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: how do you calculate a diagonal inside a 3-dimensional rectangular box?
25%
An integer is divisible by 2 if its units digit is divisible by 2.
A=pr²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


2. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/1
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the 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.
x² + 2xy + y²


3. Probability Formula
1
Favorable Outcomes/Total Possible Outcomes
360 degrees
S²


4. How many degrees does a circle contain?
V=s³
It will be a great advantage on test day to have your times table memorized from 1 through 15.
360 degrees
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


5. Explain how to use an 'Average Pie'
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Not reading the problems carefully enough!
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


6. HIGH: Area of a triangle?
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%.
Order does matter for a permutation - but does not matter for a combination.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


7. HIGH: how do you calculate the surface area of a rectangular box?
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.
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.
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.


8. HIGH: Rough est. of v1 =
40%
1
Multiply numerator times numerator and denominator times denominator.
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.


9. How do you add or subtract fractions?
Percentage Change = Difference/Original * 100
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find a common denominator and make equivalent fractions. Then add or subtract.


10. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
Probability A + Probability B
(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


11. 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.
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
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.


12. HIGH: Area of a circle
x² + 2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³
A=pr²


13. In a coordinate system - what is the origin?
1.4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A=pr²
(0 -0)


14. Convert to a percentage: 1/4
25%
A 90-degree angle.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x² + 2xy + y²


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

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16. How do you multiply fractions?
Percentage Change = Difference/Original * 100
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1/x^n For example - 6-² = 1/6² = 1/36
Multiply numerator times numerator and denominator times denominator.


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

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18. Define 'proportionate' values
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
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.
x² -2xy + y²


19. What number goes on the bottom of a probability fraction?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The total # of possible outcomes.
An integer is divisible by 5 if its units digit is either 0 or 5.
A 90-degree angle.


20. v4 =
Arrangements - orders - schedules - or lists.
Not reading the problems carefully enough!
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2


21. Explain the special properties of zero.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Favorable Outcomes/Total Possible Outcomes
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.
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.


22. Define the range of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.


23. An integer is divisible by 5 if...
25%
An integer is divisible by 5 if its units digit is either 0 or 5.
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 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. How is a range expressed with inequalities?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Example: 1 < x < 10


25. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.


26. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
(0 -0)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A radius


27. What degree angle is a line?
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. 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 line is a 180-degree angle.
A radius


28. List all the prime numbers that are less than 30:
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 2 if its units digit is divisible by 2.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


29. Convert to a percentage: 2/5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
40%
An integer is divisible by 5 if its units digit is either 0 or 5.


30. How do you solve a combination?

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31. Solve this: v6 * -v6 = ?
Between 0 and 1.
2r
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
6


32. What is the formula to determine probability?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x²-y²
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.


33. Does order matter for a permutation? How about for a combination?
Find a common denominator and make equivalent fractions. Then add or subtract.
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
Order does matter for a permutation - but does not matter for a combination.
The total # of possible outcomes.


34. What is a 'Right' angle?
A triangle in which one of the three interior angles is 90 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 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.


35. HIGH: How do you multiply powers with the same base?
An integer is divisible by 5 if its units digit is either 0 or 5.
(0 -0)
An integer is divisible by 2 if its units digit is divisible by 2.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


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

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37. HIGH: What is the unfactored version of (x+y)² ?
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%.
(a+b)(a-b)
x² + 2xy + y²
Multiply numerator times numerator and denominator times denominator.


38. For a bell curve - what three terms might be used to describe the number in the middle?
'Big' angles and 'Small' angles.
S*v2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The average - mean - median - or mode.


39. HIGH: What is the unfactored version of (x-y)² ?
2r
90 degrees each.
x² -2xy + y²
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.


40. HIGH: To divide powers with the same base...
An integer is divisible by 5 if its units digit is either 0 or 5.
The value that appears most often in a data set.
60%
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


41. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
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.
The value that appears most often in a data set.
A line is a 180-degree angle.


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


43. Explain the difference between handling a permutation versus a combination.
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.
3:4:5 5:12:13
Groups - teams - or committees.
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.


44. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Multiply numerator times numerator and denominator times denominator.
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.
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.
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


45. HIGH: What is the equation of a line?

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46. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
Arrangements - orders - schedules - or lists.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x² + 2xy + y²


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

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48. HIGH: Volume of a cube?
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.
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 5 if its units digit is either 0 or 5.
V=s³


49. What'S the most important thing to remember about charts you'll see on the GRE?
(x-y)²
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.
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.
Multiply numerator times numerator and denominator times denominator.


50. What is the key to dealing with ratio questions?
An integer is divisible by 2 if its units digit is divisible by 2.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1.4
Find the total - or whole - first - and then set up a Ratio Box.