GRE High Frequency Math Terms

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. Probability Formula
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
180 degrees.
Favorable Outcomes/Total Possible Outcomes
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.


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

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3. What is the 'distributive law'?
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.
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
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.
Find the total - or whole - first - and then set up a Ratio Box.


4. List all the prime numbers that are less than 30:
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.
Probability A + Probability B
A radius
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


5. HIGH: Volume of a cube?
V=s³
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.
6
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


6. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
25%
An integer is divisible by 9 if the sum of its digits is divisible by 9.


7. HIGH: To divide powers with the same base...
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Multiply numerator times numerator and denominator times denominator.


8. HIGH: What is the unfactored version of (x+y)² ?
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
The average - mean - median - or mode.
Order does matter for a permutation - but does not matter for a combination.
x² + 2xy + y²


9. How is a range expressed with inequalities?
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.
A triangle in which one of the three interior angles is 90 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.
Example: 1 < x < 10


10. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Not reading the problems carefully enough!
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.
Order does matter for a permutation - but does not matter for a combination.


11. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 2 if its units digit is divisible by 2.


12. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
60%
A radius


13. Area of a parallelogram?
(a+b)(a-b)
40%
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.
Bh


14. The three interior angles of a triangle add up to...
360 degrees
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
180 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.


15. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Order does matter for a permutation - but does not matter for a combination.
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
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 6 if it'S divisible by BOTH 2 and 3.


16. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The value that appears most often in a data set.


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

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18. What are 'vertical angles'?
40%
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


19. What is the name of a line that extends from the center of a circle to the edge of a circle?
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
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
A radius
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


20. 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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A triangle in which one of the three interior angles is 90 degrees.
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.


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

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22. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Probability A * Probability B
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


23. HIGH: What is a '30:60:90' triangle?
Find the total - or whole - first - and then set up a Ratio Box.
Groups - teams - or committees.
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 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.


24. HIGH: Rough est. of v3 =
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 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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1.7


25. HIGH: What is the factored version of (x+y)(x-y) ?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
40%
x²-y²
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.


26. Does order matter for a permutation? How about for a combination?
40%
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.
Order does matter for a permutation - but does not matter for a combination.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


27. How do you divide fractions?
80%
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)+
6
Invert the second fraction (reciprocal) and multiply


28. In a coordinate system - identify the quadrants and describe their location.
A line is a 180-degree angle.
(x+y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.


29. The three exterior angles of a triangle add up to...
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.
(x+y)(x-y)
360 degrees
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


30. Diameter of a circle?
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.
2r
90 degrees each.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


31. What is the sum of any 'big' angle and any 'Small' angle?
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 average - mean - median - or mode.
4 angles are formed. Their sum is 360 degrees
180 degrees.


32. Explain how to divide fractions.
Multiply numerator times numerator and denominator times denominator.
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
(x-y)²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


33. HIGH: how do you calculate the surface area of a rectangular box?
2pr -or- pd
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.
The total # of possible outcomes.
The average - mean - median - or mode.


34. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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%.


35. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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
Bh


36. Convert to a percentage: 1/4
A=pr²
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.
25%
6


37. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
180 degrees
Not reading the problems carefully enough!


38. Explain the difference between handling a permutation versus a combination.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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.


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

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40. What is an 'equilateral' triangle?
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.
S*v2
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


41. How do you solve a combination?

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42. If something is possible but not certain - what is the numeric range of probability of it happening?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
An integer is divisible by 2 if its units digit is divisible by 2.
Between 0 and 1.


43. List two odd behaviors of exponents
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.
The # falling in the center of an ordered data set
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.
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


44. HIGH: Simplify this: v75/v27
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.
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.
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.
360 degrees


45. HIGH: Rough est. of v2 =
Not reading the problems carefully enough!
Find the total - or whole - first - and then set up a Ratio Box.
(x+y)(x-y)
1.4


46. HIGH: Describe how to deal with 2 sets of parentheses.
x² -2xy + y²
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)+
'Big' angles and 'Small' angles.
80%


47. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
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
(x+y)(x-y)
A triangle in which one of the three interior angles is 90 degrees.


48. Define a factorial of a number - and how it is written.
Probability A * Probability 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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.


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

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50. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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
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'.