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. In a coordinate system - identify the quadrants and describe their location.
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.
3:4:5 5:12:13
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


2. 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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
6
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


3. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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 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.
Not necessarily. This is a trick question - because x could be either positive or negative.
2


4. What are the side ratios 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.
x² -2xy + y²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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


5. Explain how to use a 'Rate Pie'
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
2
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


6. HIGH: What is a 'Right isosceles' triangle?
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.
3:4:5 5:12:13
The value that appears most often in a data set.
Find a common denominator and make equivalent fractions. Then add or subtract.


7. What is the sum of any 'big' angle and any 'Small' angle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(a+b)(a-b)
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
180 degrees.


8. HIGH: What is the factored version of (x+y)(x-y) ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
S*v2
x²-y²


9. HIGH: What is the factored version of x² + 2xy + y² ?
1
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Order does matter for a permutation - but does not matter for a combination.
(x+y)²


10. 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.
180 degrees.
360 degrees
Find the total - or whole - first - and then set up a Ratio Box.


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


12. HIGH: What is the unfactored version of (x-y)² ?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
x² -2xy + y²


13. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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 5 if its units digit is either 0 or 5.
The average - mean - median - or mode.


14. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
'Big' angles and 'Small' angles.
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.


15. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 5 if its units digit is either 0 or 5.
4 angles are formed. Their sum is 360 degrees
25%


16. What is the 'Third side' rule for triangles?
1.4
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
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.


17. HIGH: What is the unfactored version of x²-y² ?
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.
(x+y)(x-y)
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
'Big' angles and 'Small' angles.


18. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


19. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Order does matter for a permutation - but does not matter for a combination.
1. Given event A: A + notA = 1.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


20. HIGH: To divide powers with the same base...
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.
A line is a 180-degree angle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


21. 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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
V=s³
4 angles are formed. Their sum is 360 degrees


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

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23. HIGH: x^-n is equal to
1/1
1/x^n For example - 6-² = 1/6² = 1/36
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.


24. HIGH: Rough est. of v3 =
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1.7
Find a common denominator and make equivalent fractions. Then add or subtract.


25. An integer is divisible by 3 if...
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.
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.
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.
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.


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

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27. If x² = 144 - does v144 = x?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Not necessarily. This is a trick question - because x could be either positive or negative.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a+b)(a-b)


28. HIGH: How do you multiply powers with the same base?
25%
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
S²
6


29. v4 =
x² + 2xy + y²
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.
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.
2


30. HIGH: What is a '30:60:90' triangle?
1.4
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.
Not reading the problems carefully enough!


31. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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)
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'.


32. HIGH: Rough est. of v1 =
1
A triangle in which one of the three interior angles is 90 degrees.
Between 0 and 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.


33. How many degrees does a circle contain?
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.
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.
360 degrees
4 angles are formed. Their sum is 360 degrees


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

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35. What is a 'Right' triangle?
60%
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 triangle in which one of the three interior angles is 90 degrees.
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.


36. What do permutation problems often ask for?
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.
Not reading the problems carefully enough!
Arrangements - orders - schedules - or lists.


37. Define the mode of a set of numbers.
A radius
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 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 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.


38. How do you calculate the percentage of change?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
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.
Percentage Change = Difference/Original * 100


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

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40. HIGH: How do you multiply and divide square roots?
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.
1.4
Example: 1 < x < 10
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


41. Does order matter for a permutation? How about for a combination?
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
Not necessarily. This is a trick question - because x could be either positive or negative.
Order does matter for a permutation - but does not matter for a combination.
25%


42. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
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%.
1
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


43. What is the factored version of x² -2xy + y² ?
(x-y)²
360 degrees
The total # of possible outcomes.
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.


44. Solve this: v6 * -v6 = ?
6
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.
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%.


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

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46. How do you solve a combination?

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47. On the GRE - should you ever assume that diagrams are truthful?
x²-y²
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.


48. Probability Formula
Find the total - or whole - first - and then set up a Ratio Box.
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.
Not reading the problems carefully enough!
Favorable Outcomes/Total Possible Outcomes


49. In a coordinate system - what is the origin?
(0 -0)
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.
4 angles are formed. Their sum is 360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.


50. If something is certain to happen - how is the probability of this event expressed mathematically?
90 degrees each.
80%
1/1
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.