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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. independence of two events E and F
P(E and F) = P(E)P(F)
1
P(E) + P(F) - P(E and F)
Pi * r^2

2. area of rectangle
The sum of the areas of the six faces: 2(lw + lh + wh)
All its interior angles are congruent
(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

3. circumference of circle
A list is ordered and can have duplicates
P(E and F) = P(E)P(F)
2pi*r
Last three digits (taken together) are divisible by 8

4. divisible by 9
101010
N-2
Number of outcomes yielding E / number of total outcomes
Sum of its digits is divisible by 9

5. area of trapezoid
P(E and F) = P(E)P(F)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Opposite angles formed by two intersecting lines; always congruent
P(E or F) = P(E) + P(F)

6. (x/y)^a
1/2 base * height
(x^a)/(y^a)
Number of outcomes yielding E / number of total outcomes
1 - 1 - root(2)

7. probability that either E or F occur
2(pir^2) + 2pirh; the two bases and the side
P(E) + P(F) - P(E and F)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
A + B - their intersection

8. sum of measures of interior angles of a polygon with n sides
The sum of the areas of the six faces: 2(lw + lh + wh)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
(n-2)(180 degrees)
Opposite angles formed by two intersecting lines; always congruent

9. area of a non-right triangle
(x^a)/(y^a)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
(n-2)(180 degrees)
Always equal - i.e. 9 choose 3 = 9 choose 6

10. mutually exclusive
At least two congruent sides; the angles opposite these sides are also congruent
(xy)^a
Opposite angles formed by two intersecting lines; always congruent
P(E or F) = P(E) + P(F)

11. how many triangles can a polygon of n sides be divided into?
N-2
N(n-1)(n-2)...(2)(1) = n!
Base * height
Invert the second fraction and multiply them

12. sum of relative frequencies in a frequency distribution
The sum of the areas of the six faces: 2(lw + lh + wh)
1 if decimals - 100 if percents
Number of outcomes yielding E / number of total outcomes
Sum of its digits is divisible by 3

13. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
N(n-1)(n-2)...(2)(1) = n!
(xy)^a
Pi*r^2h

14. chord
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
A list is ordered and can have duplicates
Any line connecting two points on a circle. The diameter is a chord
P(E) + P(F) - P(E and F)

15. permutations of n different objects
N(n-1)(n-2)...(2)(1) = n!
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.
(x^a)/(y^a)

16. isosceles triangle
P(E or F) = P(E) + P(F)
At least two congruent sides; the angles opposite these sides are also congruent
A list is ordered and can have duplicates
Last three digits (taken together) are divisible by 8

17. hypotenuse
Opposite angles formed by two intersecting lines; always congruent
Any line connecting two points on a circle. The diameter is a chord
Number of outcomes yielding E / number of total outcomes
Side opposite the right angle

18. 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.
Sum of its digits is divisible by 9
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1

19. permutations of n objects taken k at a time (order counts)
Sum of its digits is divisible by 9
x^(a-b) or a/x^(b-a)
(xy)^a
N!/(n-k)!

20. divisible by 4
Last two digits (taken together) are divisible by 4
|S|
The sum of the areas of the six faces: 2(lw + lh + wh)
1/x^a

21. divisible by 11
x^(a-b) or a/x^(b-a)
x^ab
(n-2)(180 degrees)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

22. differences between a set and a list
101010
P(E) + P(F) - P(E and F)
A list is ordered and can have duplicates
Mean of the two middle ones

23. sides of 30/60/90 triangle
1 - 2 - root(3); note that this is half of an equilateral triangle
Any line connecting two points on a circle. The diameter is a chord
1098 etc
Less affected by outliers than the mean

24. divisible by 3
x^ab
Less affected by outliers than the mean
Sum of its digits is divisible by 3
Subtract the mean from each value and divide by the standard deviation

25. probability of an event E
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Number of outcomes yielding E / number of total outcomes
Pi*r^2h
|S|

26. dividing fractions
x^(a+b)
(n-2)(180 degrees)
Invert the second fraction and multiply them
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

27. volume of cylinder
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
N(n-1)(n-2)...(2)(1) = n!
Number of outcomes yielding E / number of total outcomes
Pi*r^2h

28. x^0
Sum of its digits is divisible by 3
N-2
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1

29. area of cylinder
Last three digits (taken together) are divisible by 8
2(pir^2) + 2pirh; the two bases and the side
1/2 base * height
101010

30. (x^a)(y^a)
1
N!/(n-k)!
(xy)^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

31. advantage of median
Less affected by outliers than the mean
A list is ordered and can have duplicates
1/x^a
P(E and F) = P(E)P(F)

32. union of sets A and B
A + B - their intersection
Last two digits (taken together) are divisible by 4
Always equal - i.e. 9 choose 3 = 9 choose 6
1 - 2 - root(3); note that this is half of an equilateral triangle

33. area of circle
1 - 2 - root(3); note that this is half of an equilateral triangle
Pi * r^2
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Rules for 2 and three: even and the sum of its digits is divisible by three

34. divisible by 6
N!/(n-k)!
Rules for 2 and three: even and the sum of its digits is divisible by three
Always equal - i.e. 9 choose 3 = 9 choose 6
x^ab

35. (x^a)(x^b)
x^(a+b)
Lwh
(x^a)/(y^a)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

36. sides of isoceles right triangle
1 - 1 - root(2)
Base * height
Side opposite the right angle
Subtract the mean from each value and divide by the standard deviation

37. length of arc of circle
Last two digits (taken together) are divisible by 4
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
All its interior angles are congruent
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

38. area of parallelogram
1/2 base * height
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
(x^a)/(y^a)
Base * height

39. number of elements in set S
1 - 2 - root(3); note that this is half of an equilateral triangle
|S|
P(E) + P(F) - P(E and F)
Side opposite the right angle

40. how to tell if something is prime
Lwh
1/2 base * height
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
P(E) + P(F) - P(E and F)

41. possible combinations of three digits without allowing repeats
Subtract the mean from each value and divide by the standard deviation
101010
1098 etc
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

42. regular polygon
The sum of the areas of the six faces: 2(lw + lh + wh)
Rules for 2 and three: even and the sum of its digits is divisible by three
All its interior angles are congruent
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

43. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
P(E) + P(F) - P(E and F)
(xy)^a
A list is ordered and can have duplicates

44. possible combinations of three digits allowing repeats
Lwh
101010
Pi*r^2h
x^(a+b)

45. combinations of n objects taken k at a time (order doesn'T count)
N!/k!(n-k)! which is also denotes as n choose k
Pi * r^2
Pi*r^2h
x^ab

46. similar triangles
Side opposite the right angle
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Lwh

47. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
Last three digits (taken together) are divisible by 8
Invert the second fraction and multiply them
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

48. vertical angles
Subtract the mean from each value and divide by the standard deviation
Last two digits (taken together) are divisible by 4
Less affected by outliers than the mean
Opposite angles formed by two intersecting lines; always congruent

49. difference between normal or population standard deviation and the sample standard deviation
Less affected by outliers than the mean
Side opposite the right angle
Sum of its digits is divisible by 9
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. relationship between n choose k and n choose n-k
The sum of the areas of the six faces: 2(lw + lh + wh)
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6
(x^a)/(y^a)