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: Simplify this: v75/v27
4 angles are formed. Their sum is 360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
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 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. What is the 'distributive law'?
1.4
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.
The total # of possible outcomes.
S*v2


3. Diameter of a circle?
A radius
A=pr²
2r
S²


4. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
2
The value that appears most often in a data set.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


5. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
Find the total - or whole - first - and then set up a Ratio Box.
An integer is divisible by 2 if its units digit is divisible by 2.
Bh


6. Explain how to divide fractions.
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.
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)+
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
2r


7. HIGH: What is the mode?
S²
The value that appears most often in a data set.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


8. What are the side ratios for a 30:60:90 triangle?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
6


9. Area of a square?
S²
The average - mean - median - or mode.
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 9 if the sum of its digits is divisible by 9.


10. 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.
A=pr²
x² -2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


11. Area of a parallelogram?
Bh
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
2


12. What number goes on the bottom of a probability fraction?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
The total # of possible outcomes.
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
Not reading the problems carefully enough!


13. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
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.
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.
180 degrees


14. HIGH: Rough est. of v3 =
Not necessarily. This is a trick question - because x could be either positive or negative.
1.7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
40%


15. HIGH: what is the side ratio for a Right Isosceles triangle?
40%
3:4:5 5:12:13
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Example: 1 < x < 10


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

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17. Convert to a percentage: 2/5
40%
Multiply numerator times numerator and denominator times denominator.
V=pr²h (This is just the area multiplied by the height)
S*v2


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

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19. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.


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

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21. HIGH: How do you calculate the circumference of a circle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pr -or- pd
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


22. List two odd behaviors of exponents
180 degrees
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.
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
Probability A + Probability B


23. HIGH: What is the order of math operations - and the mnemonic to remember it?
1.4
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'.
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.
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


24. HIGH: What is the factored version of (x+y)(x-y) ?
Bh
90 degrees each.
180 degrees
x²-y²


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

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26. Define the mode of a set of numbers.
A 90-degree angle.
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.
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 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.


27. HIGH: Rough est. of v1 =
(a+b)(a-b)
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%.
2pr -or- pd
1


28. 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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29. For a bell curve - what three terms might be used to describe the number in the middle?
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'.
The average - mean - median - or mode.
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
1.7


30. Define a factorial of a number - and how it is written.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
4 angles are formed. Their sum is 360 degrees
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.


31. An integer is divisible by 4 if...

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32. Does order matter for a permutation? How about for a combination?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Order does matter for a permutation - but does not matter for a combination.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
40%


33. What do combination problems usually ask for?
Groups - teams - or committees.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A radius


34. Define the range of a set of numbers.
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.
3:4:5 5:12:13
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


35. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp 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
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.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


36. HIGH: How much of your times table should you know - for the GRE?
180 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The total # of possible outcomes.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


37. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
6
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.
40%
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


38. What is the equation for a group problem?
90 degrees each.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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
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


39. What is the key to dealing with ratio questions?
Find a common denominator and make equivalent fractions. Then add or subtract.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


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

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41. a² - b² is equal to
x² -2xy + y²
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(a+b)(a-b)


42. What is the factored version of x² -2xy + y² ?
'Big' angles and 'Small' angles.
(x-y)²
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.


43. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Bh
A line is a 180-degree angle.
Groups - teams - or committees.
90 degrees each.


44. HIGH: Explain the process to solve '56 is what percent of 80?'

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45. Explain how to solve for 7/¼
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
x² -2xy + y²


46. What do permutation problems often ask for?
40%
1/x^n For example - 6-² = 1/6² = 1/36
Arrangements - orders - schedules - or lists.
Probability A * Probability B


47. HIGH: What is the factored version of x² + 2xy + y² ?
An integer is divisible by 5 if its units digit is either 0 or 5.
(x+y)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.


48. HIGH: Define the formula for calculating slope.
40%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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 line is a 180-degree angle.


49. What'S the most important thing to remember about charts you'll see on the GRE?
180 degrees
(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.
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.


50. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Order does matter for a permutation - but does not matter for a combination.
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.
V=s³