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: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Between 0 and 1.
The # falling in the center of an ordered data set
Find a common denominator and make equivalent fractions. Then add or subtract.


2. What is the 'Third side' rule for triangles?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


3. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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. 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.
Find the total - or whole - first - and then set up a Ratio Box.


4. Explain how to use an 'Average Pie'
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.
Invert the second fraction (reciprocal) and multiply
V=s³


5. What do combination problems usually ask for?
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.
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
Groups - teams - or committees.
4 angles are formed. Their sum is 360 degrees


6. What is the factored version of x² -2xy + y² ?
'Big' angles and 'Small' angles.
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'.
(x-y)²
A 90-degree angle.


7. HIGH: What is the unfactored version of x²-y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)(x-y)
Not necessarily. This is a trick question - because x could be either positive or negative.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


8. HIGH: What is the unfactored version of (x+y)² ?
Invert the second fraction (reciprocal) and multiply
(x+y)(x-y)
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


9. Convert to a percentage: 4/5
Bh
80%
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.


10. a² - b² is equal to
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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+b)(a-b)


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

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12. Explain the special properties of zero.
Probability A + Probability B
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.
S*v2
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


13. Explain how to solve for 7/¼
Favorable Outcomes/Total Possible Outcomes
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Order does matter for a permutation - but does not matter for a combination.


14. Define 'proportionate' values
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
x² + 2xy + y²


15. HIGH: What is the unfactored version of (x-y)² ?
V=pr²h (This is just the area multiplied by the height)
1. Given event A: A + notA = 1.
x² -2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


16. What do permutation problems often ask for?
1.7
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%.
Example: 1 < x < 10
Arrangements - orders - schedules - or lists.


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

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18. HIGH: List the two most common side ratios for right triangles
A line is a 180-degree angle.
3:4:5 5:12:13
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


19. What is the name of a line that extends from the center of a circle to the edge of a circle?
Invert the second fraction (reciprocal) and multiply
Groups - teams - or committees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
A radius


20. HIGH: Rough est. of v3 =
Not necessarily. This is a trick question - because x could be either positive or negative.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
1.7


21. What is the sum of any 'big' angle and any 'Small' angle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
180 degrees.
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.


22. An integer is divisible by 2 if...
80%
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 2 if its units digit is divisible by 2.


23. What is a 'Right' triangle?
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.
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A triangle in which one of the three interior angles is 90 degrees.


24. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/1
Find the total - or whole - first - and then set up a Ratio Box.
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.


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

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26. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Arrangements - orders - schedules - or lists.
Probability A * Probability B


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


28. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Multiply numerator times numerator and denominator times denominator.
Between 0 and 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.


29. HIGH: What is a '30:60:90' triangle?
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
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
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


30. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
25%


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

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

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33. How many degrees does a circle contain?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
360 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S²


34. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.
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


35. HIGH: Area of a circle
An integer is divisible by 2 if its units digit is divisible by 2.
A=pr²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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


36. How do you add or subtract fractions?
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
S*v2
Find a common denominator and make equivalent fractions. Then add or subtract.
1


37. How is a range expressed with inequalities?
V=pr²h (This is just the area multiplied by the height)
Example: 1 < x < 10
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
The total # of possible outcomes.


38. List two odd behaviors of exponents
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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.
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.
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


39. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The value that appears most often in a data set.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 2 if its units digit is divisible by 2.


40. What is the 'distributive law'?
180 degrees
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.
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.
(x+y)²


41. HIGH: What is the factored version of (x+y)(x-y) ?
Favorable Outcomes/Total Possible Outcomes
x²-y²
The total # of possible outcomes.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


42. What is a 'Right' angle?
S²
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
A 90-degree angle.


43. HIGH: Rough est. of v2 =
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Example: 1 < x < 10
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1.4


44. In a coordinate system - what is the origin?
(0 -0)
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%.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.


45. Explain the difference between handling a permutation versus a combination.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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'.
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.
2pr -or- pd


46. If something is certain to happen - how is the probability of this event expressed mathematically?
60%
1/1
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


47. What'S the most important thing to remember about charts you'll see on the GRE?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
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.
Bh


48. What degree angle is a line?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A line is a 180-degree angle.
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.
Percentage Change = Difference/Original * 100


49. HIGH: What is the factored version of x² + 2xy + y² ?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x+y)²
360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


50. Probability Formula
x²-y²
360 degrees
Favorable Outcomes/Total Possible Outcomes
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.