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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. Explain the difference between handling a permutation versus a combination.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
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.

2. The three interior angles of a triangle add up to...
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
60%
180 degrees

3. What do combination problems usually ask for?
4 angles are formed. Their sum is 360 degrees
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.
Groups - teams - or committees.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

4. How is a range expressed with inequalities?
Percentage Change = Difference/Original * 100
Example: 1 < x < 10
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.
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

5. What is a 'Right' triangle?
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.
x² + 2xy + y²
A radius
A triangle in which one of the three interior angles is 90 degrees.

6. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

7. Define a factorial of a number - and how it is written.
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.
S*v2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

8. What is the factored version of x² -2xy + y² ?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1. Given event A: A + notA = 1.
(x-y)²
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

9. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
'Big' angles and 'Small' angles.
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.

10. a² - b² is equal to
Probability A + Probability B
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(a+b)(a-b)

11. Convert to a percentage: 4/5
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
80%
An integer is divisible by 9 if the sum of its digits is divisible by 9.

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

13. HIGH: Volume of a cube?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

14. What is a 'Right' angle?
A 90-degree angle.
A radius
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%.
180 degrees

15. HIGH: What is the Pythagorean theorem?

16. HIGH: What is the factored version of x² + 2xy + y² ?
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd
(x+y)²
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.

17. v4 =
2
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.
3:4:5 5:12:13
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

18. For a bell curve - what three terms might be used to describe the number in the middle?
Arrangements - orders - schedules - or lists.
The average - mean - median - or mode.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

19. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 2 if its units digit is divisible by 2.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

20. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.
Groups - teams - or committees.
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group

21. In a coordinate system - what is the origin?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
(0 -0)
1. Given event A: A + notA = 1.
4 angles are formed. Their sum is 360 degrees

22. Define the mode of a set of numbers.
(x+y)²
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

23. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
1.4
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
V=s³

24. What is an 'equilateral' triangle?
S*v2
'Big' angles and 'Small' angles.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2

25. Does order matter for a permutation? How about for a combination?
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.
360 degrees
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Order does matter for a permutation - but does not matter for a combination.

26. HIGH: Simplify this: v75/v27
S²
x² -2xy + y²
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.
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.

27. Explain how to solve for 7/¼
Order does matter for a permutation - but does not matter for a combination.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group

28. Explain the special properties of zero.
Groups - teams - or committees.
Not necessarily. This is a trick question - because x could be either positive or negative.
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.
3:4:5 5:12:13

29. HIGH: What is 'absolute value' - and how is it represented?

30. Area of a parallelogram?
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 2 if its units digit is divisible by 2.
Bh

31. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Between 0 and 1.
(x+y)²

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

33. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
(0 -0)
Arrangements - orders - schedules - or lists.
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.

34. HIGH: Rough est. of v3 =
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S
2r
1.7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

35. HIGH: How do you multiply and divide square roots?
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1.4
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

36. 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.
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.
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.

37. HIGH: Rough est. of v1 =
1
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group
The value that appears most often in a data set.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

38. Define the range of a set of numbers.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
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 average - mean - median - or mode.

39. Convert to a percentage: 3/5
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Groups - teams - or committees.
An integer is divisible by 2 if its units digit is divisible by 2.
60%

40. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
A line is a 180-degree angle.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
90 degrees each.

41. What degree angle is a line?
x² -2xy + y²
A line is a 180-degree angle.
Probability A * Probability B
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.

42. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
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
1.4
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

43. HIGH: Describe how to deal with 2 sets of parentheses.
3:4:5 5:12:13
The average - mean - median - or mode.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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)+

44. HIGH: What is the unfactored version of (x-y)² ?
2
x² -2xy + y²
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A + Probability B
A 90-degree angle.

46. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
It will be a great advantage on test day to have your times table memorized from 1 through 15.
The average - mean - median - or mode.

47. HIGH: What is a '30:60:90' triangle?
(a+b)(a-b)
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
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

48. List all the prime numbers that are less than 30:
'Big' angles and 'Small' angles.
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

49. An integer is divisible by 3 if...
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.
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.
1
A 90-degree angle.

50. HIGH: What is the median?
The # falling in the center of an ordered data set
Between 0 and 1.
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.
x²-y²