Test your basic knowledge |

GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. HIGH: What is the order of math operations - and the mnemonic to remember it?
S²
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through
V=s³
Groups - teams - or committees.

2. Probability Formula
Order does matter for a permutation - but does not matter for a combination.
(x+y)²
Favorable Outcomes/Total Possible Outcomes
Groups - teams - or committees.

3. List two odd behaviors of exponents
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Order does matter for a permutation - but does not matter for a combination.
V=s³
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.

4. HIGH: Rough est. of v2 =
Arrangements - orders - schedules - or lists.
Between 0 and 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4

5. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²

6. In a coordinate system - identify the quadrants and describe their location.
2
(0 -0)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
An integer is divisible by 2 if its units digit is divisible by 2.

7. How do you calculate the percentage of change?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1.7
Percentage Change = Difference/Original * 100

8. How do you calculate the probability of two events in a row? (Probability of A and B)
x² -2xy + y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Probability A * Probability B
Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for 'Trap' answers that look temptingly correct at first glance.

9. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

10. An integer is divisible by 4 if...

11. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
1.4
The average - mean - median - or mode.

12. Explain how to use a 'Rate Pie'
Bh
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through
1.7
This is similar to an Average Pie - and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate. Rate * Time = Amount

13. List all the prime numbers that are less than 30:
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
90 degrees each.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. Area of a parallelogram?
Bh
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
2pr -or- pd
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

15. What causes 80% of errors on the math section of the GRE?
V=s³
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
If order matters - then you have a permutation -- do NOT divide. If order does NOT matter - then you have a combination -- divide by the factorial of the number of available slots.
Not reading the problems carefully enough!

16. HIGH: Define the formula for calculating slope.
Probability A + Probability B
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

17. What do permutation problems often ask for?
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
Find a common denominator and make equivalent fractions. Then add or subtract.
Arrangements - orders - schedules - or lists.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

18. HIGH: What is a 'Right isosceles' triangle?
1. Figure out how many slots you have (i.e. you'Re supposed to bring home 3 different types of ice cream) 2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store - 5 options for the 1st slot - 4 options fo
(x-y)²
A triangle in which one of the three interior angles is 90 degrees.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

19. What is the key to dealing with ratio questions?
(a+b)(a-b)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Find the total - or whole - first - and then set up a Ratio Box.

20. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
360 degrees
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A triangle in which one of the three interior angles is 90 degrees.

21. An integer is divisible by 6 if...

22. What'S one way to avoid mistakes on algebra questions in the GRE?

23. How do you add or subtract fractions?
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.
Find a common denominator and make equivalent fractions. Then add or subtract.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.

24. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
The # falling in the center of an ordered data set
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.
(x+y)(x-y)

25. An integer is divisible by 5 if...
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.
An integer is divisible by 2 if its units digit is divisible by 2.

26. Explain how to solve for 7/¼
Order does matter for a permutation - but does not matter for a combination.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

27. HIGH: What is the unfactored version of (x-y)² ?
Example: 1 < x < 10
The total # of possible outcomes.
x² -2xy + y²
2pr -or- pd

28. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.

29. HIGH: Volume of a cylinder?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
V=pr²h (This is just the area multiplied by the height)
80%

30. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
Order does matter for a permutation - but does not matter for a combination.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The value that appears most often in a data set.

31. Convert to a percentage: 3/5
The value that appears most often in a data set.
60%
A=pr²
Multiply numerator times numerator and denominator times denominator.

32. Define the mode of a set of numbers.
80%
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
Bh
An integer is divisible by 5 if its units digit is either 0 or 5.

33. What should you do BEFORE you start to solve a GRE math problem?

34. Explain the difference between a digit and a number.

35. How do you solve a combination?

36. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
V=s³
Not necessarily. This is a trick question - because x could be either positive or negative.

37. HIGH: Explain the process to solve '56 is what percent of 80?'

38. v4 =
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.
2
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

39. HIGH: What is a '30:60:90' triangle?
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 5 if its units digit is either 0 or 5.
V=pr²h (This is just the area multiplied by the height)

40. HIGH: What is the side ratio for a 30:60:90 triangle?
1/x^n For example - 6-² = 1/6² = 1/36
180 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1. Given event A: A + notA = 1.

41. Define a factorial of a number - and how it is written.
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.
Not necessarily. This is a trick question - because x could be either positive or negative.

42. Define 'proportionate' values
(0 -0)
(a+b)(a-b)
A line is a 180-degree angle.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

43. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

44. What are 'vertical angles'?
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.
S*v2
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

45. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
Probability A + Probability B
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.

46. What degree angle is a line?
A line is a 180-degree angle.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
2
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

47. An integer is divisible by 3 if...
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.

48. In a coordinate system - what is the origin?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(0 -0)
1. Figure out how many slots you have (i.e. you'Re supposed to bring home 3 different types of ice cream) 2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store - 5 options for the 1st slot - 4 options fo
The average - mean - median - or mode.

49. How many degrees does a circle contain?
360 degrees
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A 90-degree angle.
Find a common denominator and make equivalent fractions. Then add or subtract.

50. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
Invert the second fraction (reciprocal) and multiply
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.