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GRE High Frequency Math Terms

Subjects : gre, math

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 do you calculate the length of an arc?

2. HIGH: To divide powers with the same base...
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%.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

3. HIGH: What is a '30:60:90' triangle?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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'.
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

4. HIGH: What are the percentages for standard deviation?
V=pr²h (This is just the area multiplied by the height)
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

5. What is an 'equilateral' triangle?
Find a common denominator and make equivalent fractions. Then add or subtract.
Arrangements - orders - schedules - or lists.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

7. HIGH: What is the order of math operations - and the mnemonic to remember it?
The value that appears most often in a data set.
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
Arrangements - orders - schedules - or lists.
A triangle in which one of the three interior angles is 90 degrees.

8. Convert to a percentage: 4/5
Find the total - or whole - first - and then set up a Ratio Box.
80%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Bh

9. 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.
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
1. Given event A: A + notA = 1.
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.

10. a² - b² is equal to
(a+b)(a-b)
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%.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(x+y)²

11. What is a 'Right' triangle?
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.
The # falling in the center of an ordered data set
A triangle in which one of the three interior angles is 90 degrees.
Order does matter for a permutation - but does not matter for a combination.

12. On the GRE - should you ever assume that diagrams are truthful?
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Order does matter for a permutation - but does not matter for a combination.
1.7

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

14. Area of a square?
S²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Not necessarily. This is a trick question - because x could be either positive or negative.
Example: 1 < x < 10

15. HIGH: What is the side ratio for a 30:60:90 triangle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A line is a 180-degree angle.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=pr²h (This is just the area multiplied by the height)

16. If x² = 144 - does v144 = x?
An integer is divisible by 2 if its units digit is divisible by 2.
Not necessarily. This is a trick question - because x could be either positive or negative.
2r
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

17. List all the prime numbers that are less than 30:
A=pr²
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
x²-y²

18. How is a range expressed with inequalities?
Example: 1 < x < 10
(x-y)²
Arrangements - orders - schedules - or lists.
An integer is divisible by 2 if its units digit is divisible by 2.

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

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.
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

21. What is the formula to determine probability?
25%
Between 0 and 1.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

22. Explain how to divide fractions.
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

23. Convert to a percentage: 3/5
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.
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 # falling in the center of an ordered data set
60%

24. HIGH: Rough est. of v2 =
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4
x² -2xy + y²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

25. HIGH: Rough est. of v3 =
(x+y)(x-y)
Bh
1.7
1.4

26. What is the 'distributive law'?
Probability A * Probability B
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.
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.
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

27. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
90 degrees each.
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. Explain the special properties of zero.
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 - and greater than the difference between the other two sides.
Find the total - or whole - first - and then set up a Ratio Box.
Find a common denominator and make equivalent fractions. Then add or subtract.

29. Area of a parallelogram?
Bh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Find a common denominator and make equivalent fractions. Then add or subtract.
(a+b)(a-b)

30. Define the range of a set of numbers.
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
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
A radius
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.

31. How many degrees does a circle contain?
A triangle in which one of the three interior angles is 90 degrees.
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.
360 degrees
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

32. HIGH: What is the unfactored version of x²-y² ?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
25%
2pr -or- pd
(x+y)(x-y)

33. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
Not reading the problems carefully enough!
x² + 2xy + y²

34. 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'.
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.
Invert the second fraction (reciprocal) and multiply
A radius

35. HIGH: Area of a circle
1/x^n For example - 6-² = 1/6² = 1/36
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
Percentage Change = Difference/Original * 100
A=pr²

36. HIGH: how do you calculate the surface area of a rectangular box?
360 degrees
The total # of possible outcomes.
The # falling in the center of an ordered data set
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.

37. An integer is divisible by 3 if...
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.
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'.
Favorable Outcomes/Total 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

38. HIGH: What is the unfactored version of (x+y)² ?
1/x^n For example - 6-² = 1/6² = 1/36
x² + 2xy + y²
Percentage Change = Difference/Original * 100
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.

39. What'S the most important thing to remember about charts you'll see on the GRE?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²
An integer is divisible by 2 if its units digit is divisible by 2.
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.

40. HIGH: What is the Pythagorean theorem?

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

42. Explain the difference between handling a permutation versus a combination.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Order does matter for a permutation - but does not matter for a combination.
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.

43. What is the equation for a group problem?
25%
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
Not necessarily. This is a trick question - because x could be either positive or negative.
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. Solve this: v6 * -v6 = ?
6
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.
60%
An integer is divisible by 5 if its units digit is either 0 or 5.

45. HIGH: What is the factored version of x² + 2xy + y² ?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A + Probability B
(x+y)²
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.

46. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Not necessarily. This is a trick question - because x could be either positive or negative.
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
(a+b)(a-b)
90 degrees each.

47. What is the 'Third side' rule for triangles?
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.
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.
x² + 2xy + y²
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.

48. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

49. HIGH: What is the formula for the diagonal of any square?
Order does matter for a permutation - but does not matter for a combination.
S*v2
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

50. HIGH: What is the factored version of (x+y)(x-y) ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x²-y²
A triangle in which one of the three interior angles is 90 degrees.
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