Instructions:

• 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 unfactored version of x²-y² ?
(x+y)(x-y)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
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


2. What is the factored version of x² -2xy + y² ?
(x-y)²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
25%
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.


3. How many degrees does a circle contain?
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.
360 degrees
(0 -0)


4. HIGH: What is the mode?
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.
Bh
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


5. HIGH: What is a 'Right isosceles' triangle?
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.
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
80%
2r


6. HIGH: List the two most common side ratios for right triangles
2pr -or- pd
(x+y)²
3:4:5 5:12:13
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


7. HIGH: What is the factored version of x² + 2xy + y² ?
360 degrees
(x+y)²
Find a common denominator and make equivalent fractions. Then add or subtract.
Bh


8. HIGH: What is the formula for the diagonal of any square?
1/1
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


9. What is the 'Third side' rule for triangles?
An integer is divisible by 2 if its units digit is divisible by 2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
Bh


10. Diameter of a circle?
2r
Groups - teams - or committees.
An integer is divisible by 2 if its units digit is divisible by 2.
A triangle in which one of the three interior angles is 90 degrees.


11. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find the total - or whole - first - and then set up a Ratio Box.
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.


12. Define the range of a set of numbers.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


13. How do you solve a permutation?
S*v2
ZONE-F numbers: Zero - One - Negatives - Extreme values - 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
x²-y²


14. If something is possible but not certain - what is the numeric range of probability of it happening?
2r
3:4:5 5:12:13
Between 0 and 1.
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.


15. What is an 'equilateral' triangle?
2r
40%
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.


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

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17. Explain how to use an 'Average Pie'
x²-y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Groups - teams - or committees.


18. 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.
x²-y²
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.


19. Simplify this: v32
S*v2
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


20. What degree angle is a line?
A line is a 180-degree angle.
1.7
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(a+b)(a-b)


21. What causes 80% of errors on the math section of the GRE?
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.
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.
S²
Not reading the problems carefully enough!


22. What is the equation for a group problem?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


23. HIGH: Simplify this: v75/v27
V=s³
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.
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.


24. What is the sum of any 'big' angle and any 'Small' angle?
(a+b)(a-b)
2
180 degrees.
(0 -0)


25. Define 'proportionate' values
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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
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.


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

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27. HIGH: To divide powers with the same base...
A radius
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


28. What is the 'distributive law'?
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.
Probability A * Probability B
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Favorable Outcomes/Total Possible Outcomes


29. What do combination problems usually ask for?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Groups - teams - or committees.
V=pr²h (This is just the area multiplied by the height)


30. Does order matter for a permutation? How about for a combination?
1.4
4 angles are formed. Their sum is 360 degrees
A triangle in which one of the three interior angles is 90 degrees.
Order does matter for a permutation - but does not matter for a combination.


31. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(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.
25%


32. v4 =
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.
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.
(x+y)(x-y)
2


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

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


35. The probability of an event happening and the probability of an event NOT happening must add up to what number?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
1. Given event A: A + notA = 1.
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.


36. List all the prime numbers that are less than 30:
x²-y²
x² + 2xy + y²
(0 -0)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


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

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38. What do permutation problems often ask for?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Arrangements - orders - schedules - or lists.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Favorable Outcomes/Total Possible Outcomes


39. Explain how to divide fractions.
1
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.
x² + 2xy + y²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


40. List two odd behaviors of exponents
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 total # of possible outcomes.
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.
6


41. Convert to a percentage: 1/4
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A 90-degree angle.
25%


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

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43. 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.
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
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.


44. HIGH: Rough est. of v3 =
180 degrees.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1.7
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


45. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.


46. An integer is divisible by 3 if...
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.
(x+y)²
(x+y)(x-y)
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.


47. HIGH: What is the unfactored version of (x-y)² ?
Groups - teams - or committees.
x² -2xy + y²
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.
25%


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

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49. HIGH: What is the median?
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. 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 # falling in the center of an ordered data set
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.


50. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1
(x+y)²
4 angles are formed. Their sum is 360 degrees