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: List the two most common side ratios for right triangles
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Probability A + Probability 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.
3:4:5 5:12:13


2. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
(0 -0)
1/1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


3. What degree angle is a line?
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.
(0 -0)
The total # of possible outcomes.
A line is a 180-degree angle.


4. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
The average - mean - median - or mode.
Probability A * Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


5. What do permutation problems often ask for?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
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'.
Arrangements - orders - schedules - or lists.


6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
Invert the second fraction (reciprocal) and multiply


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

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8. How do you multiply fractions?
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
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.
Multiply numerator times numerator and denominator times denominator.


9. 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.
(x+y)²
1. Given event A: A + notA = 1.
2pr -or- pd


10. HIGH: What is the factored version of 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.
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.
1
(x+y)²


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

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12. HIGH: What is the formula for the diagonal of any square?
A radius
S*v2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x²-y²


13. HIGH: What is the Pythagorean theorem?

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14. HIGH: What are the percentages for standard deviation?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
S*v2


15. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
3:4:5 5:12:13
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Order does matter for a permutation - but does not matter for a combination.


16. Explain how to solve for 7/¼
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
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.
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


17. Does order matter for a permutation? How about for a combination?
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


18. What'S the most important thing to remember about charts you'll see on the GRE?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
2pr -or- pd
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.


19. HIGH: Rough est. of v2 =
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.
80%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1.4


20. If x² = 144 - does v144 = x?
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.
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
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
Not necessarily. This is a trick question - because x could be either positive or negative.


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

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22. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
x² + 2xy + y²
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.
60%
4 angles are formed. Their sum is 360 degrees


23. Convert to a percentage: 4/5
1.7
A=pr²
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.
80%


24. How do you solve a combination?

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25. What is the key to dealing with ratio questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Find the total - or whole - first - and then set up a Ratio Box.


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

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27. HIGH: Describe how to deal with 2 sets of parentheses.
4 angles are formed. Their sum is 360 degrees
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.
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
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. An integer is divisible by 9 if...
Favorable Outcomes/Total Possible Outcomes
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
An integer is divisible by 9 if the sum of its digits is divisible by 9.


29. HIGH: What is the unfactored version of (x+y)² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
x² + 2xy + y²
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.


30. If something is possible but not certain - what is the numeric range of probability of it happening?
x² + 2xy + y²
Between 0 and 1.
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.
S²


31. HIGH: What is a 'Right isosceles' triangle?
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.
360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |


32. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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 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.
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.


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


34. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
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
(x-y)²


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

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36. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Probability A * Probability B
'Big' angles and 'Small' angles.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


37. HIGH: What is the median?
The # falling in the center of an ordered data set
6
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.


38. What number goes on the bottom of a probability fraction?
Arrangements - orders - schedules - or lists.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The total # of possible outcomes.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


39. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
x² + 2xy + y²
3:4:5 5:12:13
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


40. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
1/x^n For example - 6-² = 1/6² = 1/36
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.
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.


41. HIGH: Define the formula for calculating slope.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Probability A * Probability B
(x+y)(x-y)


42. 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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43. Diameter of a circle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
2r


44. Area of a square?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² + 2xy + y²
S²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


45. Simplify this: v32
(x+y)(x-y)
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


46. HIGH: Rough est. of v1 =
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1
(x-y)²
Arrangements - orders - schedules - or lists.


47. The three exterior angles of a triangle add up to...
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
360 degrees
Multiply numerator times numerator and denominator times denominator.


48. What is a 'Right' angle?
1/x^n For example - 6-² = 1/6² = 1/36
A 90-degree angle.
V=pr²h (This is just the area multiplied by the height)
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.


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

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50. Define the mode of a set of numbers.
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.
(x-y)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.
A radius