Instructions:

• Answer 50 questions in 15 minutes.
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• 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 (x+y)² ?
V=pr²h (This is just the area multiplied by the height)
x² + 2xy + y²
1/x^n For example - 6-² = 1/6² = 1/36
Groups - teams - or committees.


2. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Groups - teams - or committees.
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.


3. For a bell curve - what three terms might be used to describe the number in the middle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
180 degrees
40%
The average - mean - median - or mode.


4. HIGH: Describe how to deal with 2 sets of parentheses.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Find the total - or whole - first - and then set up a Ratio Box.
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)+


5. What is the 'distributive law'?
60%
(0 -0)
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.
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.


6. What degree angle is a line?
The total # of possible outcomes.
A line is a 180-degree angle.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
'Big' angles and 'Small' angles.


7. HIGH: What is a '30:60:90' triangle?
3:4:5 5:12:13
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
Invert the second fraction (reciprocal) and multiply
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


8. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
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
1.4
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


9. HIGH: What is the order of math operations - and the mnemonic to remember it?
The # falling in the center of an ordered data set
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
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.
1.4


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

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

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12. Does order matter for a permutation? How about for a combination?
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.
Order does matter for a permutation - but does not matter for a combination.
2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


13. List two odd behaviors of exponents
1.7
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 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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


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

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15. HIGH: What is the median?
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.
The # falling in the center of an ordered data set
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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


16. Diameter of a circle?
180 degrees.
2r
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.
Percentage Change = Difference/Original * 100


17. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1/x^n For example - 6-² = 1/6² = 1/36
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


18. HIGH: What is the Pythagorean theorem?

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19. The three exterior angles of a triangle add up to...
1/1
360 degrees
The value that appears most often in a data set.
Find a common denominator and make equivalent fractions. Then add or subtract.


20. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
The value that appears most often in a data set.
The total # of 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.


21. 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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A 90-degree angle.
Percentage Change = Difference/Original * 100


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

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23. Explain the difference between handling a permutation versus a combination.
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.
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.
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.


24. Convert to a percentage: 2/5
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Not necessarily. This is a trick question - because x could be either positive or negative.
40%
6


25. HIGH: What is the unfactored version of (x-y)² ?
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.
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%.
The average - mean - median - or mode.


26. HIGH: Rough est. of v1 =
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.
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
1.4
1


27. How do you multiply fractions?
A radius
Multiply numerator times numerator and denominator times denominator.
V=pr²h (This is just the area multiplied by the height)
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.


28. HIGH: What is the formula for the diagonal of any square?
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.
S*v2
x² -2xy + y²


29. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


30. The three interior angles of a triangle add up to...
Not reading the problems carefully enough!
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.
180 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


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

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32. Area of a parallelogram?
Bh
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%.
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.
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.


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


34. HIGH: Area of a circle
A=pr²
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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


35. Probability Formula
Favorable Outcomes/Total Possible Outcomes
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Example: 1 < x < 10
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


36. What is the factored version of x² -2xy + 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.
(x-y)²
The value that appears most often in a data set.
x²-y²


37. An integer is divisible by 9 if...
The value that appears most often in a data set.
Probability A + Probability B
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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)+


38. HIGH: How do you multiply powers with the same base?
Arrangements - orders - schedules - or lists.
4 angles are formed. Their sum is 360 degrees
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


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

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40. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
180 degrees


41. Explain how to calculate an average (arithmetic mean)
2
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The total # of possible outcomes.
A radius


42. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
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.
S*v2


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

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44. HIGH: Rough est. of v3 =
1.4
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Multiply numerator times numerator and denominator times denominator.
1.7


45. HIGH: What is the mode?
Percentage Change = Difference/Original * 100
1.4
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The value that appears most often in a data set.


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

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47. What is the sum of any 'big' angle and any 'Small' angle?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
180 degrees.
The average - mean - median - or mode.


48. Explain how to use a 'Rate Pie'
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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: Volume of a cube?
V=s³
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


50. What are the side ratios for a 30:60:90 triangle?
S*v2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S²
'Big' angles and 'Small' angles.