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 do permutation problems often ask for?
V=s³
Arrangements - orders - schedules - or lists.
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


2. Explain the difference between handling a permutation versus a combination.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
x² -2xy + y²
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.
Not reading the problems carefully enough!


3. What causes 80% of errors on the math section of the GRE?
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.
Not reading the problems carefully enough!
Probability A * Probability B
4 angles are formed. Their sum is 360 degrees


4. HIGH: What is the mode?
The value that appears most often in a data set.
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
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.
(a+b)(a-b)


5. v4 =
2
40%
x² -2xy + y²
The value that appears most often in a data set.


6. What is the key to dealing with ratio questions?
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
Find the total - or whole - first - and then set up a Ratio Box.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
180 degrees.


7. HIGH: What is the factored version of 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.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
(x+y)²


8. 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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9. HIGH: Rough est. of v1 =
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1
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.
A line is a 180-degree angle.


10. HIGH: Volume of a cube?
V=s³
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(0 -0)
x² -2xy + y²


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

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12. An integer is divisible by 3 if...
1
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.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


13. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
2
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=pr²


14. What is the 'Third side' rule for triangles?
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 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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Invert the second fraction (reciprocal) and multiply


15. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
1
Find the total - or whole - first - and then set up a Ratio Box.
Probability A * Probability B


16. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
An integer is divisible by 2 if its units digit is divisible by 2.
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.
A=pr²


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

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18. How do you multiply fractions?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
60%
Multiply numerator times numerator and denominator times denominator.
x² + 2xy + y²


19. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


20. On the GRE - should you ever assume that diagrams are truthful?
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.
Probability A + Probability B
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.


21. What is a 'Right' angle?
A 90-degree angle.
180 degrees
360 degrees
Percentage Change = Difference/Original * 100


22. What is the 'distributive law'?
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.
V=pr²h (This is just the area multiplied by the height)
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.
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.


23. What'S the most important thing to remember about charts you'll see on the GRE?
The total # of possible outcomes.
180 degrees
S²
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.


24. Define a factorial of a number - and how it is written.
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.
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
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'.
80%


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

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26. How do you add or subtract fractions?
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Find a common denominator and make equivalent fractions. Then add or subtract.
90 degrees each.


27. HIGH: What is the median?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The # falling in the center of an ordered data set
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


28. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
80%
x² + 2xy + y²
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.


29. Explain the special properties of zero.
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
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.
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 triangle in which one of the three interior angles is 90 degrees.


30. In a coordinate system - what is the origin?
(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')
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.
40%


31. The three interior angles of a triangle add up to...
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.
V=s³
Arrangements - orders - schedules - or lists.
180 degrees


32. What is the sum of any 'big' angle and any 'Small' angle?
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
180 degrees.
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


33. HIGH: What is the factored version of (x+y)(x-y) ?
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 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-y²
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.


34. What is a 'Right' triangle?
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.
Invert the second fraction (reciprocal) and multiply
A triangle in which one of the three interior angles is 90 degrees.
1. Given event A: A + notA = 1.


35. For a bell curve - what three terms might be used to describe the number in the middle?
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
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.
(0 -0)
The average - mean - median - or mode.


36. HIGH: Area of a triangle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
1/1
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


37. 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.
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%.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.


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

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39. Area of a square?
The average - mean - median - or mode.
Invert the second fraction (reciprocal) and multiply
1.7
S²


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


41. In a coordinate system - identify the quadrants and describe their location.
3:4:5 5:12:13
An integer is divisible by 2 if its units digit is divisible by 2.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


42. What is the formula to determine probability?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
3:4:5 5:12:13
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Not necessarily. This is a trick question - because x could be either positive or negative.


43. What do combination problems usually ask for?
Groups - teams - or committees.
A 90-degree angle.
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.
Order does matter for a permutation - but does not matter for a combination.


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

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45. What is the name of a line that extends from the center of a circle to the edge of a circle?
Find the total - or whole - first - and then set up a Ratio Box.
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
V=s³
A radius


46. How is a range expressed with inequalities?
Find a common denominator and make equivalent fractions. Then add or subtract.
1.7
Example: 1 < x < 10
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


47. a² - b² is equal to
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.
(a+b)(a-b)
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.
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


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

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49. HIGH: To divide powers with the same base...
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


50. Explain how to use a 'Rate Pie'
Find the total - or whole - first - and then set up a Ratio Box.
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
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
V=s³