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. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
x² + 2xy + y²
A=pr²
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.


2. If something is certain to happen - how is the probability of this event expressed mathematically?
(x-y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A radius
1/1


3. Simplify this: v32
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.
90 degrees each.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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%.


4. What is an 'equilateral' triangle?
Bh
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.
V=pr²h (This is just the area multiplied by the height)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


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

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6. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(x+y)²
360 degrees
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Probability A + Probability B


7. HIGH: What is a 'Right isosceles' triangle?
Order does matter for a permutation - but does not matter for a combination.
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.
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.
(x-y)²


8. HIGH: What is a '30:60:90' triangle?
A line is a 180-degree angle.
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.
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'.
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


9. HIGH: Simplify this: v75/v27
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
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
Percentage Change = Difference/Original * 100


10. What is a 'Right' angle?
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.
A 90-degree angle.
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.
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'.


11. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Bh
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.


12. Define a factorial of a number - and how it is written.
60%
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.
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
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.


13. What causes 80% of errors on the math section of the GRE?
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
V=s³
x²-y²
Not reading the problems carefully enough!


14. HIGH: What is the unfactored version of x²-y² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
(x+y)(x-y)
(a+b)(a-b)


15. HIGH: Define the formula for calculating slope.
3:4:5 5:12:13
(x+y)(x-y)
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


16. What is the key to dealing with ratio questions?
Example: 1 < x < 10
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.
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
Find the total - or whole - first - and then set up a Ratio Box.


17. a² - b² is equal to
The # falling in the center of an ordered data set
A 90-degree angle.
(x+y)²
(a+b)(a-b)


18. What is the 'Third side' rule for triangles?
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.
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.
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


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


20. Explain how to use a 'Rate Pie'
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
2pr -or- pd
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.
80%


21. HIGH: What is the side ratio 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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


22. HIGH: Rough est. of v3 =
1.7
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.
Between 0 and 1.
An integer is divisible by 2 if its units digit is divisible by 2.


23. What'S the most important thing to remember about charts you'll see on the GRE?
Groups - teams - or committees.
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 line is a 180-degree angle.
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.


24. Explain how to solve for 7/¼
(x+y)(x-y)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
4 angles are formed. Their sum is 360 degrees
1. Given event A: A + notA = 1.


25. For a bell curve - what three terms might be used to describe the number in the middle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1.4
The average - mean - median - or mode.
(a+b)(a-b)


26. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Bh
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2pr -or- pd


27. Convert to a percentage: 3/5
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=pr²
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
60%


28. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
Multiply numerator times numerator and denominator times denominator.
90 degrees each.
40%


29. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2
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.


30. Area of a parallelogram?
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.
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
60%
Bh


31. HIGH: What are the percentages for standard deviation?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.


32. What is the 'distributive law'?
Find a common denominator and make equivalent fractions. Then add or subtract.
60%
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.


33. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
25%
A line is a 180-degree angle.
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.
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.


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

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

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36. What is the factored version of 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.
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.
(x-y)²
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


37. Define the range of a set of numbers.
1
Order does matter for a permutation - but does not matter for a combination.
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.
Arrangements - orders - schedules - or lists.


38. Diameter of a circle?
The total # of possible outcomes.
2r
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.


39. What is the sum of any 'big' angle and any 'Small' angle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)(x-y)
180 degrees.
2pr -or- pd


40. On the GRE - should you ever assume that diagrams are truthful?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1.7
The average - mean - median - or mode.


41. 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)+
A=pr²
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
Arrangements - orders - schedules - or lists.


42. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
90 degrees each.
Arrangements - orders - schedules - or lists.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


43. HIGH: Volume of a cube?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
V=s³
A radius


44. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A radius
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


45. HIGH: Rough est. of v2 =
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1.4
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
(x+y)²


46. How do you solve a combination?

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


48. What degree angle is a line?
A line is a 180-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
V=s³


49. What is the name of a line that extends from the center of a circle to the edge of a circle?
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
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 radius
Percentage Change = Difference/Original * 100


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

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