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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. On the GRE - should you ever assume that diagrams are truthful?
(0 -0)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
180 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

2. Explain how to use an 'Average Pie'
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.
Invert the second fraction (reciprocal) and multiply
6
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

3. a² - b² is equal to
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.
(a+b)(a-b)
4 angles are formed. Their sum is 360 degrees
1/x^n For example - 6-² = 1/6² = 1/36

4. HIGH: Define the 'Third side' rule for triangles

5. How precise do you need to be - using p on the GRE?

6. What are the side ratios for a 30:60:90 triangle?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
80%
1/1

7. What causes 80% of errors on the math section of the GRE?
x²-y²
90 degrees each.
(a+b)(a-b)
Not reading the problems carefully enough!

8. v4 =
Favorable Outcomes/Total Possible Outcomes
2
The value that appears most often in a data set.
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

9. HIGH: To divide powers with the same base...
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
Order does matter for a permutation - but does not matter for a combination.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

10. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
60%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

11. What are 'vertical angles'?
6
180 degrees.
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

12. HIGH: Rough est. of v3 =
The average - mean - median - or mode.
A triangle in which one of the three interior angles is 90 degrees.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.7

13. HIGH: What are the percentages for standard deviation?
Probability A + Probability 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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

14. If something is certain to happen - how is the probability of this event expressed mathematically?
A triangle in which one of the three interior angles is 90 degrees.
1/1
The # falling in the center of an ordered data set
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.

15. HIGH: What is the formula for the diagonal of any square?
S*v2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.
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.

16. Convert to a percentage: 1/4
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.
25%
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Arrangements - orders - schedules - or lists.

17. Define the range of a set of numbers.
Multiply numerator times numerator and denominator times denominator.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Example: 1 < x < 10
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.

18. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
A radius
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
180 degrees

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

20. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A line is a 180-degree angle.
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. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Multiply numerator times numerator and denominator times denominator.
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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

22. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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%.

23. Area of a parallelogram?
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Bh
25%

24. HIGH: How do you multiply and divide square roots?
1/x^n For example - 6-² = 1/6² = 1/36
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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

26. HIGH: How do you multiply powers with the same base?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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

27. What is the 'Third side' rule for triangles?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
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.
Between 0 and 1.

28. Define 'proportionate' values
6
40%
(x-y)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

29. The three interior angles of a triangle add up to...
1/1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
180 degrees
Groups - teams - or committees.

30. Define a factorial of a number - and how it is written.
1/1
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A line is a 180-degree angle.

31. What is a 'Right' angle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A 90-degree angle.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

32. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
90 degrees each.
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.
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

33. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
2r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

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

35. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

36. Does order matter for a permutation? How about for a combination?
The total # of possible outcomes.
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.
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.
Order does matter for a permutation - but does not matter for a combination.

37. Convert to a percentage: 2/5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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.
40%

38. HIGH: How do you calculate the length of an arc?

39. HIGH: What is the order of math operations - and the mnemonic to remember it?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

40. Define the mode of a set of numbers.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
180 degrees.
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.
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.

41. HIGH: how do you calculate the surface area of a rectangular box?
A line is a 180-degree angle.
x² + 2xy + y²
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.
Multiply numerator times numerator and denominator times denominator.

42. HIGH: What is the factored version of (x+y)(x-y) ?
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
x²-y²
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

43. Explain how to use a 'Rate Pie'
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
180 degrees.
1
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

44. The three exterior angles of a triangle add up to...
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

45. What degree angle is a line?
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
A line is a 180-degree angle.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2

46. Explain how to solve for 7/¼
The value that appears most often in a data set.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
2pr -or- pd

47. Explain how to calculate an average (arithmetic mean)
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.
60%
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1

48. What number goes on the bottom of a probability fraction?
An integer is divisible by 2 if its units digit is divisible by 2.
1.4
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The total # of possible outcomes.

49. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
S*v2
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

50. If something is possible but not certain - what is the numeric range of probability of it happening?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A 90-degree angle.
Between 0 and 1.