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. List all the prime numbers that are less than 30:
The value that appears most often in a data set.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


2. How do you add or subtract fractions?
180 degrees.
Find a common denominator and make equivalent fractions. Then add or subtract.
(x+y)(x-y)
It will be a great advantage on test day to have your times table memorized from 1 through 15.


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. HIGH: Define the formula for calculating slope.
S²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A + Probability B
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


5. Define 'proportionate' values
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.7
V=s³
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


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

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7. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
x²-y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


8. HIGH: What is a 'Right isosceles' triangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S*v2
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.
Example: 1 < x < 10


9. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


10. How is a range expressed with inequalities?
S²
Example: 1 < x < 10
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.


11. 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
An integer is divisible by 5 if its units digit is either 0 or 5.
(x+y)²
Favorable Outcomes/Total Possible Outcomes


12. HIGH: To divide powers with the same base...
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 line is a 180-degree angle.
1.7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


13. Define a factorial of a number - and how it is written.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 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
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.
4 angles are formed. Their sum is 360 degrees


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

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15. Convert to a percentage: 4/5
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.
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%.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
80%


16. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
1/1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)


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

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

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19. An integer is divisible by 9 if...
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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


20. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
V=s³
Favorable Outcomes/Total Possible Outcomes
90 degrees each.


21. What is the key to dealing with ratio questions?
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
Find the total - or whole - first - and then set up a Ratio Box.
40%
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.


22. HIGH: What are the percentages for standard deviation?
V=s³
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |


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

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24. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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


25. HIGH: What is the unfactored version of x²-y² ?
A=pr²
(x+y)(x-y)
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


26. 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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Find the total - or whole - first - and then set up a Ratio Box.


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


28. Explain how to divide fractions.
Bh
180 degrees
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1. Given event A: A + notA = 1.


29. HIGH: What is the mode?
'Big' angles and 'Small' angles.
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.
The value that appears most often in a data set.
A line is a 180-degree angle.


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


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

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32. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
4 angles are formed. Their sum is 360 degrees


33. Convert to a percentage: 2/5
40%
The # falling in the center of an ordered data set
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'.
S²


34. HIGH: How do you multiply powers with the same base?
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.
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
Arrangements - orders - schedules - or lists.


35. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
'Big' angles and 'Small' angles.
S*v2
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'.


36. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
Find a common denominator and make equivalent fractions. Then add or subtract.
Order does matter for a permutation - but does not matter for a combination.


37. HIGH: What is the unfactored version of (x-y)² ?
Bh
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
60%
x² -2xy + y²


38. Convert to a percentage: 1/4
25%
Between 0 and 1.
40%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


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

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40. HIGH: What is the order of math operations - and the mnemonic to remember it?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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)+
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.


41. 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.
(x+y)²
(a+b)(a-b)
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.


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

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43. What causes 80% of errors on the math section of the GRE?
25%
Not reading the problems carefully enough!
1/x^n For example - 6-² = 1/6² = 1/36
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


44. HIGH: Rough est. of v1 =
1
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Multiply numerator times numerator and denominator times denominator.
2r


45. Solve this: v6 * -v6 = ?
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.
6
'Big' angles and 'Small' angles.
2r


46. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


47. Diameter of a circle?
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.
90 degrees each.
2r
The value that appears most often in a data set.


48. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A triangle in which one of the three interior angles is 90 degrees.
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%.
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.


49. Probability Formula
180 degrees
A 90-degree angle.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Favorable Outcomes/Total Possible Outcomes


50. What is the name of a line that extends from the center of a circle to the edge of a circle?
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
Example: 1 < x < 10
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A radius