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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. What number goes on the bottom of a probability fraction?
x² -2xy + y²
1/x^n For example - 6-² = 1/6² = 1/36
The total # of possible outcomes.
A=pr²

2. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

3. HIGH: What must be true before a quadratic equation can be solved?

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

5. What is a 'Right' angle?
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A 90-degree angle.

6. v4 =
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Find a common denominator and make equivalent fractions. Then add or subtract.

7. What do combination problems usually ask for?
Groups - teams - or committees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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 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.

8. 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.
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.
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.
(0 -0)

9. How do you solve a permutation?
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Probability A * Probability B
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

10. How do you multiply fractions?
Arrangements - orders - schedules - or lists.
Multiply numerator times numerator and denominator times denominator.
80%
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

11. HIGH: Volume of a cylinder?
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
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.
A radius
V=pr²h (This is just the area multiplied by the height)

12. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7
S*v2
Between 0 and 1.

13. 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
Favorable Outcomes/Total Possible Outcomes
3:4:5 5:12:13
80%

14. HIGH: What is a 'Right isosceles' triangle?
(0 -0)
1/x^n For example - 6-² = 1/6² = 1/36
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

15. How do you add or subtract fractions?
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
Find a common denominator and make equivalent fractions. Then add or subtract.
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).

16. Area of a square?
A 90-degree angle.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x² -2xy + y²
S²

17. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
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.
The # falling in the center of an ordered data set

18. Define 'proportionate' values
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
The # falling in the center of an ordered data set
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Invert the second fraction (reciprocal) and multiply

19. HIGH: How do you multiply and divide square roots?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

20. List two odd behaviors of exponents
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
S*v2
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.
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.

21. What are 'vertical angles'?
A 90-degree angle.
180 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A=pr²

22. HIGH: What is the factored version of (x+y)(x-y) ?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A triangle in which one of the three interior angles is 90 degrees.
x²-y²
The # falling in the center of an ordered data set

23. HIGH: Describe how to deal with 2 sets of parentheses.
A 90-degree angle.
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 5 if its units digit is either 0 or 5.
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

24. What is the factored version of x² -2xy + y² ?
Invert the second fraction (reciprocal) and multiply
Bh
(x-y)²
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.

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

26. HIGH: What is the mode?
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.
The value that appears most often in a data set.
The total # of possible outcomes.
Groups - teams - or committees.

27. HIGH: Rough est. of v3 =
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.
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)+
1.7
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

28. Convert to a percentage: 2/5
180 degrees
Bh
40%
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.

29. HIGH: What is the median?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
The # falling in the center of an ordered data set

30. What is the 'distributive law'?
Not reading the problems carefully enough!
Groups - teams - or committees.
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(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.

31. Explain how to divide fractions.
Order does matter for a permutation - but does not matter for a combination.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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

32. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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. 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
180 degrees
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

33. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

34. If x² = 144 - does v144 = x?
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.

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

36. The three exterior angles of a triangle add up to...
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
360 degrees
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.
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)+

37. HIGH: What are the percentages for standard deviation?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Example: 1 < x < 10
A 90-degree angle.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

38. If something is certain to happen - how is the probability of this event expressed mathematically?
A line is a 180-degree angle.
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.
1/1
2pr -or- pd

39. a² - b² is equal to
S²
The # falling in the center of an ordered data set
(a+b)(a-b)
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.

40. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7
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

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

42. Explain how to solve for 7/¼
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Not necessarily. This is a trick question - because x could be either positive or negative.
2

43. Define the range of a set of numbers.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A=pr²
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

44. HIGH: Rough est. of v2 =
Not necessarily. This is a trick question - because x could be either positive or negative.
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
1.4
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

45. Convert to a percentage: 1/4
A=pr²
1.4
25%
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

46. How do you divide fractions?
Not reading the problems carefully enough!
A 90-degree angle.
(x+y)²
Invert the second fraction (reciprocal) and multiply

47. HIGH: How do you multiply powers with the same base?
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

48. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(x-y)²
An integer is divisible by 2 if its units digit is divisible by 2.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

49. 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.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

50. HIGH: How do you calculate the circumference of a circle?
S²
2pr -or- pd
The # falling in the center of an ordered data set
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.