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 unfactored version of (x+y)² ?
1. Given event A: A + notA = 1.
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.
Groups - teams - or committees.
x² + 2xy + y²


2. HIGH: What is the formula for the diagonal of any square?
Favorable Outcomes/Total Possible Outcomes
S*v2
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


3. Explain how to calculate an average (arithmetic mean)
Probability A * Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
(x+y)²


4. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
(a+b)(a-b)
90 degrees each.
A triangle in which one of the three interior angles is 90 degrees.
Not necessarily. This is a trick question - because x could be either positive or negative.


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


6. How is a range expressed with inequalities?
Example: 1 < x < 10
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


7. Convert to a percentage: 1/4
x² -2xy + y²
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'.
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.
25%


8. How many degrees does a circle contain?
360 degrees
180 degrees
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.
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.


9. HIGH: x^-n is equal to
S*v2
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.
1/x^n For example - 6-² = 1/6² = 1/36
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


10. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
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.
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.


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

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12. The three interior angles of a triangle add up to...
180 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1/x^n For example - 6-² = 1/6² = 1/36
(x+y)²


13. HIGH: What is the Pythagorean theorem?

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14. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S²
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.


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

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16. How do you solve a combination?

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17. HIGH: Area of a triangle?
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. 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
80%
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


18. Define a factorial of a number - and how it is written.
1. Given event A: A + notA = 1.
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.
x² -2xy + y²
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. HIGH: Rough est. of v3 =
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.7


20. HIGH: How do you multiply powers with the same base?
x² + 2xy + y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Bh
Not reading the problems carefully enough!


21. How do you multiply fractions?
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.
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.
The value that appears most often in a data set.


22. What is a 'Right' angle?
A 90-degree angle.
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
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.
Multiply numerator times numerator and denominator times denominator.


23. If something is certain to happen - how is the probability of this event expressed mathematically?
25%
1/1
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


24. HIGH: What is the mode?
'Big' angles and 'Small' angles.
180 degrees.
The value that appears most often in a data set.
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.


25. How do you calculate the probability of two events in a row? (Probability of A and B)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Invert the second fraction (reciprocal) and multiply
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Probability A * Probability B


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

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27. What causes 80% of errors on the math section of the GRE?
(0 -0)
x² + 2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Not reading the problems carefully enough!


28. HIGH: What is the factored version of (x+y)(x-y) ?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1.4
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
x²-y²


29. The three exterior angles of a triangle add up to...
Not necessarily. This is a trick question - because x could be either positive or negative.
360 degrees
'Big' angles and 'Small' angles.
4 angles are formed. Their sum is 360 degrees


30. HIGH: What must be true before a quadratic equation can be solved?

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31. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
4 angles are formed. Their sum is 360 degrees
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.


32. HIGH: Define the formula for calculating slope.
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.
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.
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.


33. 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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34. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Probability A + Probability B
A 90-degree angle.


35. What is the 'Third side' rule for triangles?
(x+y)(x-y)
2
(a+b)(a-b)
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.


36. In a coordinate system - what is the origin?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)
The value that appears most often in a data set.


37. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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
The # falling in the center of an ordered data set
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.


38. What is the sum of any 'big' angle and any 'Small' angle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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
180 degrees.


39. How do you solve a permutation?
Groups - teams - or committees.
1/x^n For example - 6-² = 1/6² = 1/36
Probability A + Probability B
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


40. HIGH: Area of a circle
180 degrees
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)+
A=pr²
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. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

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42. Explain how to divide fractions.
Order does matter for a permutation - but does not matter for a combination.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


43. Define the mode of a set of numbers.
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.
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
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


44. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Groups - teams - or committees.
80%
6


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

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46. Probability Formula
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
Favorable Outcomes/Total Possible Outcomes
A 90-degree angle.
(a+b)(a-b)


47. What is the equation for a group problem?
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
90 degrees each.
(a+b)(a-b)
Probability A * Probability B


48. HIGH: What is the unfactored version of x²-y² ?
S²
A 90-degree angle.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(x+y)(x-y)


49. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7
V=pr²h (This is just the area multiplied by the height)
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. HIGH: Volume of a cylinder?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V=pr²h (This is just the area multiplied by the height)
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.
1.4