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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. HIGH: What is the unfactored version of (x-y)² ?
'Big' angles and 'Small' angles.
x² -2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

2. How do you calculate the probability of two events in a row? (Probability of A and B)
1/x^n For example - 6-² = 1/6² = 1/36
Multiply numerator times numerator and denominator times denominator.
4 angles are formed. Their sum is 360 degrees
Probability A * Probability B

3. HIGH: What is the Pythagorean theorem?

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

5. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.

6. Define 'proportionate' values
A radius
Between 0 and 1.
180 degrees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

7. How do you solve a permutation?
Arrangements - orders - schedules - or lists.
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'.
Probability A * Probability B
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

8. How do you solve a combination?

9. HIGH: Rough est. of v1 =
360 degrees
1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

10. What do permutation problems often ask for?
1.7
Find a common denominator and make equivalent fractions. Then add or subtract.
Arrangements - orders - schedules - or lists.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

11. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1

12. In a coordinate system - what is the origin?
(0 -0)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Find the total - or whole - first - and then set up a Ratio Box.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

13. Convert to a percentage: 2/5
The # falling in the center of an ordered data set
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.
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
40%

14. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S*v2
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

15. Convert to a percentage: 4/5
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.
2pr -or- pd
80%
Percentage Change = Difference/Original * 100

16. HIGH: How much of your times table should you know - for the GRE?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
The # falling in the center of an ordered data set
It will be a great advantage on test day to have your times table memorized from 1 through 15.

17. 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a+b)(a-b)
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%.

18. An integer is divisible by 5 if...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
An integer is divisible by 5 if its units digit is either 0 or 5.
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.

19. v4 =
360 degrees
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.
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.
2

20. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
90 degrees each.
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%

21. HIGH: What are the percentages for standard deviation?
The value that appears most often in a data set.
40%
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

22. If something is possible but not certain - what is the numeric range of probability of it happening?
A triangle in which one of the three interior angles is 90 degrees.
4 angles are formed. Their sum is 360 degrees
Between 0 and 1.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

23. Does order matter for a permutation? How about for a combination?
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.
180 degrees.
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
Order does matter for a permutation - but does not matter for a combination.

24. HIGH: Rough est. of v2 =
The average - mean - median - or mode.
1.4
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

26. Define the mode of a set of numbers.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

27. What is the 'Third side' rule for triangles?
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.
60%
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A 90-degree angle.

28. Explain how to calculate an average (arithmetic mean)
A radius
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
80%
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

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

30. HIGH: What is the unfactored version of (x+y)² ?
x²-y²
25%
x² + 2xy + y²
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

31. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Invert the second fraction (reciprocal) and multiply

32. Convert to a percentage: 3/5
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.
60%
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
S²

33. List two odd behaviors of exponents
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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
3:4:5 5:12:13
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.

34. HIGH: Simplify this: v75/v27
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=s³
(x+y)²
Not reading the problems carefully enough!

35. HIGH: what is the side ratio for a Right Isosceles triangle?
A triangle in which one of the three interior angles is 90 degrees.
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. Explain how to use a 'Rate Pie'
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
1. Given event A: A + notA = 1.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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

37. What do combination problems usually ask for?
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.
Groups - teams - or committees.
80%
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.

38. How do you divide fractions?
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
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
2pr -or- pd
Invert the second fraction (reciprocal) and multiply

39. How many degrees does a circle contain?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

40. What is the key to dealing with ratio questions?
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
Not necessarily. This is a trick question - because x could be either positive or negative.
Find the total - or whole - first - and then set up a Ratio Box.
80%

41. HIGH: What is the factored version of (x+y)(x-y) ?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
V=s³
x²-y²

42. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A radius

43. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Between 0 and 1.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Groups - teams - or committees.

44. On the GRE - should you ever assume that diagrams are truthful?
1/1
360 degrees
2r
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

45. What is an 'equilateral' triangle?
1.4
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

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

47. What is a 'Right' angle?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A 90-degree angle.
x² + 2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

48. Explain how to divide fractions.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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.

49. HIGH: x^-n is equal to
A line is a 180-degree angle.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/x^n For example - 6-² = 1/6² = 1/36

50. Explain the special properties of zero.
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.
V=s³
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5