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. How do you divide fractions?
2
Example: 1 < x < 10
Invert the second fraction (reciprocal) and multiply
A triangle in which one of the three interior angles is 90 degrees.


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


3. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2pr -or- pd
A=pr²
6


4. What causes 80% of errors on the math section of the GRE?
Order does matter for a permutation - but does not matter for a combination.
Find the total - or whole - first - and then set up a Ratio Box.
Not reading the problems carefully enough!
Not necessarily. This is a trick question - because x could be either positive or negative.


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

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6. The three interior angles of a triangle add up to...
180 degrees
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
6
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'.


7. For a bell curve - what three terms might be used to describe the number in the middle?
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 average - mean - median - or mode.
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. Given event A: A + notA = 1.


8. a² - b² is equal to
(a+b)(a-b)
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.
(x-y)²
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.


9. Area of a square?
A triangle in which one of the three interior angles is 90 degrees.
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%.
S²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


10. What is the equation for a group problem?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


11. Define the mode of a set of numbers.
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.
Not reading the problems carefully enough!
Groups - teams - or committees.
S²


12. An integer is divisible by 3 if...
V=s³
4 angles are formed. Their sum is 360 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.
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.


13. In a coordinate system - identify the quadrants and describe their location.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees.


14. What are the side ratios for a 30:60:90 triangle?
Probability A + Probability B
25%
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.


15. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Invert the second fraction (reciprocal) and multiply
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.
2pr -or- pd


16. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(0 -0)
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.


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

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

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19. How is a range expressed with inequalities?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Example: 1 < x < 10
1/x^n For example - 6-² = 1/6² = 1/36
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.


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

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21. What is the formula to determine probability?
V=s³
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+b)(a-b)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


22. HIGH: How do you multiply and divide square roots?
Find a common denominator and make equivalent fractions. Then add or subtract.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
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


23. HIGH: Volume of a cube?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
S*v2


24. HIGH: What is the side ratio for a 30:60:90 triangle?
25%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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.


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


26. 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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27. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
6
A radius
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.


28. HIGH: What is the mode?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The value that appears most often in a data set.


29. HIGH: x^-n is equal to
Arrangements - orders - schedules - or lists.
1/x^n For example - 6-² = 1/6² = 1/36
The # falling in the center of an ordered data set
'Big' angles and 'Small' angles.


30. Does order matter for a permutation? How about for a combination?
40%
Order does matter for a permutation - but does not matter for a combination.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
6


31. How do you calculate the percentage of change?
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Percentage Change = Difference/Original * 100


32. Explain the special properties of zero.
(x+y)(x-y)
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 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.
x²-y²


33. Define a factorial of a number - and how it is written.
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.
An integer is divisible by 2 if its units digit is divisible by 2.
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 5 if its units digit is either 0 or 5.


34. HIGH: Define the 'Third side' rule for triangles

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35. HIGH: Volume of a cylinder?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
V=pr²h (This is just the area multiplied by the height)
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.
Multiply numerator times numerator and denominator times denominator.


36. What degree angle is a line?
A line is a 180-degree angle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)²
A triangle in which one of the three interior angles is 90 degrees.


37. Explain how to calculate an average (arithmetic mean)
Probability A * Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


38. Explain how to use an 'Average Pie'
1
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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


39. Convert to a percentage: 2/5
(x+y)(x-y)
40%
Probability A * Probability B
3:4:5 5:12:13


40. The three exterior angles of a triangle add up to...
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
2
360 degrees
Percentage Change = Difference/Original * 100


41. What is the sum of any 'big' angle and any 'Small' angle?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
180 degrees.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


42. HIGH: What is the unfactored version of (x+y)² ?
1
x² + 2xy + y²
180 degrees.
The average - mean - median - or mode.


43. What number goes on the bottom of a probability fraction?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The total # of possible outcomes.
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
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


44. An integer is divisible by 5 if...
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
180 degrees


45. Explain how to solve for 7/¼
A radius
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1.4


46. List two odd behaviors of exponents
A radius
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%.
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.
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.


47. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
1/x^n For example - 6-² = 1/6² = 1/36


48. HIGH: Rough est. of v2 =
1.4
x² -2xy + y²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.


49. v4 =
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
2


50. What kind of triangle is this: has two sides of equal length - and a 90 degree 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.
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.
Order does matter for a permutation - but does not matter for a combination.
Invert the second fraction (reciprocal) and multiply