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GRE Math Rules

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. area of sector of circle
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Always equal - i.e. 9 choose 3 = 9 choose 6
N!/(n-k)!
P(E) + P(F) - P(E and F)

2. (x^a)(y^a)
Always equal - i.e. 9 choose 3 = 9 choose 6
101010
(xy)^a
Base * height

3. (x^a)^b
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N(n-1)(n-2)...(2)(1) = n!
A + B - their intersection
x^ab

4. sum of measures of interior angles of a polygon with n sides
Rules for 2 and three: even and the sum of its digits is divisible by three
2pi*r
(n-2)(180 degrees)
P(E and F) = P(E)P(F)

5. possible combinations of three digits allowing repeats
P(E and F) = P(E)P(F)
101010
At least two congruent sides; the angles opposite these sides are also congruent
Invert the second fraction and multiply them

6. area of a non-right triangle
P(E and F) = P(E)P(F)
1 - 2 - root(3); note that this is half of an equilateral triangle
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
A + B - their intersection

7. sides of isoceles right triangle
(n-2)(180 degrees)
At least two congruent sides; the angles opposite these sides are also congruent
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
1 - 1 - root(2)

8. area of circle
All its interior angles are congruent
Pi * r^2
101010
Last three digits (taken together) are divisible by 8

9. mutually exclusive
1098 etc
Mean of the two middle ones
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
P(E or F) = P(E) + P(F)

10. independence of two events E and F
A list is ordered and can have duplicates
Mean of the two middle ones
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
P(E and F) = P(E)P(F)

11. possible combinations of three digits without allowing repeats
At least two congruent sides; the angles opposite these sides are also congruent
(x^a)/(y^a)
1098 etc
Subtract the mean from each value and divide by the standard deviation

12. hypotenuse
(xy)^a
Side opposite the right angle
x^(a-b) or a/x^(b-a)
1

13. differences between a set and a list
A list is ordered and can have duplicates
Last two digits (taken together) are divisible by 4
Number of outcomes yielding E / number of total outcomes
Sum of its digits is divisible by 3

14. divisible by 4
Last two digits (taken together) are divisible by 4
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Always equal - i.e. 9 choose 3 = 9 choose 6
2pi*r

15. length of arc of circle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Opposite angles formed by two intersecting lines; always congruent
N-2
(x^a)/(y^a)

16. area of trapezoid
1 if decimals - 100 if percents
Last two digits (taken together) are divisible by 4
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

17. standardization/normalization
A list is ordered and can have duplicates
Subtract the mean from each value and divide by the standard deviation
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
|S|

18. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
1 if decimals - 100 if percents
N!/k!(n-k)! which is also denotes as n choose k
The sum of the areas of the six faces: 2(lw + lh + wh)

19. area of parallelogram
N(n-1)(n-2)...(2)(1) = n!
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Base * height
(xy)^a

20. volume of cylinder
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Pi*r^2h
Base * height
A list is ordered and can have duplicates

21. vertical angles
Pi * r^2
Opposite angles formed by two intersecting lines; always congruent
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
The sum of the areas of the six faces: 2(lw + lh + wh)

22. probability that either E or F occur
Three sides congruent - two sides and included angle - two angles and included side
1 - 2 - root(3); note that this is half of an equilateral triangle
N(n-1)(n-2)...(2)(1) = n!
P(E) + P(F) - P(E and F)

23. advantage of median
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Less affected by outliers than the mean
P(E) + P(F) - P(E and F)
P(E and F) = P(E)P(F)

24. divisible by 6
x^ab
Rules for 2 and three: even and the sum of its digits is divisible by three
P(E or F) = P(E) + P(F)
x^(a-b) or a/x^(b-a)

25. area of triangle
1/2 base * height
All its interior angles are congruent
x^(a+b)
|S|

26. divisible by 9
Last three digits (taken together) are divisible by 8
Sum of its digits is divisible by 9
1098 etc
1 - 2 - root(3); note that this is half of an equilateral triangle

27. permutations of n objects taken k at a time (order counts)
2pi*r
Side opposite the right angle
Invert the second fraction and multiply them
N!/(n-k)!

28. difference between normal or population standard deviation and the sample standard deviation
Subtract the mean from each value and divide by the standard deviation
Sum of its digits is divisible by 9
Last two digits (taken together) are divisible by 4
In computing the average squared difference from the mean (taking the root of this is the standard deviation) - divide by n-1 instead of n

29. similar triangles
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

30. circumference of circle
x^ab
Number of outcomes yielding E / number of total outcomes
2pi*r
Base * height

31. how to tell if something is prime
Any line connecting two points on a circle. The diameter is a chord
Last two digits (taken together) are divisible by 4
1 if decimals - 100 if percents
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

32. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
1
P(E and F) = P(E)P(F)
Any line connecting two points on a circle. The diameter is a chord

33. x^0
Pi*r^2h
|S|
1
N(n-1)(n-2)...(2)(1) = n!

34. what'S the median if there are an even number of data points?
x^(a-b) or a/x^(b-a)
All its interior angles are congruent
Mean of the two middle ones
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

35. sum of relative frequencies in a frequency distribution
Mean of the two middle ones
Lwh
1 if decimals - 100 if percents
Three sides congruent - two sides and included angle - two angles and included side

36. divisible by 8
Last three digits (taken together) are divisible by 8
Number of outcomes yielding E / number of total outcomes
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

37. divisible by 11
2pi*r
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
(n-2)(180 degrees)
1098 etc

38. permutations of n different objects
Rules for 2 and three: even and the sum of its digits is divisible by three
N(n-1)(n-2)...(2)(1) = n!
All its interior angles are congruent
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

39. relationship between n choose k and n choose n-k
All its interior angles are congruent
Always equal - i.e. 9 choose 3 = 9 choose 6
N-2
P(E or F) = P(E) + P(F)

40. combinations of n objects taken k at a time (order doesn'T count)
N(n-1)(n-2)...(2)(1) = n!
The sum of the areas of the six faces: 2(lw + lh + wh)
Number of outcomes yielding E / number of total outcomes
N!/k!(n-k)! which is also denotes as n choose k

41. volume of rectangle
Rules for 2 and three: even and the sum of its digits is divisible by three
Lwh
2(pir^2) + 2pirh; the two bases and the side
x^(a+b)

42. chord
Mean of the two middle ones
Any line connecting two points on a circle. The diameter is a chord
N!/(n-k)!
Pi*r^2h

43. how many triangles can a polygon of n sides be divided into?
P(E and F) = P(E)P(F)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
N-2
Pi * r^2

44. (x/y)^a
(x^a)/(y^a)
In computing the average squared difference from the mean (taking the root of this is the standard deviation) - divide by n-1 instead of n
The sum of the areas of the six faces: 2(lw + lh + wh)
Lwh

45. x^-a
N(n-1)(n-2)...(2)(1) = n!
(n-2)(180 degrees)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1/x^a

46. (x^a)(x^b)
x^(a+b)
Pi*r^2h
Mean of the two middle ones
Opposite angles formed by two intersecting lines; always congruent

47. area of rectangle
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
N!/(n-k)!
The sum of the areas of the six faces: 2(lw + lh + wh)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

48. number of elements in set S
A + B - their intersection
|S|
Pi*r^2h
P(E and F) = P(E)P(F)

49. area of cylinder
2pi*r
2(pir^2) + 2pirh; the two bases and the side
Mean of the two middle ones
In computing the average squared difference from the mean (taking the root of this is the standard deviation) - divide by n-1 instead of n

50. regular polygon
x^ab
(x^a)/(y^a)
All its interior angles are congruent
Subtract the mean from each value and divide by the standard deviation