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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. What is a 'Right' angle?
A 90-degree angle.
x²-y²
2pr -or- pd
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.

2. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Between 0 and 1.

3. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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.
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

4. HIGH: What is the Pythagorean theorem?

5. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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)+
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
90 degrees each.

6. How do you solve a permutation?
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. 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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
It will be a great advantage on test day to have your times table memorized from 1 through 15.

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

8. Area of a parallelogram?
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.
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

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

10. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
180 degrees
V=pr²h (This is just the area multiplied by the height)
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.
4 angles are formed. Their sum is 360 degrees

11. What is the equation for a group problem?
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
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

12. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
60%

13. Solve this: v6 * -v6 = ?
V=s³
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.
6
(x+y)²

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

15. What degree angle is a line?
V=s³
V=pr²h (This is just the area multiplied by the height)
A line is a 180-degree angle.
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.

16. In a coordinate system - identify the quadrants and describe their location.
'Big' angles and 'Small' angles.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x+y)²

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

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

19. Diameter of a circle?
2r
Multiply numerator times numerator and denominator times denominator.
6
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

20. HIGH: x^-n is equal to
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)+
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/x^n For example - 6-² = 1/6² = 1/36

21. Explain how to solve for 7/¼
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
3:4:5 5:12:13
(x-y)²

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

23. What is the formula to determine probability?
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Invert the second fraction (reciprocal) and multiply

24. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
x²-y²
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
25%
Probability A + Probability B

25. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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.
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.
A=pr²

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

27. Convert to a percentage: 4/5
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.
80%
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.
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. Explain the special properties of zero.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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 average - mean - median - or mode.
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.

29. HIGH: What is the factored version of (x+y)(x-y) ?
80%
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'.
Order does matter for a permutation - but does not matter for a combination.
x²-y²

30. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A radius
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

31. What is the factored version of x² -2xy + y² ?
(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'.
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.
180 degrees.

32. HIGH: What is the formula for the diagonal of any square?
'Big' angles and 'Small' angles.
S*v2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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)+

33. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

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

35. HIGH: What is a 'Right isosceles' triangle?
90 degrees each.
The value that appears most often in a data set.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

36. HIGH: How do you multiply and divide square roots?
Bh
1. Given event A: A + notA = 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/1

37. HIGH: What are the percentages for standard deviation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Between 0 and 1.
(x+y)(x-y)
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

38. How do you calculate the percentage of change?
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.
Percentage Change = Difference/Original * 100
(0 -0)
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.

39. How do you divide fractions?
S²
Invert the second fraction (reciprocal) and multiply
Order does matter for a permutation - but does not matter for a combination.
2pr -or- pd

40. Area of a square?
(0 -0)
360 degrees
S²
4 angles are formed. Their sum is 360 degrees

41. Convert to a percentage: 1/4
25%
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.
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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

42. What is the 'distributive law'?
A triangle in which one of the three interior angles is 90 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.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

43. What is the name of a line that extends from the center of a circle to the edge of a circle?
Arrangements - orders - schedules - or lists.
A radius
Not necessarily. This is a trick question - because x could be either positive or negative.
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

44. Explain how to use an 'Average Pie'
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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.

45. List all the prime numbers that are less than 30:
V=s³
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
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

46. Define the range of a set of numbers.
x² -2xy + y²
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.
Not reading the problems carefully enough!
S*v2

47. Does order matter for a permutation? How about for a combination?
V=s³
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Order does matter for a permutation - but does not matter for a combination.

48. The three exterior angles of a triangle add up to...
A triangle in which one of the three interior angles is 90 degrees.
Arrangements - orders - schedules - or lists.
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.
360 degrees

49. How do you solve a combination?

50. HIGH: What is the factored version of x² + 2xy + y² ?
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.
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
(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.