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. If something is certain to happen - how is the probability of this event expressed mathematically?
Groups - teams - or committees.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Find a common denominator and make equivalent fractions. Then add or subtract.
1/1


2. 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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3. An integer is divisible by 9 if...
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.
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%.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


4. HIGH: Rough est. of v1 =
Not necessarily. This is a trick question - because x could be either positive or negative.
1/1
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.
1


5. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
6


6. Diameter of a circle?
40%
2r
The average - mean - median - or mode.
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.


7. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
2
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


8. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
6
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.
1.7


9. On the GRE - should you ever assume that diagrams are truthful?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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. Given event A: A + notA = 1.


10. HIGH: Volume of a cylinder?
S*v2
(x+y)(x-y)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
V=pr²h (This is just the area multiplied by the height)


11. How do you calculate the percentage of change?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Percentage Change = Difference/Original * 100


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

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13. HIGH: Volume of a cube?
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
V=s³


14. HIGH: What is the unfactored version of (x-y)² ?
Groups - teams - or committees.
40%
x² -2xy + y²
1/1


15. How precise do you need to be - using p on the GRE?

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16. What is the sum of any 'big' angle and any 'Small' 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.
A 90-degree angle.
180 degrees.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


17. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
2
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Probability A * Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


18. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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19. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
x² -2xy + y²
An integer is divisible by 2 if its units digit is divisible by 2.
Between 0 and 1.


20. HIGH: How do you calculate the circumference of a circle?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
V=s³
2pr -or- pd
6


21. a² - b² is equal to
1. Given event A: A + notA = 1.
(a+b)(a-b)
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


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

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23. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Order does matter for a permutation - but does not matter for a combination.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)(x-y)


24. What is the 'distributive law'?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
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.
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.


25. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1. Given event A: A + notA = 1.
1/1
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'.


26. The three exterior angles of a triangle add up to...
Bh
Find a common denominator and make equivalent fractions. Then add or subtract.
360 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.


27. What'S the most important thing to remember about charts you'll see on the GRE?
2pr -or- pd
Percentage Change = Difference/Original * 100
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.
Find the total - or whole - first - and then set up a Ratio Box.


28. HIGH: What is the mode?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
The value that appears most often in a data set.
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


29. HIGH: What is the equation of a line?

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30. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
3:4:5 5:12:13
Percentage Change = Difference/Original * 100
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


31. What do permutation problems often ask for?
x² -2xy + y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Find the total - or whole - first - and then set up a Ratio Box.
Arrangements - orders - schedules - or lists.


32. HIGH: Define the formula for calculating slope.
The total # of possible outcomes.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


33. Probability Formula
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Favorable Outcomes/Total Possible Outcomes
60%
360 degrees


34. Area of a parallelogram?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh
(x+y)(x-y)
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.


35. What is the name of a line that extends from the center of a circle to the edge of a circle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A 90-degree angle.
A radius
1


36. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Probability A * Probability B
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
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.


37. An integer is divisible by 2 if...
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
An integer is divisible by 2 if its units digit is divisible by 2.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/1


38. HIGH: What is the factored version of x² + 2xy + y² ?
V=pr²h (This is just the area multiplied by the height)
(x+y)²
S*v2
90 degrees each.


39. What is the 'Third side' rule for triangles?
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.
Invert the second fraction (reciprocal) and multiply
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.
90 degrees each.


40. HIGH: How do you multiply and divide square roots?
An integer is divisible by 5 if its units digit is either 0 or 5.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Probability A + Probability B
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


41. Explain how to use a 'Rate Pie'
A=pr²
Find the total - or whole - first - and then set up a Ratio Box.
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.
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


42. Explain the difference between handling a permutation versus a combination.
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.
Order does matter for a permutation - but does not matter for a combination.
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


43. HIGH: What is the factored version of (x+y)(x-y) ?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=s³
Find a common denominator and make equivalent fractions. Then add or subtract.
x²-y²


44. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.


45. 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.
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)+
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


46. HIGH: What is a '30:60:90' triangle?
1/x^n For example - 6-² = 1/6² = 1/36
Invert the second fraction (reciprocal) and multiply
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
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.


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

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48. HIGH: Simplify this: v75/v27
40%
V=pr²h (This is just the area multiplied by the height)
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 6 if it'S divisible by BOTH 2 and 3.


49. HIGH: To divide powers with the same base...
3:4:5 5:12:13
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.


50. List two odd behaviors of exponents
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=pr²
A radius
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.