real challenge with GRE quant lies in the complexity of applying these seemingly basic concepts. Deciphering what each question truly asks can be far more difficult than the actual math involved in solving it. Since you won’t receive partial credit for showing your work, answering effectively becomes even more critical.

21 Must-Know GRE Math Formulas

1. Rectangle: Area = Length x Width

2. Triangle: Area = ½ Base x Height

3. Circle: Area = πr² Circumference = 2πr (π ≈ 3.14)

4. Cylinder: Volume = πr²h

5. Sphere: Volume = (43)πr³

6. Pyramid: Volume = V = ⅓ length x width x height

7. Area of Parallelogram = base x height

8. Slope of a line: y = mx + b

10. Percentage:

• Percent increase: new amount-original amountoriginal amount x 100
• Percent decrease: original amount-new amountoriginal amount x 100

11. Pythagorean Theorem: a² + b² = c²

12. Permutations: P(n, r) = n! / (n - r)!

Where:

• n = total number of objects
• r = number of objects you're choosing to arrange
• ! (factorial) symbol represents multiplying a number by all the positive integers less than itself. (e.g., 3! = 3 x 2 x 1)

13. Combinations: C(n, r) = n! / [r! x (n - r)!]

Where:

• n = total number of objects
• r = number of objects you're choosing to arrange
• ! (factorial) symbol represents multiplying a number by all the positive integers less than itself.

13. Divisibility

• 3: sum of digits divisible by 3
• 4: the last two digits of number are divisible by 4
• 5: the last digit is either a 5 or zero
• 6: even number and sum of digits is divisible by 3
• 8: if the last three digits are divisible by 8
• 9: sum of digits is divisible by 9

14. Prime Numbers and Integers

• 1 is not a prime. 2 is the smallest prime and the only even prime.
• An integer is any counting number including negative numbers (e.g., -3, -1, 2, 7, but not 2.5).

15. Average:

• Average = sum of n numbersn
• Average = total distancetotal time

16. Probability:

• Probability of an event = number of ways that fit the requirementnumber of total ways

17. Percentile (P) = (n / N) × 100

Where:

• P represents the percentile you’re interested in (e.g., 25th percentile, 70th percentile).
• n represents the number of values in the dataset that are less than the value you're considering.
• N represents the total number of values in the dataset.

18. Slope Formula: m = (y₂ - y₁) / (x₂ - x₁)

Where:

• m represents the slope of the line.
• (y₂, x₂) and (y₁, x₁) are the coordinates of two different points on the line.
• (y₂ - y₁) represents the change in the y-coordinate (rise).
• (x₂ - x₁) represents the change in the x-coordinate (run).

19. Distance formulas:

1. In two dimensions (2D): d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

• √ represents the square root.
• (x₂ - x₁)² represents the difference in x-coordinates squared.
• (y₂ - y₁)² represents the difference in y-coordinates squared.

2. In three dimensions (3D): d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Where the additional term (z₂ - z₁)² accounts for the difference in z-coordinates squared.

20. Quadratic formula: ax² + bx + c = 0

Where:

• a, b, and c are real numbers, and a ≠ 0.
• x is the unknown variable.

21. Quadratic function: f(x) = ax2 + bx + c

Where:

• a, b, and c are real numbers, and a ≠ 0 (otherwise it wouldn’t be a quadratic function).
• x is the variable.

Suggested: 15 Hardest GRE Math Questions with Answers

Are the GRE Math Formulas Enough?

While memorising formulas is an important step in preparing for the GRE quant section, it’s definitely not enough to secure a top GRE score. The GRE quant section assesses your overall math competency, not just your ability to recall formulas. You’ll need strong foundational knowledge in various areas like data interpretation, understanding question prompts, and basic mathematical terms. 

Being comfortable with concepts like quotients, prime numbers, and factoring polynomials is essential. Additionally, the ability to compare quantities using ratios is frequently tested. This vast array of topics highlights the importance of going beyond memorization and building a well-rounded understanding of mathematical concepts.

5 Tips to Use Math Formulas in the GRE

1. Focus on understanding, not just memorization

Don’t just memorise formulas by heart. Try to grasp the underlying concepts they represent. This will help you apply them correctly and identify when they’re relevant. For example, understand why the area of a rectangle is calculated by multiplying length and width, not just memorising the formula (A = lw).

2. Practice applying formulas

Regularly practise applying formulas to different problem types. Numerous GRE prep resources offer practice questions categorised by formula usage. This helps you develop problem-solving skills and recognize situations where specific formulas are needed.

3. Look for formula cues

The question itself might offer clues about which formula to use. Keywords like “average,” “rate,” “distance,” or “percent change” often point towards specific formulas. Hone your ability to identify these cues to pick the right tool for the job. Don’t just blindly plug numbers into a formula; understand what each variable represents in the context of the question. This will prevent you from applying the wrong formula or misinterpreting the answer.

4. Don’t forget estimation

Formulas are great for precise calculations, but estimation can be a valuable time-saving technique. Knowing the ballpark range of the answer using estimation can help you verify if your formula application yields a reasonable result.

5. Practice makes perfect

As with any skill, consistent practice is key. Regularly work on GRE practice questions that involve formula application. This will boost your confidence, speed, and accuracy in using formulas during the actual GRE quant section.

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From the Desk of Yocket

The GRE math formulas are an important aspect of success on the test, but they shouldn’t be the sole focus of your preparation. Understanding the underlying concepts is much more valuable in the long run. Memorising formulas can help you answer certain question types quickly and efficiently. However, the GRE exam often tries to trip up test-takers by presenting questions in unfamiliar contexts or with slightly tweaked wording. If you simply rely on memorization, you might not recognise how to apply the formula to the specific problem.

Here’s a better approach: solidify your grasp of the math concepts that the formulas represent. For instance, instead of just memorizing the area formula for a rectangle (A = l x w), understand why multiplying the length by the width gives you the total area. This conceptual understanding will allow you to solve problems even if the formula isn’t explicitly given.

That being said, there are definitely some formulas that are particularly useful to know on the GRE. Familiarity with formulas for areas, volumes, rates, and percentages will come in handy for many quant problems. The key is to strike a balance between memorization and comprehension. Consider leveraging resources like Yocket GRE prep to enhance your mastery of these math formulas.