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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. Diameter of a circle?
1
2r
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
x² + 2xy + y²

2. Define a factorial of a number - and how it is written.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

3. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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
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
180 degrees.

4. Define 'proportionate' values
4 angles are formed. Their sum is 360 degrees
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

5. In a coordinate system - what is the origin?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
The 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.
(0 -0)

6. Convert to a percentage: 3/5
60%
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.
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.
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.

7. List all the prime numbers that are less than 30:
2
A line is a 180-degree angle.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
6

8. a² - b² is equal to
(a+b)(a-b)
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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 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.

9. HIGH: What is the median?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The # falling in the center of an ordered data set
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
S²

10. If something is possible but not certain - what is the numeric range of probability of it happening?
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.
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.
x² -2xy + y²

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

12. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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 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. 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
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.

13. 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.
Probability A * Probability B
S*v2
Order does matter for a permutation - but does not matter for a combination.

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

15. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
1. Given event A: A + notA = 1.
A radius
60%

16. Area of a parallelogram?
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.
Bh
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.
'Big' angles and 'Small' angles.

17. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Invert the second fraction (reciprocal) and multiply
A radius
A line is a 180-degree angle.

18. HIGH: Volume of a cylinder?
An integer is divisible by 2 if its units digit is divisible by 2.
The # falling in the center of an ordered data set
80%
V=pr²h (This is just the area multiplied by the height)

19. HIGH: What is the mode?
Invert the second fraction (reciprocal) and multiply
The value that appears most often in a data set.
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.
An integer is divisible by 2 if its units digit is divisible by 2.

20. How do you multiply fractions?
The average - mean - median - or mode.
Groups - teams - or committees.
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.
Multiply numerator times numerator and denominator times denominator.

21. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

22. HIGH: What is 'absolute value' - and how is it represented?

23. An integer is divisible by 2 if...
2r
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

24. HIGH: What are the percentages for standard deviation?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
S*v2
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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

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

26. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
1

27. Define the range of a set of numbers.
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
Example: 1 < x < 10
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.
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)+

28. What is the 'Third side' rule for triangles?
A radius
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.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

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

30. 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
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.
V=pr²h (This is just the area multiplied by the height)

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

32. HIGH: x^-n is equal to
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Groups - teams - or committees.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/x^n For example - 6-² = 1/6² = 1/36

33. What is a 'Right' triangle?
Between 0 and 1.
2
A triangle in which one of the three interior angles is 90 degrees.
Invert the second fraction (reciprocal) and multiply

34. What is the equation for a group problem?
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
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
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

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

36. What do permutation problems often ask for?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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'.
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.

37. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
25%
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.
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.

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

39. What is the key to dealing with ratio questions?
Between 0 and 1.
Find the total - or whole - first - and then set up a Ratio Box.
360 degrees
(x+y)(x-y)

40. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x²-y²

41. What is an 'equilateral' triangle?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
(x-y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

42. 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
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
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.
x² + 2xy + y²

43. Convert to a percentage: 1/4
1/x^n For example - 6-² = 1/6² = 1/36
360 degrees
80%
25%

44. List two odd behaviors of exponents
Find a common denominator and make equivalent fractions. Then add or subtract.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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.

45. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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.
Multiply numerator times numerator and denominator times denominator.
Not necessarily. This is a trick question - because x could be either positive or negative.

46. In a coordinate system - identify the quadrants and describe their location.
40%
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.
The # falling in the center of an ordered data set
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. What is the factored version of x² -2xy + y² ?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x-y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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

48. HIGH: What is the unfactored version of (x+y)² ?
1/1
x² + 2xy + y²
1.4
90 degrees each.

49. What is a 'Right' angle?
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.
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.
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.

50. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2