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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. how many triangles can a polygon of n sides be divided into?
N(n-1)(n-2)...(2)(1) = n!
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
N-2

2. area of rectangle
Any line connecting two points on a circle. The diameter is a chord
The sum of the areas of the six faces: 2(lw + lh + wh)
1
Subtract the mean from each value and divide by the standard deviation

3. sum of measures of interior angles of a polygon with n sides
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-1)(n-2)...(2)(1) = n!
(n-2)(180 degrees)
1 if decimals - 100 if percents

4. what'S the median if there are an even number of data points?
1/x^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
N!/(n-k)!
Mean of the two middle ones

5. isosceles triangle
All its interior angles are congruent
Any line connecting two points on a circle. The diameter is a chord
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
At least two congruent sides; the angles opposite these sides are also congruent

6. vertical angles
N!/(n-k)!
1
Opposite angles formed by two intersecting lines; always congruent
Pi * r^2

7. probability that either E or F occur
2pi*r
Rules for 2 and three: even and the sum of its digits is divisible by three
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
P(E) + P(F) - P(E and F)

8. independence of two events E and F
P(E and F) = P(E)P(F)
N!/k!(n-k)! which is also denotes as n choose k
A list is ordered and can have duplicates
(x^a)/(y^a)

9. union of sets A and B
Mean of the two middle ones
1 - 1 - root(2)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
A + B - their intersection

10. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
1098 etc
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

11. sides of isoceles right triangle
1 - 1 - root(2)
P(E and F) = P(E)P(F)
Rules for 2 and three: even and the sum of its digits is divisible by three
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

12. advantage of median
Subtract the mean from each value and divide by the standard deviation
Less affected by outliers than the mean
At least two congruent sides; the angles opposite these sides are also congruent
|S|

13. volume of cylinder
(xy)^a
Any line connecting two points on a circle. The diameter is a chord
Pi*r^2h
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

14. 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
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
Number of outcomes yielding E / number of total outcomes

15. divisible by 6
Rules for 2 and three: even and the sum of its digits is divisible by three
N(n-1)(n-2)...(2)(1) = n!
P(E and F) = P(E)P(F)
P(E) + P(F) - P(E and F)

16. regular polygon
All its interior angles are congruent
Less affected by outliers than the mean
Base * height
At least two congruent sides; the angles opposite these sides are also congruent

17. permutations of n objects taken k at a time (order counts)
N!/(n-k)!
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-b) or a/x^(b-a)

18. number of elements in set S
|S|
A + B - their intersection
(xy)^a
Subtract the mean from each value and divide by the standard deviation

19. area of parallelogram
(x^a)/(y^a)
1098 etc
Base * height
A list is ordered and can have duplicates

20. x^0
1
Mean of the two middle ones
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Base * height

21. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
A + B - their intersection
|S|
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

22. (x^a)(x^b)
x^(a+b)
1/2 base * height
x^(a-b) or a/x^(b-a)
Invert the second fraction and multiply them

23. divisible by 11
101010
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Any line connecting two points on a circle. The diameter is a chord
P(E or F) = P(E) + P(F)

24. permutations of n different objects
At least two congruent sides; the angles opposite these sides are also congruent
2pi*r
N(n-1)(n-2)...(2)(1) = n!
Last two digits (taken together) are divisible by 4

25. divisible by 9
Three sides congruent - two sides and included angle - two angles and included side
P(E) + P(F) - P(E and F)
Sum of its digits is divisible by 9
N(n-1)(n-2)...(2)(1) = n!

26. relationship between n choose k and n choose n-k
x^ab
Always equal - i.e. 9 choose 3 = 9 choose 6
Less affected by outliers than the mean
N-2

27. difference between normal or population standard deviation and the sample standard deviation
N!/k!(n-k)! which is also denotes as n choose 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
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
A list is ordered and can have duplicates

28. area of triangle
|S|
Last three digits (taken together) are divisible by 8
1/2 base * height
(xy)^a

29. hypotenuse
Side opposite the right angle
Less affected by outliers than the mean
2pi*r
Base * height

30. probability of an event E
Number of outcomes yielding E / number of total outcomes
1
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

31. divisible by 3
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
(x^a)/(y^a)
N!/k!(n-k)! which is also denotes as n choose k
Sum of its digits is divisible by 3

32. similar triangles
(xy)^a
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Less affected by outliers than the mean
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

33. how to tell if something is prime
101010
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1 - 1 - root(2)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

34. x^-a
Sum of its digits is divisible by 3
1/x^a
1 if decimals - 100 if percents
1 - 2 - root(3); note that this is half of an equilateral triangle

35. standardization/normalization
1 if decimals - 100 if percents
1 - 2 - root(3); note that this is half of an equilateral triangle
Number of outcomes yielding E / number of total outcomes
Subtract the mean from each value and divide by the standard deviation

36. (x^a)^b
x^ab
Less affected by outliers than the mean
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
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

37. area of a non-right triangle
A list is ordered and can have duplicates
Lwh
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

38. sides of 30/60/90 triangle
Less affected by outliers than the mean
1 - 2 - root(3); note that this is half of an equilateral triangle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Number of outcomes yielding E / number of total outcomes

39. volume of rectangle
Sum of its digits is divisible by 3
Lwh
1 - 1 - root(2)
P(E) + P(F) - P(E and F)

40. length of arc of circle
(n-2)(180 degrees)
A + B - their intersection
P(E) + P(F) - P(E and F)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

41. area of trapezoid
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
All its interior angles are congruent
(n-2)(180 degrees)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

42. divisible by 4
1 - 2 - root(3); note that this is half of an equilateral triangle
Sum of its digits is divisible by 9
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Last two digits (taken together) are divisible by 4

43. differences between a set and a list
1
x^ab
A list is ordered and can have duplicates
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

44. area of sector of circle
x^(a+b)
Lwh
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Three sides congruent - two sides and included angle - two angles and included side

45. divisible by 8
Sum of its digits is divisible by 9
1
Base * height
Last three digits (taken together) are divisible by 8

46. area of circle
1
Pi * r^2
Last three digits (taken together) are divisible by 8
The sum of the areas of the six faces: 2(lw + lh + wh)

47. possible combinations of three digits without allowing repeats
1098 etc
(x^a)/(y^a)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Pi*r^2h

48. (x^a)/(x^b)
P(E or F) = P(E) + P(F)
x^(a-b) or a/x^(b-a)
x^(a+b)
P(E and F) = P(E)P(F)

49. dividing fractions
Three sides congruent - two sides and included angle - two angles and included side
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Invert the second fraction and multiply them
Lwh

50. (x/y)^a
(x^a)/(y^a)
Invert the second fraction and multiply them
At least two congruent sides; the angles opposite these sides are also congruent
(n-2)(180 degrees)