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. HIGH: To divide powers with the same base...
1.7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Arrangements - orders - schedules - or lists.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


2. Explain how to use a 'Rate Pie'
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'.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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. Given event A: A + notA = 1.


3. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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.
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'.


4. HIGH: Rough est. of v1 =
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
360 degrees


5. What is the 'distributive law'?
The average - mean - median - or mode.
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
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.


6. On the GRE - should you ever assume that diagrams are truthful?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.


7. Define 'proportionate' values
2r
180 degrees
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


8. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
80%
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


9. HIGH: What is the unfactored version of (x-y)² ?
The average - mean - median - or mode.
x² -2xy + y²
V=s³
x²-y²


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

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11. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
A line is a 180-degree angle.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.


12. In a coordinate system - what is the origin?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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 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.
(0 -0)


13. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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
80%
V=s³
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.


14. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
1/x^n For example - 6-² = 1/6² = 1/36
6
An integer is divisible by 2 if its units digit is divisible by 2.


15. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
1.4
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.
The total # of possible outcomes.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


16. HIGH: Area of a 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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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.


17. What is the 'Third side' rule for triangles?
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. Given event A: A + notA = 1.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


18. Probability Formula
The value that appears most often in a data set.
Favorable Outcomes/Total Possible Outcomes
4 angles are formed. Their sum is 360 degrees
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


19. 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.
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. 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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


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

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21. Explain how to use an 'Average Pie'
6
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


22. Explain the difference between handling a permutation versus a combination.
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.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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


23. HIGH: x^-n is equal to
A=pr²
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.
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.
1/x^n For example - 6-² = 1/6² = 1/36


24. Solve this: v6 * -v6 = ?
6
Groups - teams - or committees.
1.7
V=s³


25. What is the equation for a group problem?
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
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
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).


26. An integer is divisible by 2 if...
Probability A * Probability B
Example: 1 < x < 10
An integer is divisible by 2 if its units digit is divisible by 2.
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.


27. What number goes on the bottom of a probability fraction?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1.7
180 degrees
The total # of possible outcomes.


28. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Percentage Change = Difference/Original * 100
4 angles are formed. Their sum is 360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


29. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A triangle in which one of the three interior angles is 90 degrees.
x² -2xy + y²
Order does matter for a permutation - but does not matter for a combination.


30. How do you solve a combination?

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31. Define the range of a set of numbers.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
Invert the second fraction (reciprocal) and multiply
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


32. What is the formula to determine probability?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


33. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


34. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
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.
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.


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

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36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Probability A * Probability B
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.
S*v2
3:4:5 5:12:13


37. HIGH: What is a '30:60:90' triangle?
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.
An integer is divisible by 2 if its units digit is divisible by 2.
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
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.


38. HIGH: How do you multiply powers with the same base?
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.
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.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


39. HIGH: What is the median?
x² -2xy + y²
A radius
(x+y)²
The # falling in the center of an ordered data set


40. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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 6 if it'S divisible by BOTH 2 and 3.
A line is a 180-degree angle.


41. v4 =
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1
Not reading the problems carefully enough!
2


42. Convert to a percentage: 3/5
60%
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.
(x+y)(x-y)
Favorable Outcomes/Total Possible Outcomes


43. Does order matter for a permutation? How about for a combination?
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.
Order does matter for a permutation - but does not matter for a combination.
S²
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)+


44. HIGH: Simplify this: v75/v27
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Groups - teams - or committees.


45. What is the factored version of x² -2xy + y² ?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
180 degrees
(x-y)²
2r


46. HIGH: What is the formula for the diagonal of any square?
1
Groups - teams - or committees.
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.
S*v2


47. HIGH: Rough est. of v3 =
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/x^n For example - 6-² = 1/6² = 1/36
S²
1.7


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

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49. HIGH: How much of your times table should you know - for the GRE?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A 90-degree angle.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


50. Convert to a percentage: 1/4
V=s³
(x+y)²
25%
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.