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. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(a+b)(a-b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


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

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3. HIGH: Rough est. of v2 =
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.
1.4
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


4. What is the equation for a group problem?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
A 90-degree angle.
(x+y)²


5. How do you calculate the probability of two events in a row? (Probability of A and B)
The average - mean - median - or mode.
Probability A * Probability B
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.


6. What is a 'Right' triangle?
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.
A triangle in which one of the three interior angles is 90 degrees.
Multiply numerator times numerator and denominator times denominator.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


7. How do you divide fractions?
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
Invert the second fraction (reciprocal) and multiply
A line is a 180-degree angle.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


8. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
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.


9. For a bell curve - what three terms might be used to describe the number in the middle?
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.
Favorable Outcomes/Total Possible Outcomes
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 average - mean - median - or mode.


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

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11. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
(x+y)(x-y)
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.


12. How do you multiply fractions?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V=pr²h (This is just the area multiplied by the height)
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.
Multiply numerator times numerator and denominator times denominator.


13. HIGH: x^-n is equal to
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/x^n For example - 6-² = 1/6² = 1/36


14. What is the formula to determine probability?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
V=pr²h (This is just the area multiplied by the height)
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.


15. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
The value that appears most often in a data set.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
S²


16. What is the sum of any 'big' angle and any 'Small' angle?
25%
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.
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.


17. HIGH: Rough est. of v3 =
An integer is divisible by 9 if the sum of its digits is divisible by 9.
1.7
Arrangements - orders - schedules - or lists.
Probability A + Probability B


18. HIGH: Area of a circle
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
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.
A=pr²


19. If something is certain to happen - how is the probability of this event expressed mathematically?
1.7
Find a common denominator and make equivalent fractions. Then add or subtract.
1/1
The total # of possible outcomes.


20. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
90 degrees each.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4 angles are formed. Their sum is 360 degrees


21. HIGH: How much of your times table should you know - for the GRE?
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.
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%.
360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.


22. HIGH: How do you multiply powers with the same base?
A radius
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


23. List two odd behaviors of exponents
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.
1.4
x² -2xy + y²
360 degrees


24. In a coordinate system - what is the origin?
(0 -0)
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The # falling in the center of an ordered data set


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

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26. The three exterior angles of a triangle add up to...
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Multiply numerator times numerator and denominator times denominator.
360 degrees
Groups - teams - or committees.


27. Explain the difference between handling a permutation versus a combination.
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.
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Multiply numerator times numerator and denominator times denominator.


28. Area of a parallelogram?
(x+y)(x-y)
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Bh


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


30. Simplify this: v32
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.
Probability A * Probability B
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


31. What'S the most important thing to remember about charts you'll see on the GRE?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Between 0 and 1.
2r
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.


32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1. Given event A: A + notA = 1.
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 value that appears most often in a data set.


33. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
360 degrees
x²-y²
S*v2


34. 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
1
Multiply numerator times numerator and denominator times denominator.
V=pr²h (This is just the area multiplied by the height)


35. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
180 degrees.
x² -2xy + y²
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
Probability A + Probability B


36. How many degrees does a circle contain?
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 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.
360 degrees


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

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38. If x² = 144 - does v144 = x?
(x-y)²
Not necessarily. This is a trick question - because x could be either positive or negative.
Order does matter for a permutation - but does not matter for a combination.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


39. Define the mode of a set of numbers.
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
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
1/1
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.


40. HIGH: What are the percentages for standard deviation?
6
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


41. HIGH: What is the median?
Arrangements - orders - schedules - or lists.
90 degrees each.
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 # falling in the center of an ordered data set


42. How is a range expressed with inequalities?
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
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)+
2


43. Convert to a percentage: 1/4
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh
A line is a 180-degree angle.
25%


44. HIGH: To divide powers with the same base...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |


45. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
The average - mean - median - or mode.
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.
'Big' angles and 'Small' angles.


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

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47. What number goes on the bottom of a probability fraction?
Not necessarily. This is a trick question - because x could be either positive or negative.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The total # of possible outcomes.
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)+


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

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49. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4 angles are formed. Their sum is 360 degrees
25%


50. What is a 'Right' angle?
A 90-degree angle.
A radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Invert the second fraction (reciprocal) and multiply