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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. sum of measures of interior angles of a polygon with n sides
Less affected by outliers than the mean
(n-2)(180 degrees)
1098 etc
1 - 1 - root(2)

2. area of trapezoid
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(b1 + b2)h - where b1 and b2 are the two parallel sides
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
(xy)^a

3. number of elements in set S
Mean of the two middle ones
|S|
Rules for 2 and three: even and the sum of its digits is divisible by three
Last three digits (taken together) are divisible by 8

4. mutually exclusive
P(E or F) = P(E) + P(F)
N(n-1)(n-2)...(2)(1) = n!
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Opposite angles formed by two intersecting lines; always congruent

5. (x/y)^a
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1/2 base * height
(x^a)/(y^a)
2(pir^2) + 2pirh; the two bases and the side

6. possible combinations of three digits without allowing repeats
P(E and F) = P(E)P(F)
1098 etc
1 - 2 - root(3); note that this is half of an equilateral triangle
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

7. how many triangles can a polygon of n sides be divided into?
Sum of its digits is divisible by 3
N-2
1/x^a
A list is ordered and can have duplicates

8. divisible by 9
Pi*r^2h
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
Sum of its digits is divisible by 9
101010

9. area of rectangle
Sum of its digits is divisible by 3
1/x^a
The sum of the areas of the six faces: 2(lw + lh + wh)
P(E) + P(F) - P(E and F)

10. (x^a)(x^b)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
101010
x^(a+b)
1 if decimals - 100 if percents

11. 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
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Base * height
Pi*r^2h

12. probability that either E or F occur
x^ab
Opposite angles formed by two intersecting lines; always congruent
P(E) + P(F) - P(E and F)
The sum of the areas of the six faces: 2(lw + lh + wh)

13. congruency of triangles
At least two congruent sides; the angles opposite these sides are also congruent
1 - 1 - root(2)
Three sides congruent - two sides and included angle - two angles and included side
2pi*r

14. area of cylinder
N!/(n-k)!
2(pir^2) + 2pirh; the two bases and the side
N-2
Last two digits (taken together) are divisible by 4

15. union of sets A and B
x^(a+b)
A + B - their intersection
Any line connecting two points on a circle. The diameter is a chord
A list is ordered and can have duplicates

16. similar triangles
Any line connecting two points on a circle. The diameter is a chord
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
1098 etc
Base * height

17. divisible by 11
Pi * r^2
2(pir^2) + 2pirh; the two bases and the side
(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

18. regular polygon
Less affected by outliers than the mean
All its interior angles are congruent
x^(a+b)
1

19. (x^a)(y^a)
Pi * r^2
N-2
Any line connecting two points on a circle. The diameter is a chord
(xy)^a

20. hypotenuse
1098 etc
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
Side opposite the right angle

21. circumference of circle
1 - 1 - root(2)
2pi*r
Last two digits (taken together) are divisible by 4
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

22. area of a non-right triangle
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
(xy)^a
2pi*r
N(n-1)(n-2)...(2)(1) = n!

23. divisible by 4
N!/k!(n-k)! which is also denotes as n choose k
Opposite angles formed by two intersecting lines; always congruent
P(E and F) = P(E)P(F)
Last two digits (taken together) are divisible by 4

24. permutations of n different objects
The sum of the areas of the six faces: 2(lw + lh + wh)
N(n-1)(n-2)...(2)(1) = n!
2pi*r
Sum of its digits is divisible by 3

25. x^0
Sum of its digits is divisible by 3
1
Opposite angles formed by two intersecting lines; always congruent
x^(a+b)

26. divisible by 8
N!/(n-k)!
1 - 2 - root(3); note that this is half of an equilateral triangle
Last three digits (taken together) are divisible by 8
x^(a+b)

27. dividing fractions
Invert the second fraction and multiply them
Three sides congruent - two sides and included angle - two angles and included side
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
P(E) + P(F) - P(E and F)

28. sides of isoceles right triangle
|S|
Last three digits (taken together) are divisible by 8
Sum of its digits is divisible by 9
1 - 1 - root(2)

29. sides of 30/60/90 triangle
x^(a-b) or a/x^(b-a)
N-2
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

30. independence of two events E and F
P(E and F) = P(E)P(F)
Opposite angles formed by two intersecting lines; always congruent
(xy)^a
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

31. chord
Any line connecting two points on a circle. The diameter is a chord
Invert the second fraction and multiply them
Side opposite the right angle
N(n-1)(n-2)...(2)(1) = n!

32. volume of rectangle
1 - 2 - root(3); note that this is half of an equilateral triangle
x^ab
Lwh
Always equal - i.e. 9 choose 3 = 9 choose 6

33. area of parallelogram
2pi*r
P(E and F) = P(E)P(F)
Base * height
Last three digits (taken together) are divisible by 8

34. (x^a)^b
x^ab
All its interior angles are congruent
1098 etc
Mean of the two middle ones

35. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
N-2
Opposite angles formed by two intersecting lines; always congruent
Lwh

36. volume of cylinder
A list is ordered and can have duplicates
(x^a)/(y^a)
Pi*r^2h
At least two congruent sides; the angles opposite these sides are also congruent

37. isosceles triangle
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Last two digits (taken together) are divisible by 4
At least two congruent sides; the angles opposite these sides are also congruent
2(pir^2) + 2pirh; the two bases and the side

38. possible combinations of three digits allowing repeats
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
101010
Number of outcomes yielding E / number of total outcomes
The sum of the areas of the six faces: 2(lw + lh + wh)

39. differences between a set and a list
A list is ordered and can have duplicates
Less affected by outliers than the mean
N-2
Sum of its digits is divisible by 3

40. permutations of n objects taken k at a time (order counts)
P(E and F) = P(E)P(F)
Always equal - i.e. 9 choose 3 = 9 choose 6
N!/(n-k)!
Sum of its digits is divisible by 3

41. divisible by 6
x^ab
Rules for 2 and three: even and the sum of its digits is divisible by three
N!/k!(n-k)! which is also denotes as n choose k
x^(a+b)

42. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
N!/(n-k)!
x^ab
All its interior angles are congruent

43. x^-a
N-2
1/x^a
N!/(n-k)!
A + B - their intersection

44. length of arc of circle
P(E or F) = P(E) + P(F)
P(E) + P(F) - P(E and F)
1/x^a
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

45. area of circle
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Pi * r^2
P(E or F) = P(E) + P(F)
2pi*r

46. relationship between n choose k and n choose n-k
1098 etc
Always equal - i.e. 9 choose 3 = 9 choose 6
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
N(n-1)(n-2)...(2)(1) = n!

47. area of sector of circle
P(E) + P(F) - P(E and F)
At least two congruent sides; the angles opposite these sides are also congruent
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

48. difference between normal or population standard deviation and the sample standard deviation
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
Less affected by outliers than the mean
x^(a-b) or a/x^(b-a)
Side opposite the right angle

49. how to tell if something is prime
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Rules for 2 and three: even and the sum of its digits is divisible by three
A + B - their intersection

50. vertical angles
x^(a+b)
Opposite angles formed by two intersecting lines; always congruent
At least two congruent sides; the angles opposite these sides are also congruent
Any line connecting two points on a circle. The diameter is a chord