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. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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2. HIGH: What is the unfactored version of x²-y² ?
1.7
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
(x+y)(x-y)
360 degrees


3. Simplify this: v32
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%.
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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


4. HIGH: How much of your times table should you know - for the GRE?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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


5. HIGH: Rough est. of v2 =
The value that appears most often in a data set.
1.4
40%
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


6. HIGH: What are the percentages for standard deviation?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
40%
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


7. How do you solve a permutation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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. 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
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.


8. Explain the special properties of zero.
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. 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
2r
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


9. What do combination problems usually ask for?
Groups - teams - or committees.
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)+
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


10. HIGH: How do you multiply powers with the same base?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


11. 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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Arrangements - orders - schedules - or lists.


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

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13. HIGH: x^-n is equal to
2r
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/x^n For example - 6-² = 1/6² = 1/36
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


14. Explain how to use an 'Average Pie'
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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


15. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
An integer is divisible by 5 if its units digit is either 0 or 5.
25%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.


16. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


17. HIGH: Volume of a cylinder?
6
4 angles are formed. Their sum is 360 degrees
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


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

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19. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Order does matter for a permutation - but does not matter for a combination.
A 90-degree angle.
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.


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

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21. HIGH: Volume of a cube?
(0 -0)
The # falling in the center of an ordered data set
V=s³
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


22. How do you solve a combination?

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

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24. HIGH: What is the Pythagorean theorem?

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25. What are the side ratios for a 30:60:90 triangle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B


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

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27. How is a range expressed with inequalities?
90 degrees each.
Example: 1 < x < 10
S²
An integer is divisible by 9 if the sum of its digits is divisible by 9.


28. What degree angle is a line?
A line is a 180-degree angle.
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.
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.


29. HIGH: What is the mode?
1.4
1. Given event A: A + notA = 1.
The value that appears most often in a data set.
1/1


30. What is the name of a line that extends from the center of a circle to the edge of a circle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A triangle in which one of the three interior angles is 90 degrees.
A radius
Probability A + Probability B


31. HIGH: List the two most common side ratios for right triangles
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
3:4:5 5:12:13
Example: 1 < x < 10
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.


32. HIGH: What must be true before a quadratic equation can be solved?

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33. a² - b² is equal to
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+b)(a-b)
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
'Big' angles and 'Small' angles.


34. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
A 90-degree angle.
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.


35. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
360 degrees
Bh
1


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

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37. HIGH: Define the 'Third side' rule for triangles

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38. An integer is divisible by 2 if...
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 2 if its units digit is divisible by 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


39. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
x² + 2xy + y²


40. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
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.
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.
180 degrees


41. An integer is divisible by 9 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


42. How do you add or subtract fractions?
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1/1
Find a common denominator and make equivalent fractions. Then add or subtract.


43. What is the formula to determine probability?
40%
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
25%


44. HIGH: Rough est. of v3 =
1.7
80%
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


45. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
The total # of possible outcomes.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
6


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

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47. Explain the difference between handling a permutation versus a combination.
6
Percentage Change = Difference/Original * 100
360 degrees
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.


48. What is a 'Right' angle?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
A 90-degree angle.
360 degrees
1.4


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

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50. The three exterior angles of a triangle add up to...
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
360 degrees
S²