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 sum of any 'big' angle and any 'Small' angle?
V=pr²h (This is just the area multiplied by the height)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
180 degrees.


2. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
60%
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


3. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Invert the second fraction (reciprocal) and multiply


4. Probability Formula
An integer is divisible by 9 if the sum of its digits is divisible by 9.
180 degrees.
Favorable Outcomes/Total Possible Outcomes
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


5. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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 9 if the sum of its digits is divisible by 9.


6. What is an 'equilateral' triangle?
(x+y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.


7. How do you calculate the probability of two events in a row? (Probability of A and B)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A line is a 180-degree angle.
Probability A * Probability B
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.


8. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
180 degrees
x² -2xy + y²


9. HIGH: Volume of a cube?
V=s³
(x-y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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


10. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
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.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


11. HIGH: Simplify this: v75/v27
The value that appears most often in a data set.
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.
360 degrees
'Big' angles and 'Small' angles.


12. How do you divide fractions?
The # falling in the center of an ordered data set
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Invert the second fraction (reciprocal) and multiply
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


13. The probability of an event happening and the probability of an event NOT happening must add up to what number?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1. Given event A: A + notA = 1.
(x-y)²
An integer is divisible by 2 if its units digit is divisible by 2.


14. List two odd behaviors of exponents
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%.
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.
A radius


15. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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
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.


16. Define 'proportionate' values
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.
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 line is a 180-degree angle.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


17. Explain the special properties of zero.
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.
The total # of possible outcomes.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(a+b)(a-b)


18. HIGH: How much of your times table should you know - for the GRE?
3:4:5 5:12:13
Multiply numerator times numerator and denominator times denominator.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.


19. a² - b² is equal to
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.
The # falling in the center of an ordered data set
(a+b)(a-b)
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


20. HIGH: Rough est. of v1 =
360 degrees
V=pr²h (This is just the area multiplied by the height)
1
x²-y²


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

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22. Convert to a percentage: 3/5
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.
V=pr²h (This is just the area multiplied by the height)
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.
60%


23. How do you solve a combination?

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24. What is a 'Right' angle?
x² + 2xy + y²
S²
A 90-degree angle.
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.


25. Explain how to use a 'Rate Pie'
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(x+y)(x-y)
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


26. What is the factored version of x² -2xy + y² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V=pr²h (This is just the area multiplied by the height)
Percentage Change = Difference/Original * 100
(x-y)²


27. In a coordinate system - identify the quadrants and describe their location.
x² + 2xy + 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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A + Probability B


28. If x² = 144 - does v144 = x?
(# 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


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

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30. HIGH: How do you calculate the circumference of a circle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
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)+
2pr -or- pd


31. HIGH: What is the Pythagorean theorem?

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32. HIGH: What is a 'Right isosceles' triangle?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
(x+y)²
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)+


33. v4 =
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2
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.


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

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35. HIGH: What is the median?
V=s³
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)+
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 # falling in the center of an ordered data set


36. What is the equation for a group problem?
1/1
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
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.
Between 0 and 1.


37. HIGH: Rough est. of v2 =
1.4
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.
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.
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.


38. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
40%
4 angles are formed. Their sum is 360 degrees
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.


39. Define a factorial of a number - and how it is written.
x² + 2xy + y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


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

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41. HIGH: What is the order of math operations - and the mnemonic to remember it?
(x+y)(x-y)
A 90-degree angle.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


42. What degree angle is a line?
90 degrees each.
A line is a 180-degree angle.
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.
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


43. Area of a parallelogram?
Bh
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
25%


44. Define the mode of a set of numbers.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
A triangle in which one of the three interior angles is 90 degrees.


45. HIGH: Area of a triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


46. Convert to a percentage: 2/5
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
40%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.


47. HIGH: To divide powers with the same base...
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.
2r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


48. What is a 'Right' triangle?
3:4:5 5:12:13
A triangle in which one of the three interior angles is 90 degrees.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


49. An integer is divisible by 3 if...
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
1.7
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.


50. HIGH: What is the unfactored version of x²-y² ?
Arrangements - orders - schedules - or lists.
80%
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x+y)(x-y)