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: How do you calculate the length of an arc?

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2. HIGH: What is the median?
The # falling in the center of an ordered data set
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.7
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


3. HIGH: what is the side ratio for a Right Isosceles triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
x² + 2xy + y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


4. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
40%
Example: 1 < x < 10
Probability A + Probability B
V=s³


5. What number goes on the bottom of a probability fraction?
Example: 1 < x < 10
The total # of possible outcomes.
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.
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.


6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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
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
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.


7. HIGH: To divide powers with the same base...
Multiply numerator times numerator and denominator times denominator.
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.


8. In a coordinate system - what is the origin?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(0 -0)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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


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

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10. If something is certain to happen - how is the probability of this event expressed mathematically?
Probability A * Probability B
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.
1/1
A 90-degree angle.


11. What is the sum of any 'big' angle and any 'Small' angle?
6
180 degrees.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.


12. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
360 degrees
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.
x²-y²


13. Explain how to use an 'Average Pie'
90 degrees each.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 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.


14. HIGH: What is the factored version of x² + 2xy + y² ?
A=pr²
Not reading the problems carefully enough!
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)+
(x+y)²


15. What are 'vertical angles'?
Find the total - or whole - first - and then set up a Ratio Box.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.


16. What degree angle is a line?
A line is a 180-degree angle.
Invert the second fraction (reciprocal) and multiply
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


17. HIGH: Volume of a cylinder?
Favorable Outcomes/Total Possible Outcomes
4 angles are formed. Their sum is 360 degrees
80%
V=pr²h (This is just the area multiplied by the height)


18. An integer is divisible by 9 if...
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 9 if the sum of its digits is divisible by 9.
Invert the second fraction (reciprocal) and multiply
A line is a 180-degree angle.


19. How do you divide fractions?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
40%
360 degrees
Invert the second fraction (reciprocal) and multiply


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

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21. HIGH: Area of a circle
Not reading the problems carefully enough!
1. Given event A: A + notA = 1.
A=pr²
A radius


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

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23. Explain how to divide fractions.
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'.
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.
A line is a 180-degree angle.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


24. HIGH: Describe how to deal with 2 sets of parentheses.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
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)+
Favorable Outcomes/Total Possible Outcomes


25. HIGH: What is the Pythagorean theorem?

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

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27. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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
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'.
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)+


28. How do you calculate the percentage of change?
Invert the second fraction (reciprocal) and multiply
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.
Percentage Change = Difference/Original * 100
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


29. Explain the difference between handling a permutation versus a combination.
(x-y)²
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.
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


30. Explain how to calculate an average (arithmetic mean)
A=pr²
Groups - teams - or committees.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
2


31. If x² = 144 - does v144 = x?
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.
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
Not necessarily. This is a trick question - because x could be either positive or negative.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


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

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33. For a bell curve - what three terms might be used to describe the number in the middle?
6
180 degrees.
The average - mean - median - or mode.
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.


34. How do you calculate the probability of two events in a row? (Probability of A and B)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Probability A * Probability B
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


35. HIGH: What is 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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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
(x-y)²


36. HIGH: What is the order of math operations - and the mnemonic to remember it?
40%
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
2
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.


37. What'S the most important thing to remember about charts you'll see on the GRE?
A radius
S*v2
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.


38. What are the side ratios for a 30:60:90 triangle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Favorable Outcomes/Total Possible Outcomes
3:4:5 5:12:13


39. HIGH: Rough est. of v1 =
Invert the second fraction (reciprocal) and multiply
It will be a great advantage on test day to have your times table memorized from 1 through 15.
1
An integer is divisible by 9 if the sum of its digits is divisible by 9.


40. Area of a parallelogram?
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 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.
40%
Bh


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

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42. Define 'proportionate' values
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.
x² + 2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Example: 1 < x < 10


43. How do you solve a permutation?
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
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees


44. An integer is divisible by 2 if...
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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 2 if its units digit is divisible by 2.


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

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46. Define a factorial of a number - and how it is written.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


47. On the GRE - should you ever assume that diagrams are truthful?
The average - mean - median - or mode.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


48. Diameter of a circle?
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
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
Not reading the problems carefully enough!


49. Explain how to use a 'Rate Pie'
(a+b)(a-b)
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
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


50. Explain the special properties of zero.
2pr -or- pd
1. Given event A: A + notA = 1.
A radius
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.