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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: Define the 'Third side' rule for triangles

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

3. What number goes on the bottom of a probability fraction?
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.
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 total # of possible outcomes.
(x+y)(x-y)

4. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

5. How do you solve a combination?

6. HIGH: What is the unfactored version of (x-y)² ?
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
x² -2xy + y²

7. How do you calculate the probability of two events in a row? (Probability of A and B)
3:4:5 5:12:13
Probability A * Probability B
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.
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.

8. Does order matter for a permutation? How about for a combination?
6
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.
Order does matter for a permutation - but does not matter for a combination.
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

9. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

10. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
Not reading the problems carefully enough!
(a+b)(a-b)

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

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Probability A + Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

13. Define 'proportionate' values
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.
x²-y²
360 degrees

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

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

16. HIGH: What is the factored version of (x+y)(x-y) ?
(a+b)(a-b)
x²-y²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2

17. How many degrees does a circle contain?
(x-y)²
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
360 degrees

18. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.

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

20. An integer is divisible by 9 if...
The average - mean - median - or mode.
40%
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 9 if the sum of its digits is divisible by 9.

21. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

22. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A * Probability B
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

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

24. What degree angle is a line?
A line is a 180-degree angle.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
V=pr²h (This is just the area multiplied by the height)
6

25. Define the mode of a set of numbers.
60%
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.
Find the total - or whole - first - and then set up a Ratio Box.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

26. HIGH: What is the formula for the diagonal of any square?
360 degrees
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.
S*v2
2

27. 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.
90 degrees each.
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.
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.

28. What is an 'equilateral' triangle?
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.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

29. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
S²
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

30. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
25%
Invert the second fraction (reciprocal) and multiply
x²-y²

31. Convert to a percentage: 4/5
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
80%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

32. Explain the special properties of zero.
360 degrees
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.
(a+b)(a-b)
Invert the second fraction (reciprocal) and multiply

33. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1
1. Given event A: A + notA = 1.
40%
An integer is divisible by 5 if its units digit is either 0 or 5.

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

35. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Example: 1 < x < 10
4 angles are formed. Their sum is 360 degrees
S²
It will be a great advantage on test day to have your times table memorized from 1 through 15.

36. Convert to a percentage: 2/5
40%
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
S*v2
2pr -or- pd

37. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1
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.
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.

38. What do permutation problems often ask for?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Arrangements - orders - schedules - or lists.
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%.

39. What is the factored version of x² -2xy + y² ?
(x-y)²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
25%

40. 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.
An integer is divisible by 5 if its units digit is either 0 or 5.
A 90-degree angle.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

41. HIGH: What is the factored version of x² + 2xy + y² ?
3:4:5 5:12:13
(x+y)²
An integer is divisible by 2 if its units digit is divisible by 2.
(x-y)²

42. 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.
A 90-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.
Percentage Change = Difference/Original * 100

43. HIGH: Area of a circle
(x+y)(x-y)
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.
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.
A=pr²

44. HIGH: Rough est. of v1 =
x² -2xy + y²
1
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The total # of possible outcomes.

45. HIGH: Define the formula for calculating slope.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1. Given event A: A + notA = 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

46. How do you solve a permutation?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
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
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.

47. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
(0 -0)
6

48. HIGH: What is the median?
V=pr²h (This is just the area multiplied by the height)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The # falling in the center of an ordered data set
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

49. HIGH: How do you multiply and divide square roots?
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
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

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