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: How much of your times table should you know - for the GRE?
6
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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


2. Area of a square?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
S²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
S*v2


3. What is the formula to determine probability?
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.
4 angles are formed. Their sum is 360 degrees
V=pr²h (This is just the area multiplied by the height)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


4. List all the prime numbers that are less than 30:
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


5. HIGH: How do you multiply and divide square roots?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Invert the second fraction (reciprocal) and multiply
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


6. List two odd behaviors of exponents
The total # of possible outcomes.
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.
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.
1/x^n For example - 6-² = 1/6² = 1/36


7. What is the equation for a group problem?
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 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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


8. What are the side ratios for a 30:60:90 triangle?
Order does matter for a permutation - but does not matter for a combination.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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'.
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.


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

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10. Explain how to use a 'Rate Pie'
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.
25%
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


11. Explain how to divide fractions.
Invert the second fraction (reciprocal) and multiply
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')
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


12. If x² = 144 - does v144 = x?
A radius
Not reading the problems carefully enough!
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Not necessarily. This is a trick question - because x could be either positive or negative.


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

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14. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
Favorable Outcomes/Total Possible Outcomes
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.
4 angles are formed. Their sum is 360 degrees


15. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The # falling in the center of an ordered data set
1


16. How do you calculate the probability of two events in a row? (Probability of A and B)
A=pr²
(a+b)(a-b)
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.
Probability A * Probability B


17. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


18. What is the name of a line that extends from the center of a circle to the edge of a circle?
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A radius


19. Probability Formula
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.
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Favorable Outcomes/Total Possible Outcomes


20. HIGH: how do you calculate the surface area of a rectangular box?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


21. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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
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.
360 degrees


22. How do you add or subtract fractions?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Find a common denominator and make equivalent fractions. Then add or subtract.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


23. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


24. 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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Find a common denominator and make equivalent fractions. Then add or subtract.
1. Given event A: A + notA = 1.


25. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Multiply numerator times numerator and denominator times denominator.
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
An integer is divisible by 2 if its units digit is divisible by 2.
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


26. Explain how to solve for 7/¼
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²
2


27. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
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.
S²
Bh


28. HIGH: Volume of a cube?
V=s³
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.
Find the total - or whole - first - and then set up a Ratio Box.
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.


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

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30. HIGH: How do you calculate the length of an arc?

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31. In a coordinate system - identify the quadrants and describe their location.
90 degrees each.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
60%


32. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Probability A + Probability B
1.4


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

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


35. What is the sum of any 'big' angle and any 'Small' angle?
1/1
180 degrees.
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
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


36. What'S one way to avoid mistakes on algebra questions in the GRE?

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

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38. v4 =
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.
Multiply numerator times numerator and denominator times denominator.
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'.
2


39. Simplify this: v32
1.7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


40. HIGH: Rough est. of v1 =
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 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.
1
Bh


41. What degree angle is a line?
180 degrees
A line is a 180-degree angle.
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.
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.


42. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
Between 0 and 1.


43. HIGH: What is the mode?
2pr -or- pd
V=pr²h (This is just the area multiplied by the height)
Percentage Change = Difference/Original * 100
The value that appears most often in a data set.


44. HIGH: What is a '30:60:90' triangle?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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
(x+y)²


45. What is the 'distributive law'?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
'Big' angles and 'Small' angles.


46. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
x² -2xy + y²
180 degrees
90 degrees each.
(x-y)²


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

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48. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
40%
S*v2
6
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


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

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50. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
40%