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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. a - b is equal to
For RIGHT triangles only: c = a + b 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(a+b)(a-b)
1. Given event A: A + notA = 1.
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. How do you add or subtract 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'.
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.
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.

3. Explain the difference between a digit and a number.
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.
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.
The average - mean - median - or mode.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

4. List two odd behaviors of exponents
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)+
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2) = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.

5. HIGH: Simplify this: v75/v27
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.
S*v2
A radius
For RIGHT triangles only: c = a + b 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Invert the second fraction (reciprocal) and multiply

7. HIGH: What must be true before a quadratic equation can be solved?
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

8. If something is possible but not certain - what is the numeric range of probability of it happening?
(x+y)(x-y)
Between 0 and 1.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

9. HIGH: What is a '30:60:90' triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)(x-y)
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 formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.

10. HIGH: What are the percentages for standard deviation?
Not necessarily. This is a trick question - because x could be either positive or negative.
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

11. What is the 'Third side' rule for triangles?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
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.
360 degrees

12. HIGH: What is the order of math operations - and the mnemonic to remember it?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 4/5 = 2/3 * 5/4
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(x-y)
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

13. Explain the special properties of zero.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
180 degrees.
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
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
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.

15. Explain the difference between handling a permutation versus a combination.
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
360 degrees
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.
A line is a 180-degree angle.

16. Convert to a percentage: 4/5
The total # of possible outcomes.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
80%

17. An integer is divisible by 6 if...
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.

18. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

19. What is the sum of any 'big' angle and any 'Small' angle?
x -2xy + y
180 degrees.
S
1. Given event A: A + notA = 1.

20. 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.
The average - mean - median - or mode.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y
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.

21. What is the equation for a group problem?
Find a common denominator and make equivalent fractions. Then add or subtract.
2r
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
(x+y)

22. Simplify this: v32
A line is a 180-degree angle.
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

23. The three interior angles of a triangle add up to...
180 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.
Percentage Change = Difference/Original * 100
An integer is divisible by 5 if its units digit is either 0 or 5.

24. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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

25. HIGH: List the two most common side ratios for right triangles
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.
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.
180 degrees
3:4:5 5:12:13

26. What is the factored version of x -2xy + y ?
(x-y)
x -2xy + y
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.
Find the total - or whole - first - and then set up a Ratio Box.

27. What is an 'equilateral' triangle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The # falling in the center of an ordered data set
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

28. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?
Not necessarily. This is a trick question - because x could be either positive or negative.
3:4:5 5:12:13
'Big' angles and 'Small' angles.
The average - mean - median - or mode.

29. HIGH: What is the Pythagorean theorem?
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
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.
For RIGHT triangles only: c = a + b 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.

30. HIGH: Rough est. of v2 =
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1.4
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2) = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.

31. HIGH: What is the mode?
For RIGHT triangles only: c = a + b 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2) = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.
The value that appears most often in a data set.
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.

32. HIGH: Rough est. of v3 =
40%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/x^n For example - 6- = 1/6 = 1/36
1.7

33. What is the formula to determine probability?
Percentage Change = Difference/Original * 100
(# of possible outcomes that satisfy the condition) (total # of possible outcomes)
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.
Between 0 and 1.

34. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
1. Given event A: A + notA = 1.
1/1
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

35. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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.
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
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

36. Probability Formula
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Favorable Outcomes/Total Possible Outcomes
x + 2xy + y

37. How do you calculate the percentage of change?
x-y
Not necessarily. This is a trick question - because x could be either positive or negative.
Percentage Change = Difference/Original * 100
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

38. An integer is divisible by 3 if...
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
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.
180 degrees

39. An integer is divisible by 5 if...
360 degrees
Find the total - or whole - first - and then set up a Ratio Box.
An integer is divisible by 5 if its units digit is either 0 or 5.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

40. HIGH: What is a 'Right isosceles' triangle?
A radius
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.
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.
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.

41. HIGH: Explain the process to solve '56 is what percent of 80?'
(0 -0)
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%.
360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.

42. What is the name of a line that extends from the center of a circle to the edge of a circle?
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
A radius

43. Diameter of a circle?
2r
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
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'.

44. What number goes on the bottom of a probability fraction?
Between 0 and 1.
V=prh (This is just the area multiplied by the height)
The total # of possible outcomes.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

45. For a bell curve - what three terms might be used to describe the number in the middle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
90 degrees each.
The average - mean - median - or mode.
(x+y)

46. What do combination problems usually ask for?
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)+
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
Groups - teams - or committees.

47. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Arrangements - orders - schedules - or lists.
A 90-degree angle.
Probability A + Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

48. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
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.
Percentage Change = Difference/Original * 100
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
60%

49. Define the range of a set of numbers.
(x+y)(x-y)
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
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.
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

50. HIGH: What is the factored version of (x+y)(x-y) ?
Percentage Change = Difference/Original * 100
(x-y)
x-y
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

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