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. HIGH: What is the unfactored version of x²-y² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)(x-y)
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
180 degrees.


2. What is the factored version of x² -2xy + y² ?
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%.
(x-y)²
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
An integer is divisible by 5 if its units digit is either 0 or 5.


3. 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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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


4. For a bell curve - what three terms might be used to describe the number in the middle?
Not reading the problems carefully enough!
'Big' angles and 'Small' angles.
The average - mean - median - or mode.
6


5. HIGH: Rough est. of v2 =
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.
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.
1.4
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


6. Define the mode of a set of numbers.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Not necessarily. This is a trick question - because x could be either positive or negative.


7. An integer is divisible by 9 if...
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.
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.
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


8. What do combination problems usually ask for?
Groups - teams - or committees.
2pr -or- pd
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
'Big' angles and 'Small' angles.


9. 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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
V=pr²h (This is just the area multiplied by the height)
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.


10. HIGH: What is the mode?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The value that appears most often in a data set.
25%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


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

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12. HIGH: What is the Pythagorean theorem?

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13. Define the range of a set of numbers.
x²-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.
2pr -or- pd
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


14. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
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.
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.
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%.


15. HIGH: Describe how to deal with 2 sets of parentheses.
360 degrees
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)+
Example: 1 < x < 10
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


16. An integer is divisible by 3 if...
(0 -0)
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.
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=pr²


17. Probability Formula
An integer is divisible by 9 if the sum of its digits is divisible by 9.
S²
The total # of possible outcomes.
Favorable Outcomes/Total Possible Outcomes


18. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.


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

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

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21. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(x-y)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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


22. HIGH: What is the factored version of x² + 2xy + y² ?
40%
(x+y)²
60%
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.


23. What is the 'distributive law'?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1. Given event A: A + notA = 1.
An integer is divisible by 2 if its units digit is divisible by 2.
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.


24. In a coordinate system - identify the quadrants and describe their location.
(a+b)(a-b)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.


25. HIGH: How much of your times table should you know - for 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.
Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


26. HIGH: Volume of a cube?
1.7
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 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.
V=s³


27. Convert to a percentage: 1/4
A radius
x² -2xy + y²
An integer is divisible by 9 if the sum of its digits is divisible by 9.
25%


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

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29. a² - b² is equal to
Favorable Outcomes/Total Possible Outcomes
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(a+b)(a-b)
2


30. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
(x-y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
60%


31. What'S one way to avoid mistakes on algebra questions in the GRE?

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32. What is the name of a line that extends from the center of a circle to the edge of a circle?
Find the total - or whole - first - and then set up a Ratio Box.
Example: 1 < x < 10
A radius
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.


33. HIGH: x^-n is equal to
4 angles are formed. Their sum is 360 degrees
360 degrees
1/x^n For example - 6-² = 1/6² = 1/36
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


34. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
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
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
1. Given event A: A + notA = 1.


35. How do you multiply fractions?
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.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Multiply numerator times numerator and denominator times denominator.


36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
The total # of possible outcomes.
(x-y)²
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.
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


37. 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
1/x^n For example - 6-² = 1/6² = 1/36
80%
(x+y)(x-y)


38. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
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.
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.
Probability A * Probability B


39. v4 =
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.
A radius
2
A=pr²


40. If x² = 144 - does v144 = x?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
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.


41. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Not reading the problems carefully enough!
A=pr²


42. Convert to a percentage: 4/5
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
80%
4 angles are formed. Their sum is 360 degrees
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.


43. How do you divide fractions?
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.
60%
Invert the second fraction (reciprocal) and multiply
The value that appears most often in a data set.


44. HIGH: What is the unfactored version of (x-y)² ?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
x² -2xy + y²
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.


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

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46. HIGH: What is a 'Right isosceles' triangle?
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.
(x-y)²
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.
Not necessarily. This is a trick question - because x could be either positive or negative.


47. List two odd behaviors of exponents
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.
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.
1.4
(0 -0)


48. Explain how to divide fractions.
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


49. HIGH: what is the side ratio for a Right Isosceles 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
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.
(x-y)²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


50. On the GRE - should you ever assume that diagrams are truthful?
Between 0 and 1.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
S²