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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. How do you calculate the percentage of change?
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.
360 degrees
Percentage Change = Difference/Original * 100
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

2. Explain how to solve for 7/¼
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

3. In a coordinate system - what is the origin?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
(0 -0)

4. What is a 'Right' triangle?
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.
A triangle in which one of the three interior angles is 90 degrees.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

5. Define the mode of a set of numbers.
1/x^n For example - 6-² = 1/6² = 1/36
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.
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 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.

6. HIGH: What is the unfactored version of x²-y² ?
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.
(x+y)(x-y)
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
60%

7. What is the name of a line that extends from the center of a circle to the edge of a circle?
A 90-degree angle.
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.
A radius
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

8. Explain how to use a 'Rate Pie'
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
'Big' angles and 'Small' angles.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

9. What is the formula to determine probability?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1

10. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
V=pr²h (This is just the area multiplied by the height)
x² + 2xy + y²

11. What is a 'Right' angle?
1/x^n For example - 6-² = 1/6² = 1/36
A 90-degree angle.
Find the total - or whole - first - and then set up a Ratio Box.
Example: 1 < x < 10

12. HIGH: Volume of a cylinder?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
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.
V=pr²h (This is just the area multiplied by the height)

13. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
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

14. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
'Big' angles and 'Small' angles.
Probability A + Probability B
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

15. What is the factored version of x² -2xy + y² ?
360 degrees
(x-y)²
'Big' angles and 'Small' angles.
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.

16. If something is certain to happen - how is the probability of this event expressed mathematically?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1/1
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

17. HIGH: Define the formula for calculating slope.
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
A=pr²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
180 degrees

18. The three exterior angles of a triangle add up to...
V=s³
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
360 degrees
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.

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

20. What is the 'distributive law'?
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.
(0 -0)
1
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

21. Define the range of a set of numbers.
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.
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
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

22. HIGH: Volume of a cube?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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
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.
V=s³

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

24. HIGH: What are the percentages for standard deviation?
Between 0 and 1.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x-y)²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

25. a² - b² is equal to
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Not reading the problems carefully enough!
(a+b)(a-b)
3:4:5 5:12:13

26. An integer is divisible by 8 if...

27. Define a factorial of a number - and how it is written.
Example: 1 < x < 10
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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.

28. HIGH: To divide powers with the same base...
(a+b)(a-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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh

29. What'S the most important thing to remember about charts you'll see on the GRE?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

30. HIGH: What is the mode?
2pr -or- pd
2r
The value that appears most often in a data set.
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.

31. HIGH: What is the equation of a line?

32. Convert to a percentage: 4/5
80%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^n For example - 6-² = 1/6² = 1/36
60%

33. An integer is divisible by 9 if...
x² -2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

34. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.

35. Explain the special properties of zero.
(0 -0)
The # falling in the center of an ordered data set
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.

36. List two odd behaviors of exponents
Groups - teams - or committees.
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
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 angles are formed. Their sum is 360 degrees

37. HIGH: what is the side ratio for a Right Isosceles triangle?
2pr -or- pd
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

38. HIGH: Rough est. of v1 =
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
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
Favorable Outcomes/Total Possible Outcomes
1

39. How do you solve a permutation?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1
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
4 angles are formed. Their sum is 360 degrees

40. Probability Formula
1/1
Favorable Outcomes/Total Possible Outcomes
A 90-degree angle.
360 degrees

41. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
(x+y)²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Example: 1 < x < 10
A=pr²

42. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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

43. HIGH: What is the factored version of x² + 2xy + y² ?
Between 0 and 1.
V=pr²h (This is just the area multiplied by the height)
(x+y)²
Arrangements - orders - schedules - or lists.

44. HIGH: Rough est. of v3 =
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
1.7
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
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

45. What degree angle is a line?
A line is a 180-degree angle.
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
Find the total - or whole - first - and then set up a Ratio Box.
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.

46. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. How is a range expressed with inequalities?
S*v2
An integer is divisible by 5 if its units digit is either 0 or 5.
2
Example: 1 < x < 10

48. HIGH: What is a 'Right isosceles' triangle?
1.7
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
Order does matter for a permutation - but does not matter for a combination.

49. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
'Big' angles and 'Small' angles.
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

50. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.