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. What is the 'distributive law'?
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
90 degrees each.


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

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3. How many degrees does a circle contain?
360 degrees
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.


4. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 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.
3:4:5 5:12:13
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.


5. HIGH: Rough est. of v3 =
1.7
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
(0 -0)


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

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7. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
(a+b)(a-b)
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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


8. HIGH: Volume of a cube?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Not necessarily. This is a trick question - because x could be either positive or negative.
3:4:5 5:12:13
V=s³


9. a² - b² is equal to
(a+b)(a-b)
2r
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


10. Solve this: v6 * -v6 = ?
6
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


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

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12. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
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.
(0 -0)


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

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14. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
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/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 9 if the sum of its digits is divisible by 9.


15. The three interior angles of a triangle add up to...
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Bh
180 degrees
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


16. What is the 'Third side' rule for triangles?
60%
Between 0 and 1.
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.
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.


17. Explain the special properties of zero.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
x²-y²


18. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
x² + 2xy + y²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Invert the second fraction (reciprocal) and multiply


19. HIGH: What is the Pythagorean theorem?

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20. Explain how to use an 'Average Pie'
6
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.
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


21. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


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

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23. Area of a square?
S²
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(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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


24. HIGH: List the two most common side ratios for right triangles
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
V=pr²h (This is just the area multiplied by the height)
3:4:5 5:12:13
A=pr²


25. How is a range expressed with inequalities?
2r
Example: 1 < x < 10
The # falling in the center of an ordered data set
80%


26. 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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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.


27. 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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28. What is the equation for a group problem?
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.
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
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
Between 0 and 1.


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

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30. HIGH: What is the order of math operations - and the mnemonic to remember it?
Invert the second fraction (reciprocal) and multiply
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/x^n For example - 6-² = 1/6² = 1/36
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


31. What is the key to dealing with ratio questions?
Between 0 and 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.
40%
Find the total - or whole - first - and then set up a Ratio Box.


32. What is the factored version of x² -2xy + y² ?
1.4
(x-y)²
Find the total - or whole - first - and then set up a Ratio Box.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


33. v4 =
2
90 degrees each.
25%
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


34. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a+b)(a-b)
Probability A + Probability B
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.


35. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
S*v2
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
180 degrees.
x²-y²


36. HIGH: Rough est. of v2 =
x²-y²
1.4
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.


37. HIGH: What is a 'Right isosceles' triangle?
Arrangements - orders - schedules - or lists.
80%
Example: 1 < x < 10
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.


38. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
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 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 - 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.


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

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40. HIGH: what is the side ratio for a Right Isosceles triangle?
2pr -or- pd
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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


41. Area of a parallelogram?
The value that appears most often in a data set.
Bh
6
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.


42. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
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
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


43. List two odd behaviors of exponents
2pr -or- pd
Arrangements - orders - schedules - or lists.
60%
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.


44. For a bell curve - what three terms might be used to describe the number in the middle?
The total # of possible outcomes.
A triangle in which one of the three interior angles is 90 degrees.
Between 0 and 1.
The average - mean - median - or mode.


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

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46. Simplify this: v32
Percentage Change = Difference/Original * 100
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1
S²


47. HIGH: What are the percentages for standard deviation?
(x+y)²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Find the total - or whole - first - and then set up a Ratio Box.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


48. Convert to a percentage: 4/5
6
80%
Multiply numerator times numerator and denominator times denominator.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


49. HIGH: Volume of a cylinder?
1.4
V=pr²h (This is just the area multiplied by the height)
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.
The # falling in the center of an ordered data set


50. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
1.7
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
'Big' angles and 'Small' angles.