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 is the side ratio for a Right Isosceles triangle?
3:4:5 5:12:13
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
'Big' angles and 'Small' angles.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


2. What is the equation for a group problem?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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 9 if the sum of its digits is divisible by 9.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


3. HIGH: List the two most common side ratios for right triangles
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)+
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
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
3:4:5 5:12:13


4. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
360 degrees
Probability A + Probability B
40%
A radius


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


6. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


7. What is the sum of any 'big' angle and any 'Small' angle?
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.
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
2
180 degrees.


8. What is the name of a line that extends from the center of a circle to the edge of a circle?
Invert the second fraction (reciprocal) and multiply
A radius
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
6


9. How do you solve a combination?

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10. HIGH: Volume of a cube?
Multiply numerator times numerator and denominator times denominator.
(0 -0)
The average - mean - median - or mode.
V=s³


11. HIGH: Area of a circle
S*v2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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


12. Simplify this: v32
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² -2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


13. For a bell curve - what three terms might be used to describe the number in the middle?
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 average - mean - median - or mode.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Example: 1 < x < 10


14. What is the factored version of x² -2xy + y² ?
(x-y)²
A radius
The # falling in the center of an ordered data set
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.


15. Explain how to solve for 7/¼
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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


16. What are the side ratios for a 30:60:90 triangle?
Not necessarily. This is a trick question - because x could be either positive or negative.
Multiply numerator times numerator and denominator times denominator.
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.


17. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
S²
A 90-degree angle.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


18. In a coordinate system - what is the origin?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(0 -0)
60%
The value that appears most often in a data set.


19. HIGH: x^-n is equal to
Not necessarily. This is a trick question - because x could be either positive or negative.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/x^n For example - 6-² = 1/6² = 1/36
Arrangements - orders - schedules - or lists.


20. HIGH: How do you multiply and divide square roots?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
'Big' angles and 'Small' angles.


21. Solve this: v6 * -v6 = ?
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%.
6
360 degrees
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


22. What are 'vertical angles'?
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
An integer is divisible by 2 if its units digit is divisible by 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


23. Convert to a percentage: 4/5
1
S²
Invert the second fraction (reciprocal) and multiply
80%


24. Define a factorial of a number - and how it is written.
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.
25%
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.


25. HIGH: What is the side ratio for a 30:60:90 triangle?
1.4
360 degrees
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


26. The three exterior angles of a triangle add up to...
The # falling in the center of an ordered data set
x² -2xy + y²
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.
360 degrees


27. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1/x^n For example - 6-² = 1/6² = 1/36
Groups - teams - or committees.
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'.


28. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Multiply numerator times numerator and denominator times denominator.
1/1


29. HIGH: What is a 'Right isosceles' triangle?
A=pr²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Bh
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.


30. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
25%
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.
Invert the second fraction (reciprocal) and multiply


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

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32. HIGH: What is the Pythagorean theorem?

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33. HIGH: how do you calculate the surface area of a rectangular box?
1/x^n For example - 6-² = 1/6² = 1/36
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


34. Explain the difference between handling a permutation versus a combination.
1
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 2 if its units digit is divisible by 2.
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.


35. Area of a square?
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
S²


36. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
360 degrees


37. How is a range expressed with inequalities?
Example: 1 < x < 10
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%.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


38. What do combination problems usually ask for?
V=pr²h (This is just the area multiplied by the height)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
V=s³
Groups - teams - or committees.


39. What number goes on the bottom of a probability fraction?
1/x^n For example - 6-² = 1/6² = 1/36
The total # of possible outcomes.
40%
Multiply numerator times numerator and denominator times denominator.


40. How do you divide fractions?
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'.
360 degrees
Invert the second fraction (reciprocal) and multiply
An integer is divisible by 2 if its units digit is divisible by 2.


41. HIGH: What is the unfactored version of (x+y)² ?
Between 0 and 1.
1.4
x² + 2xy + y²
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)+


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

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43. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
360 degrees
90 degrees each.
x²-y²
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.


44. What is the 'distributive law'?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


45. 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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46. 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
6
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1.4


47. HIGH: What is the unfactored version of (x-y)² ?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
x² -2xy + y²
(0 -0)
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.


48. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(x+y)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.


49. What is a 'Right' angle?
A 90-degree angle.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


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

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