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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. volume of cylinder
Pi*r^2h
A + B - their intersection
Invert the second fraction and multiply them
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

2. (x^a)^b
1 - 1 - root(2)
N!/k!(n-k)! which is also denotes as n choose k
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
x^ab

3. how many triangles can a polygon of n sides be divided into?
N-2
x^ab
At least two congruent sides; the angles opposite these sides are also congruent
|S|

4. 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
1
Always equal - i.e. 9 choose 3 = 9 choose 6
1098 etc

5. area of cylinder
At least two congruent sides; the angles opposite these sides are also congruent
2(pir^2) + 2pirh; the two bases and the side
1
The sum of the areas of the six faces: 2(lw + lh + wh)

6. union of sets A and B
2(pir^2) + 2pirh; the two bases and the side
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
(xy)^a
A + B - their intersection

7. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
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).
N-2

8. mutually exclusive
P(E or F) = P(E) + P(F)
P(E and F) = P(E)P(F)
Sum of its digits is divisible by 3
2pi*r

9. advantage of median
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Invert the second fraction and multiply them
Less affected by outliers than the mean
Base * height

10. sides of isoceles right triangle
Pi * r^2
1 - 1 - root(2)
N(n-1)(n-2)...(2)(1) = n!
Base * height

11. permutations of n objects taken k at a time (order counts)
Mean of the two middle ones
Always equal - i.e. 9 choose 3 = 9 choose 6
Rules for 2 and three: even and the sum of its digits is divisible by three
N!/(n-k)!

12. chord
Any line connecting two points on a circle. The diameter is a chord
P(E and F) = P(E)P(F)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Rules for 2 and three: even and the sum of its digits is divisible by three

13. dividing fractions
x^ab
Sum of its digits is divisible by 3
Invert the second fraction and multiply them
Lwh

14. divisible by 9
1/2 base * height
1098 etc
Sum of its digits is divisible by 9
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

15. independence of two events E and F
A list is ordered and can have duplicates
P(E and F) = P(E)P(F)
1/2 base * height
Lwh

16. circumference of circle
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6
x^(a+b)
(n-2)(180 degrees)

17. area of sector of circle
(n-2)(180 degrees)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
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
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

18. number of elements in set S
Pi * r^2
|S|
N!/k!(n-k)! which is also denotes as n choose k
x^(a-b) or a/x^(b-a)

19. difference between normal or population standard deviation and the sample standard deviation
1098 etc
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
Side opposite the right angle

20. volume of rectangle
x^(a+b)
Lwh
x^ab
P(E) + P(F) - P(E and F)

21. area of triangle
1/2 base * height
Pi * r^2
1 - 2 - root(3); note that this is half of an equilateral triangle
P(E) + P(F) - P(E and F)

22. divisible by 8
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Sum of its digits is divisible by 9
Mean of the two middle ones
Last three digits (taken together) are divisible by 8

23. sum of measures of interior angles of a polygon with n sides
x^ab
(n-2)(180 degrees)
P(E) + P(F) - P(E and F)
1 - 1 - root(2)

24. sides of 30/60/90 triangle
P(E) + P(F) - P(E and F)
Last two digits (taken together) are divisible by 4
1 - 2 - root(3); note that this is half of an equilateral triangle
Last three digits (taken together) are divisible by 8

25. (x^a)(x^b)
x^(a+b)
1 - 1 - root(2)
1 - 2 - root(3); note that this is half of an equilateral triangle
Subtract the mean from each value and divide by the standard deviation

26. (x/y)^a
(x^a)/(y^a)
x^(a-b) or a/x^(b-a)
N-2
Pi*r^2h

27. isosceles triangle
Three sides congruent - two sides and included angle - two angles and included side
At least two congruent sides; the angles opposite these sides are also congruent
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Lwh

28. differences between a set and a list
Three sides congruent - two sides and included angle - two angles and included side
2(pir^2) + 2pirh; the two bases and the side
A list is ordered and can have duplicates
1098 etc

29. sum of relative frequencies in a frequency distribution
Last two digits (taken together) are divisible by 4
Any line connecting two points on a circle. The diameter is a chord
1 if decimals - 100 if percents
1 - 1 - root(2)

30. possible combinations of three digits without allowing repeats
1
P(E and F) = P(E)P(F)
1098 etc
N!/k!(n-k)! which is also denotes as n choose k

31. x^0
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Three sides congruent - two sides and included angle - two angles and included side
1
P(E) + P(F) - P(E and F)

32. hypotenuse
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Side opposite the right angle
1/x^a
(x^a)/(y^a)

33. divisible by 6
Rules for 2 and three: even and the sum of its digits is divisible by three
1/2 base * height
|S|
Less affected by outliers than the mean

34. what'S the median if there are an even number of data points?
N!/(n-k)!
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Mean of the two middle ones
1

35. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
1098 etc
Mean of the two middle ones
1

36. x^-a
Mean of the two middle ones
At least two congruent sides; the angles opposite these sides are also congruent
1/x^a
Last two digits (taken together) are divisible by 4

37. vertical angles
2(pir^2) + 2pirh; the two bases and the side
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
All its interior angles are congruent
Opposite angles formed by two intersecting lines; always congruent

38. area of trapezoid
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Pi*r^2h
(n-2)(180 degrees)
Last three digits (taken together) are divisible by 8

39. divisible by 3
Last two digits (taken together) are divisible by 4
All its interior angles are congruent
Sum of its digits is divisible by 3
2pi*r

40. probability of an event E
(n-2)(180 degrees)
P(E and F) = P(E)P(F)
Number of outcomes yielding E / number of total outcomes
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

41. permutations of n different objects
P(E or F) = P(E) + P(F)
N(n-1)(n-2)...(2)(1) = n!
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.

42. divisible by 4
Last two digits (taken together) are divisible by 4
1
x^ab
(n-2)(180 degrees)

43. 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
(xy)^a
The sum of the areas of the six faces: 2(lw + lh + wh)
1/x^a

44. similar triangles
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
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)
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

45. how to tell if something is prime
Subtract the mean from each value and divide by the standard deviation
Less affected by outliers than the mean
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Pi * r^2

46. length of arc of circle
Subtract the mean from each value and divide by the standard deviation
P(E and F) = P(E)P(F)
Sum of its digits is divisible by 3
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

47. area of circle
A list is ordered and can have duplicates
Pi * r^2
x^(a-b) or a/x^(b-a)
Always equal - i.e. 9 choose 3 = 9 choose 6

48. possible combinations of three digits allowing repeats
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
101010
x^(a-b) or a/x^(b-a)

49. regular polygon
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
2pi*r
Number of outcomes yielding E / number of total outcomes
All its interior angles are congruent

50. probability that either E or F occur
At least two congruent sides; the angles opposite these sides are also congruent
P(E) + P(F) - P(E and F)
Pi*r^2h
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication