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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. How do you solve a combination?

2. How do you multiply fractions?
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
Multiply numerator times numerator and denominator times denominator.
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
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.

3. An integer is divisible by 3 if...
4 angles are formed. Their sum is 360 degrees
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.

4. What do permutation problems often ask for?
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Arrangements - orders - schedules - or lists.

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

6. What is the factored version of x² -2xy + y² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
(x-y)²
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'.

7. Convert to a percentage: 2/5
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/x^n For example - 6-² = 1/6² = 1/36
40%

8. HIGH: What is the factored version of (x+y)(x-y) ?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
x²-y²
Groups - teams - or committees.

9. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
V=pr²h (This is just the area multiplied by the height)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. Does order matter for a permutation? How about for a combination?
360 degrees
Order does matter for a permutation - but does not matter for a combination.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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)+

11. Solve this: v6 * -v6 = ?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Find the total - or whole - first - and then set up a Ratio Box.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
6

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

13. Define 'proportionate' values
6
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
(x+y)(x-y)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

15. HIGH: What is the mode?
The # falling in the center of an ordered data set
180 degrees.
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 value that appears most often in a data set.

16. HIGH: What is the median?
Invert the second fraction (reciprocal) and multiply
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The # falling in the center of an ordered data set

17. How do you divide fractions?
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.
'Big' angles and 'Small' angles.
Find the total - or whole - first - and then set up a Ratio Box.
Invert the second fraction (reciprocal) and multiply

18. HIGH: What is the formula for the diagonal of any square?
1. Given event A: A + notA = 1.
Bh
4 angles are formed. Their sum is 360 degrees
S*v2

19. HIGH: What is the Pythagorean theorem?

20. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1.7
Order does matter for a permutation - but does not matter for a combination.
A triangle in which one of the three interior angles is 90 degrees.

21. What degree angle is a line?
2
A line is a 180-degree angle.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A=pr²

22. HIGH: How do you multiply and divide square roots?
25%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 5 if its units digit is either 0 or 5.

23. What is a 'Right' triangle?
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'.
360 degrees
A triangle in which one of the three interior angles is 90 degrees.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

24. On the GRE - should you ever assume that diagrams are truthful?
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.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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. a² - b² is equal to
Probability A * Probability B
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.
(a+b)(a-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

26. HIGH: What is a 'Right isosceles' triangle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
40%
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.
1.7

27. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Find a common denominator and make equivalent fractions. Then add or subtract.
Invert the second fraction (reciprocal) and multiply

28. Probability Formula
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Favorable Outcomes/Total Possible Outcomes
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

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

30. What'S one way to avoid mistakes on algebra questions in the GRE?

31. HIGH: How do you calculate the circumference of a circle?
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.
180 degrees.
2pr -or- pd
(0 -0)

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

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

34. HIGH: Rough est. of v3 =
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
1.7
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.

35. HIGH: what is the side ratio for a Right Isosceles triangle?
Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Not reading the problems carefully enough!
Find a common denominator and make equivalent fractions. Then add or subtract.

36. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
180 degrees.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The total # of possible outcomes.

37. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

38. What are the side ratios for a 30:60:90 triangle?
V=pr²h (This is just the area multiplied by the height)
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
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.

39. If something is possible but not certain - what is the numeric range of probability of it happening?
1.4
Between 0 and 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find the total - or whole - first - and then set up a Ratio Box.

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

41. An integer is divisible by 4 if...

42. HIGH: What is the order of math operations - and the mnemonic to remember it?
Favorable Outcomes/Total Possible Outcomes
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A 90-degree angle.
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

43. HIGH: What is the unfactored version of x²-y² ?
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.
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. Given event A: A + notA = 1.
(x+y)(x-y)

44. HIGH: What is the side ratio for a 30:60:90 triangle?
360 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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 average - mean - median - or mode.

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

46. What number goes on the bottom of a probability fraction?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
The total # of possible outcomes.
Probability A * Probability B

47. HIGH: Area of a triangle?
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.

48. HIGH: Describe how to deal with 2 sets of parentheses.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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)+
1.4

49. What is the 'Third side' rule for triangles?
(x+y)²
Probability A * Probability B
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.
(x-y)²

50. Define the mode of a set of 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.
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)+
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.