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: What is the factored version of (x+y)(x-y) ?
60%
x²-y²
1/1
Not reading the problems carefully enough!


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

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3. HIGH: What is the formula for the diagonal of any square?
1/x^n For example - 6-² = 1/6² = 1/36
Bh
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
S*v2


4. What is the 'distributive law'?
1/1
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.
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.
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.


5. HIGH: Volume of a cylinder?
Example: 1 < x < 10
25%
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
V=pr²h (This is just the area multiplied by the height)


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


7. What is the formula to determine probability?
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.
2pr -or- pd
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


8. Convert to a percentage: 1/4
A triangle in which one of the three interior angles is 90 degrees.
Probability A + Probability B
Invert the second fraction (reciprocal) and multiply
25%


9. If x² = 144 - does v144 = x?
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


10. Probability Formula
Multiply numerator times numerator and denominator times denominator.
Find the total - or whole - first - and then set up a Ratio Box.
'Big' angles and 'Small' angles.
Favorable Outcomes/Total Possible Outcomes


11. HIGH: What is the mode?
The value that appears most often in a data set.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


12. HIGH: What is the median?
The # falling in the center of an ordered data set
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


13. An integer is divisible by 5 if...
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 5 if its units digit is either 0 or 5.
(x+y)²
(x+y)(x-y)


14. What is the 'Third side' rule for triangles?
Find a common denominator and make equivalent fractions. Then add or subtract.
Percentage Change = Difference/Original * 100
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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.


15. How do you calculate the probability of two events in a row? (Probability of A and B)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Probability A * Probability B


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

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17. What do permutation problems often ask for?
An integer is divisible by 2 if its units digit is divisible by 2.
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
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%.


18. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
(x-y)²
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.


19. How do you solve a combination?

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

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21. What number goes on the bottom of a probability fraction?
A radius
1.7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The total # of possible outcomes.


22. HIGH: What is a '30:60:90' triangle?
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
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.
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'.
2pr -or- pd


23. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A + Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


24. What is an 'equilateral' triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Favorable Outcomes/Total Possible Outcomes
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.


25. What is the factored version of x² -2xy + y² ?
(x-y)²
Between 0 and 1.
180 degrees
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


26. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
(a+b)(a-b)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1


27. HIGH: Rough est. of v2 =
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
6
1.4
1/1


28. Explain how to divide fractions.
Percentage Change = Difference/Original * 100
360 degrees
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


29. HIGH: Rough est. of v3 =
360 degrees
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
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.
1.7


30. Explain how to use a 'Rate Pie'
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
x² + 2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.


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

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32. HIGH: What is the factored version of x² + 2xy + y² ?
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
x² + 2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²


33. How is a range expressed with inequalities?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Example: 1 < x < 10
Favorable Outcomes/Total Possible Outcomes
(x+y)(x-y)


34. Solve this: v6 * -v6 = ?
Percentage Change = Difference/Original * 100
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
6
Bh


35. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
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.
(a+b)(a-b)
Multiply numerator times numerator and denominator times denominator.


36. What'S the most important thing to remember about charts you'll see on the GRE?
The average - mean - median - or mode.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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 # falling in the center of an ordered data set


37. HIGH: Rough est. of v1 =
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% |
40%
1


38. What causes 80% of errors on the math section of the GRE?
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 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.
x²-y²
Not reading the problems carefully enough!


39. An integer is divisible by 9 if...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


40. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
Arrangements - orders - schedules - or lists.
1.4
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.


41. HIGH: Volume of a cube?
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
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.
V=s³
Favorable Outcomes/Total Possible Outcomes


42. How do you multiply fractions?
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
Multiply numerator times numerator and denominator times denominator.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2r


43. What is a 'Right' 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.
A 90-degree angle.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1


44. How do you solve a permutation?
Favorable Outcomes/Total Possible Outcomes
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
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
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.


45. What is the sum of any 'big' angle and any 'Small' angle?
An integer is divisible by 5 if its units digit is either 0 or 5.
180 degrees.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


46. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V=s³
A line is a 180-degree angle.
Invert the second fraction (reciprocal) and multiply


47. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Percentage Change = Difference/Original * 100
The total # of possible outcomes.
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.


48. 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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49. 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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x-y)²
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.


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

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