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. Define the mode of a set of numbers.
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.
The value that appears most often in a data set.
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 radius


2. How is a range expressed with inequalities?
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Invert the second fraction (reciprocal) and multiply
Example: 1 < x < 10


3. 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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4. 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.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


5. What is the equation for a group problem?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
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
1


6. Define the range of a set of numbers.
1.7
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 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.
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.


7. HIGH: how do you calculate the surface area of a rectangular box?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
180 degrees
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 line is a 180-degree angle.


8. An integer is divisible by 2 if...
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Find a common denominator and make equivalent fractions. Then add or subtract.
40%
An integer is divisible by 2 if its units digit is divisible by 2.


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


10. HIGH: What is a 'Right isosceles' triangle?
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


11. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
x² + 2xy + y²
60%
Probability A + Probability B
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.


12. 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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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


13. HIGH: What is the median?
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
(a+b)(a-b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


14. Diameter of a circle?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
(0 -0)
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
2r


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

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

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17. Define 'proportionate' values
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


18. Simplify this: v32
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.
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=pr²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


19. HIGH: What is the unfactored version of (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.
x² + 2xy + y²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2r


20. HIGH: Rough est. of v1 =
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
2r
1
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


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

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22. HIGH: What is the mode?
The value that appears most often in a data set.
A line is a 180-degree angle.
Arrangements - orders - schedules - or lists.
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.


23. HIGH: Simplify this: v75/v27
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Bh
80%
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.


24. What'S one way to avoid mistakes on algebra questions in the GRE?

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25. What is a 'Right' angle?
x² + 2xy + y²
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.
A 90-degree angle.
Favorable Outcomes/Total Possible Outcomes


26. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
(x+y)(x-y)
4 angles are formed. Their sum is 360 degrees


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

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28. Explain the difference between a digit and a number.

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29. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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
Multiply numerator times numerator and denominator times denominator.
(0 -0)


30. HIGH: Volume of a cylinder?
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
An integer is divisible by 2 if its units digit is divisible by 2.
'Big' angles and 'Small' angles.
V=pr²h (This is just the area multiplied by the height)


31. HIGH: What are the percentages for standard deviation?
(0 -0)
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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.
Groups - teams - or committees.


32. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
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.
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.


33. HIGH: Volume of a cube?
V=s³
(x+y)²
A radius
360 degrees


34. What are the side ratios for a 30:60:90 triangle?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
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.


35. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
x²-y²
(a+b)(a-b)


36. What is the sum of any 'big' angle and any 'Small' angle?
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.
Order does matter for a permutation - but does not matter for a combination.
180 degrees.
60%


37. HIGH: What is the order of math operations - and the mnemonic to remember it?
360 degrees
S²
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
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


38. HIGH: Area of a circle
A=pr²
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
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.
4 angles are formed. Their sum is 360 degrees


39. The three exterior angles of a triangle add up to...
Find a common denominator and make equivalent fractions. Then add or subtract.
360 degrees
Percentage Change = Difference/Original * 100
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


40. Explain the difference between handling a permutation versus a combination.
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.
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.
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)+
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.


41. Area of a square?
x²-y²
S²
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.
Bh


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

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43. HIGH: Rough est. of v2 =
The average - mean - median - or mode.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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)+
1.4


44. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
Favorable Outcomes/Total Possible Outcomes
(x+y)²
3:4:5 5:12:13


45. How many degrees does a circle contain?
360 degrees
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
90 degrees each.


46. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S²


47. How do you calculate the probability of two events in a row? (Probability of A and B)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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


48. HIGH: What is the Pythagorean theorem?

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49. HIGH: Rough est. of v3 =
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1.7
Order does matter for a permutation - but does not matter for a combination.


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

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