One of the areas that students most commonly have problems with is the GRE quantitative reasoning section. There’s no magical answer to solving math problems, but if you sit down and memorize GRE math formulas, you’ll be one step closer to the perfect GRE score.
Based on my own experience, and feedback from the students I’ve helped, I’ve come up with the ultimate math formulas GRE cheat sheet.
Here’re all the most important math formulas you should know for achieving better GRE scores.
12 Important GRE Math Formulas
1. Geometry
Square
s = side
- Perimeter = 4×s - You should multiply side 4.
- Area = s^{2} - Multiply any two sides together.
Circle
r = radius ; d = diameter
- Area: πr^{2} - Square the radius and multiply it by π.
- Circumference: 2πr - Multiply 2 π and the radius.
Note: Every circle is 360 degrees.
Triangle
Triangles are the most tested shape on the GRE quant section, so pay close attention to this part.
b = base ; h = height
- Area: 1/2bh - Multiply the base by the height and divide by 2.
A right triangle is a triangle whose one side equals a 90-degree angle.
If you have a task with a right triangle, you’ll need the Pythagorean Theorem.
Pythagorean Theorem: a^{2}+b^{2}=c^{2}
The square of a plus the square of b equals the hypotenuse square. The hypotenuse is the longest of the three triangle sides.
Pro tip: When you’re doing GRE test prep, review Triangle Inequality Theorem, and the special right triangle ratios, as they also appear on the GRE quant section.
Rectangle
l = length ; w = width
- Perimeter: P = 2l + 2w
Multiply both the length and width by 2 separately, and then add them together.
- Area: A = l*w
Multiply the length by width.
Trapezoid
A trapezoid has:
- 2 parallel sides — a, b
- Height — h
Area: (a+b)2h
Add a and b, then divide them by 2, and multiply by height.
2. Divisibility
Here’s how to know if a number is divisible by:
- 2: All numbers ending with 0, 2, 4, 6, or 8 are divisible by 2.
- 3: Add up all the digits in the number. If it adds up to a number that’s divisible by 3, then the whole number is divisible by 3.
- 4: If the last two digits form a number that’s divisible by 4, then the whole number is divisible by 4
- 5: Any even number is divisible by 5
- 6: To be divisible by 6, the number must be divisible by 2 and 3
- 8: If the last three digits are divisible by 8, then the whole number is divisible by 8
- 9: same principle as 3
- 10: If a number ends in 0, it’s divisible by 10.
3. Average
Next on the list of important GRE math formulas is the average. Average, also called mean, is the sum of terms divided by the number of terms.
- average = sum of n numbers divided by n
- average speed = total distance divided by the total time
4. The Slope of a Line
m = slope ; x and y = coordinates
b = y-intercept, the value of y at the point where the line crosses the y axis
The slope formula is: y = mx+b
There are different kinds of slopes:
- Positive slope — If the line increases as it goes left to right
- Negative slope — if the line decreases
- 0 slope — If the line is horizontal.
5. Laws of Even and Odd Numbers
Another thing you’re sure to encounter on GRE standardized tests is even and odd numbers.
Here are GRE math formulas for them:
Addition:
- even + even = even
- even + odd = odd
- odd + odd = even
Multiplication:
- even * even = even
- even * odd = even
- odd * odd = odd
Subtraction:
- even − even = even
- even − odd = odd
- odd − odd = even
6. Laws of Square Roots
The square root of a number is the number that produces a specific quantity when multiplied by itself.
The square root of x is written as x.
Square root formula:
√a^{2}=a
√a√b=√ab
7. Laws of Exponents
The exponent of a number says how many times to multiply a base number by itself.
x^{1} = x
x^{0} = 1
x^{-1} = 1/x
x^{m}x^{n} = x^{m+n}
x^{m}/x^{n} = x^{m-n}
(x^{m})^{n} = x^{mn}
(xy)^{n} = x^{n}y^{n}
(x/y)^{n} = x^{n}/y^{n}
x^{-n} = 1/x^{n}
8. Probability
Probability is the desired outcome or total possible outcomes of an event.
Probability formula: Probability=number of successful outcomes divided by total possible outcomes.
Most of the time, the probability is written as a fraction, but decimals and ratios can also be used.
9. Percentage
If you get a percentage question on the GRE Quant section with unknown starting values, always pick 100.
Here’s a general percent formula for increase and decrease:
percent=change/original x100
Find the difference between the original and the increased or decreased number, and divide that by the original number.
10. Distance
R = rate ; T = time ; D = distance ; D = rt
You should multiply the rate and time to get the distance. a^2 + b^2 = c^2
11. Prime Numbers and Integers
In your GRE prep, don’t forget about prime numbers and integers.
Here’s what you should know to ace your GRE score:
- 1 isn’t a prime.
- 2 is the smallest prime and the only even prime.
- An integer is any counting number including negative numbers (for example. -3, -1, 2)
12. Interest Rate
p = principal, amount of money invested
r = rate of interest per annum
t = time, usually calculated as the number of years [1]
There are two kinds of interest rate formulas:
Simple Interest
V = P (1+ rt/100)
In simple interest, the rate is given in %, written as rt/100. The principal is the sum of money that doesn’t change every year.
Compound Interest
V = P (1+ r/100n)^{nt}
Same as in the simple interest, in compound interest, P is the amount of money invested, r is the annual interest rate expressed as a decimal value, t is time.
There’s also a new component — n. N shows how often the interest is paid per year.
Word Problems
Another task that frequently appears on the GRE quant score section is word problems. This means you’ll be asked to transfer text into basic equations.
If this is something you struggle with, any testing service, such as My GRE Exam Prep, can help you out.
Why Do You Need to Learn GRE Math Formulas
Formulas are essential for GRE for several reasons:
- They save time on the test — Once you know all the GRE math formulas and math concepts, you can start solving the task right away, saving you time for tasks that you’re insecure about.
- Get a better GRE score — Knowing formulas means doing the tasks correctly, which means getting a good GRE score and getting into the school you want.
- Often, you won’t be able to solve the task without knowing the formula.
At first, the number of formulas can be overwhelming. But, the good news is that you already studied data interpretation, data analysis, analytical writing, geometry formulas, and other underlying math concepts in middle school and high school.
After taking practice tests, chances are you’ll recall how to use them, and they won’t be so daunting.
5 Tips on Using GRE Math Formulas
Here’s what you should do in your GRE prep to ace your GRE score:
Know how formulas are tested — There are four kinds of questions on the GRE quant section:
- Quantitative Comparison: You have to compare two quantities
- Multiple Choice: Choose one answer
- Multiple Choice: Choose one or more answers
- Numeric Entry: Fill in a blank
Timed practice — Time yourself when doing the GRE math section, so you'll become time-efficient and get the best possible GRE score on test day.
Make a study plan — Test takers should make a plan and stick to it. Do a practice test, and based on its GRE score, decide how often you should review the math formula cheat sheet and do practice activities. Feel free to check our GRE math study guide.
Make flashcards — Flashcards aren't only useful for vocab. Write the formula on the front and how it’s used on the back.
Don’t just memorize the formulas but understand them — If you understand how formulas are used and how they’re connected to other formulas, it’ll be easier to remember them and solve even the hardest GRE math questions.
For example, if you can’t remember a perimeter formula or formula for quadratic equations, ask yourself what they are, and go from there.
How Do You Study Math GRE Formulas?
Make sure you’re familiar with Quantitative Comparisons. These questions consist of two quantities — A and B. Usually, the quantities will have a description.
You should compare them and choose one out of four options on the GRE test [2]:
- Quantity A is greater.
- Quantity B is greater.
- Quantities are equal.
- The relationship cannot be determined from the information given.
“There are about fifteen quantitative comparison questions, and since the entire GRE math section has only 40 questions, QC is 40% of GRE math. This means that if you do better on QC, you can significantly improve your GRE math score.”
- Corey, PrepSchoolar GRE
To study for test questions, you should:
- Write down the formulas and create your own cheat sheet
- Print out this cheat sheet
- Review the formulas regularly
- Do standardized tests and practice using the GRE math formula you struggle with
Math GRE Formulas: Final Thoughts
I’ve covered all the most important Educational Testing Service (ETS) GRE math formulas you should know.
One final tip: Don’t skip seemingly more straightforward formulas, such as odd and even numbers, or positive and negative fractions, but also give enough time to concepts that aren’t higher-level math.
If you want to improve your math formula knowledge, and cut down the time it takes you to do a task on GRE test day, memorize the formulas on the GRE cheat sheet.
References:
- https://www.calculatorsoup.com/calculators/financial/compound-interest-calculator.php
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/comparison/
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