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GRE Math Rules

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. how many triangles can a polygon of n sides be divided into?
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1 if decimals - 100 if percents
1/2 base * height
N-2

2. independence of two events E and F
Rules for 2 and three: even and the sum of its digits is divisible by three
P(E and F) = P(E)P(F)
2(pir^2) + 2pirh; the two bases and the side
1098 etc

3. chord
Always equal - i.e. 9 choose 3 = 9 choose 6
P(E) + P(F) - P(E and F)
Any line connecting two points on a circle. The diameter is a chord
Subtract the mean from each value and divide by the standard deviation

4. area of sector of circle
Pi*r^2h
N!/k!(n-k)! which is also denotes as n choose k
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Opposite angles formed by two intersecting lines; always congruent

5. circumference of circle
P(E or F) = P(E) + P(F)
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
x^ab

6. what'S the median if there are an even number of data points?
Last three digits (taken together) are divisible by 8
1/x^a
Mean of the two middle ones
N!/(n-k)!

7. how to tell if something is prime
Last three digits (taken together) are divisible by 8
(n-2)(180 degrees)
x^(a+b)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

8. divisible by 8
A list is ordered and can have duplicates
Base * height
Last three digits (taken together) are divisible by 8
Mean of the two middle ones

9. possible combinations of three digits without allowing repeats
1098 etc
N-2
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

10. 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
Sum of its digits is divisible by 3
N!/(n-k)!

11. divisible by 3
All its interior angles are congruent
x^(a+b)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Sum of its digits is divisible by 3

12. volume of rectangle
Last three digits (taken together) are divisible by 8
Rules for 2 and three: even and the sum of its digits is divisible by three
Lwh
Mean of the two middle ones

13. (x^a)(x^b)
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6
N-2
x^(a+b)

14. area of cylinder
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Subtract the mean from each value and divide by the standard deviation
2(pir^2) + 2pirh; the two bases and the side
Last three digits (taken together) are divisible by 8

15. number of elements in set S
N!/(n-k)!
|S|
1098 etc
(xy)^a

16. permutations of n objects taken k at a time (order counts)
N!/(n-k)!
Rules for 2 and three: even and the sum of its digits is divisible by three
Less affected by outliers than the mean
Sum of its digits is divisible by 9

17. difference between normal or population standard deviation and the sample standard deviation
Number of outcomes yielding E / number of total outcomes
N(n-1)(n-2)...(2)(1) = n!
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
Opposite angles formed by two intersecting lines; always congruent

18. permutations of n different objects
Last three digits (taken together) are divisible by 8
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Sum of its digits is divisible by 9
N(n-1)(n-2)...(2)(1) = n!

19. (x^a)^b
2pi*r
N!/(n-k)!
x^ab
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

20. dividing fractions
Sum of its digits is divisible by 3
(n-2)(180 degrees)
Base * height
Invert the second fraction and multiply them

21. divisible by 9
Opposite angles formed by two intersecting lines; always congruent
Sum of its digits is divisible by 9
Rules for 2 and three: even and the sum of its digits is divisible by three
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

22. divisible by 4
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.
1/2 base * height
Last two digits (taken together) are divisible by 4

23. vertical angles
1/2 base * height
Opposite angles formed by two intersecting lines; always congruent
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).

24. length of arc of circle
Lwh
A list is ordered and can have duplicates
A + B - their intersection
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

25. divisible by 11
A list is ordered and can have duplicates
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
2pi*r
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

26. divisible by 6
2pi*r
Rules for 2 and three: even and the sum of its digits is divisible by three
N(n-1)(n-2)...(2)(1) = n!
1/x^a

27. volume of cylinder
Pi*r^2h
Last two digits (taken together) are divisible by 4
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Any line connecting two points on a circle. The diameter is a chord

28. x^-a
1/x^a
P(E or F) = P(E) + P(F)
(n-2)(180 degrees)
P(E and F) = P(E)P(F)

29. sum of measures of interior angles of a polygon with n sides
(n-2)(180 degrees)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
N(n-1)(n-2)...(2)(1) = n!
Opposite angles formed by two intersecting lines; always congruent

30. combinations of n objects taken k at a time (order doesn'T count)
1 - 2 - root(3); note that this is half of an equilateral triangle
N!/k!(n-k)! which is also denotes as n choose k
Pi*r^2h
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

31. area of rectangle
1/x^a
Any line connecting two points on a circle. The diameter is a chord
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
The sum of the areas of the six faces: 2(lw + lh + wh)

32. (x^a)(y^a)
P(E or F) = P(E) + P(F)
2pi*r
(xy)^a
N!/(n-k)!

33. union of sets A and B
A + B - their intersection
1/2 base * height
Subtract the mean from each value and divide by the standard deviation
1 - 2 - root(3); note that this is half of an equilateral triangle

34. standardization/normalization
Last two digits (taken together) are divisible by 4
Subtract the mean from each value and divide by the standard deviation
Any line connecting two points on a circle. The diameter is a chord
Opposite angles formed by two intersecting lines; always congruent

35. x^0
101010
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
1
At least two congruent sides; the angles opposite these sides are also congruent

36. regular polygon
2(pir^2) + 2pirh; the two bases and the side
Opposite angles formed by two intersecting lines; always congruent
Side opposite the right angle
All its interior angles are congruent

37. area of a non-right triangle
Three sides congruent - two sides and included angle - two angles and included side
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
P(E and F) = P(E)P(F)

38. area of parallelogram
1
Base * height
Last two digits (taken together) are divisible by 4
1/x^a

39. relationship between n choose k and n choose n-k
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
N!/k!(n-k)! which is also denotes as n choose k
Always equal - i.e. 9 choose 3 = 9 choose 6
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

40. probability that either E or F occur
Rules for 2 and three: even and the sum of its digits is divisible by three
Less affected by outliers than the mean
P(E) + P(F) - P(E and F)
x^(a-b) or a/x^(b-a)

41. (x/y)^a
Pi * r^2
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Mean of the two middle ones
(x^a)/(y^a)

42. possible combinations of three digits allowing repeats
101010
x^(a-b) or a/x^(b-a)
Number of outcomes yielding E / number of total outcomes
1 - 2 - root(3); note that this is half of an equilateral triangle

43. area of trapezoid
1
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
Always equal - i.e. 9 choose 3 = 9 choose 6

44. area of circle
Rules for 2 and three: even and the sum of its digits is divisible by three
Pi * r^2
101010
A + B - their intersection

45. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
A + B - their intersection
x^ab
|S|

46. differences between a set and a list
Sum of its digits is divisible by 9
A list is ordered and can have duplicates
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

47. advantage of median
x^(a-b) or a/x^(b-a)
x^(a+b)
Side opposite the right angle
Less affected by outliers than the mean

48. mutually exclusive
P(E or F) = P(E) + P(F)
N(n-1)(n-2)...(2)(1) = n!
2(pir^2) + 2pirh; the two bases and the side
(n-2)(180 degrees)

49. similar triangles
Sum of its digits is divisible by 9
101010
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Lwh

50. probability of an event E
(n-2)(180 degrees)
Number of outcomes yielding E / number of total outcomes
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
All its interior angles are congruent

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