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• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
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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 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.
1/x^n For example - 6-² = 1/6² = 1/36
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+b)(a-b)


2. HIGH: What is the order of math operations - and the mnemonic to remember it?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
Find a common denominator and make equivalent fractions. Then add or subtract.


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

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4. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
360 degrees
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


5. Explain how to calculate an average (arithmetic mean)
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'.
Groups - teams - or committees.
Probability A * Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


6. HIGH: How do you multiply powers with the same base?
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 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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


7. HIGH: Area of a circle
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
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 radius


8. Area of a parallelogram?
Order does matter for a permutation - but does not matter for a combination.
'Big' angles and 'Small' angles.
Bh
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.


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

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10. Define a factorial of a number - and how it is written.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
x²-y²
V=pr²h (This is just the area multiplied by the height)
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.


11. Area of a square?
A line is a 180-degree angle.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
S²
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


12. What causes 80% of errors on the math section of the GRE?
(x+y)²
2pr -or- pd
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!


13. 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
(a+b)(a-b)
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Favorable Outcomes/Total Possible Outcomes


14. What are 'vertical angles'?
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)+
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


15. How do you solve a permutation?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
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
Order does matter for a permutation - but does not matter for a combination.


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

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17. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
'Big' angles and 'Small' angles.
Bh
Between 0 and 1.


18. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
x² -2xy + y²
An integer is divisible by 2 if its units digit is divisible by 2.


19. HIGH: What is the mode?
x² -2xy + y²
180 degrees
The value that appears most often in a data set.
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.


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

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21. HIGH: What is a 'Right isosceles' triangle?
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.
Invert the second fraction (reciprocal) and multiply
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


22. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A radius
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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


23. What is the key to dealing with ratio questions?
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
Find the total - or whole - first - and then set up a Ratio Box.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


24. Solve this: v6 * -v6 = ?
The total # of possible outcomes.
6
180 degrees.
V=s³


25. HIGH: Simplify this: v75/v27
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.
180 degrees.
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.
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.


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

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27. Define the range of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
40%
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.
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.


28. HIGH: Rough est. of v3 =
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'.
1.4
1.7
2r


29. HIGH: What is the formula for the diagonal of any square?
S*v2
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
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.


30. The three exterior angles of a triangle add up to...
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


31. An integer is divisible by 5 if...
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 5 if its units digit is either 0 or 5.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A triangle in which one of the three interior angles is 90 degrees.


32. How do you divide fractions?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Bh
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.
Invert the second fraction (reciprocal) and multiply


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

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34. 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The average - mean - median - or mode.


35. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1/1
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
25%
It will be a great advantage on test day to have your times table memorized from 1 through 15.


36. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)²
The total # of possible outcomes.


37. How do you add or subtract fractions?
2
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
The total # of possible outcomes.


38. HIGH: What is the unfactored version of (x+y)² ?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
x² + 2xy + y²
180 degrees.


39. Define 'proportionate' values
Probability A + Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=pr²
90 degrees each.


40. How is a range expressed with inequalities?
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
1/x^n For example - 6-² = 1/6² = 1/36
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
Example: 1 < x < 10


41. What is a 'Right' triangle?
180 degrees
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
A triangle in which one of the three interior angles is 90 degrees.


42. Convert to a percentage: 1/4
25%
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.
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
(a+b)(a-b)


43. Explain the special properties of zero.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Bh
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.
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.


44. 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
The # falling in the center of an ordered data set
6


45. What do combination problems usually ask for?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Groups - teams - or committees.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(x+y)²


46. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
1.7
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
360 degrees


47. What is a 'Right' angle?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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 90-degree angle.


48. HIGH: What is the median?
The # falling in the center of an ordered data set
180 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.
x² -2xy + y²


49. Explain how to solve for 7/¼
2
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The value that appears most often in a data set.
An integer is divisible by 2 if its units digit is divisible by 2.


50. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
6
An integer is divisible by 9 if the sum of its digits is divisible by 9.