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: What numbers does ETS hope you'll forget to consider - for quant comp questions?
180 degrees
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


2. a² - b² is equal to
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 5 if its units digit is either 0 or 5.
(a+b)(a-b)


3. What degree angle is a line?
A line is a 180-degree angle.
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.
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'.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


4. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


5. In a coordinate system - what is the origin?
x²-y²
(0 -0)
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


6. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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 radius


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


8. Explain the difference between handling a permutation versus a combination.
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
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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. If something is possible but not certain - what is the numeric range of probability of it happening?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
S²
(x+y)(x-y)
Between 0 and 1.


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

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11. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
1.4
25%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S*v2


12. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
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
The average - mean - median - or mode.


13. How many degrees does a circle contain?
4 angles are formed. Their sum is 360 degrees
360 degrees
1.4
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.


14. Define the range of a set of numbers.
40%
The value that appears most often in a data set.
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


15. Convert to a percentage: 4/5
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
80%
1.7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


16. What is the key to dealing with ratio questions?
2pr -or- pd
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find the total - or whole - first - and then set up a Ratio Box.
90 degrees each.


17. What is the formula to determine probability?
V=pr²h (This is just the area multiplied by the height)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
'Big' angles and 'Small' angles.
Multiply numerator times numerator and denominator times denominator.


18. Define the mode of a set of numbers.
Invert the second fraction (reciprocal) and multiply
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%
Bh


19. What is the 'distributive law'?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
Invert the second fraction (reciprocal) and multiply
(x-y)²


20. Define a factorial of a number - and how it is written.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.


21. HIGH: Rough est. of v1 =
Example: 1 < x < 10
1
(x-y)²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


22. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
6
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.
Find a common denominator and make equivalent fractions. Then add or subtract.


23. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(x+y)(x-y)
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
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.
x² + 2xy + y²


24. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
Arrangements - orders - schedules - or lists.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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


25. Convert to a percentage: 3/5
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.
60%
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
(x-y)²


26. How is a range expressed with inequalities?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
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


27. HIGH: Define the formula for calculating slope.
(x-y)²
S*v2
Order does matter for a permutation - but does not matter for a combination.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


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

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29. What do combination problems usually ask for?
Groups - teams - or committees.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V=pr²h (This is just the area multiplied by the height)


30. 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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31. Does order matter for a permutation? How about for a combination?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
180 degrees.
Order does matter for a permutation - but does not matter for a combination.
2pr -or- pd


32. Explain how to divide fractions.
180 degrees.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


33. What is a 'Right' angle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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 90-degree angle.
V=s³


34. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
1/1
A triangle in which one of the three interior angles is 90 degrees.


35. What is the 'Third side' rule for triangles?
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
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.
A=pr²
Favorable Outcomes/Total Possible Outcomes


36. How do you divide fractions?
Order does matter for a permutation - but does not matter for a combination.
Multiply numerator times numerator and denominator times denominator.
2r
Invert the second fraction (reciprocal) and multiply


37. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(0 -0)
Multiply numerator times numerator and denominator times denominator.
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.


38. 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 - and greater than the difference between the other two sides.
Find a common denominator and make equivalent fractions. Then add or subtract.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
It will be a great advantage on test day to have your times table memorized from 1 through 15.


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

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40. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
(0 -0)
Probability A + Probability B
An integer is divisible by 9 if the sum of its digits is divisible by 9.


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

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42. The three interior angles of a triangle add up to...
180 degrees
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


43. HIGH: How do you multiply and divide square roots?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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%.
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.


44. Convert to a percentage: 1/4
Find the total - or whole - first - and then set up a Ratio Box.
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.
25%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


45. What'S the most important thing to remember about charts you'll see on the GRE?
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.
The value that appears most often in a data set.
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.


46. 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 triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A + Probability B


47. HIGH: What is the Pythagorean theorem?

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48. What are the side ratios for a 30:60:90 triangle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2pr -or- pd
An integer is divisible by 2 if its units digit is divisible by 2.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


49. HIGH: What is the unfactored version of (x-y)² ?
6
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.
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.
x² -2xy + y²


50. HIGH: Describe how to deal with 2 sets of parentheses.
S*v2
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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)+
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.