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

2. relationship between n choose k and n choose n-k
P(E or F) = P(E) + P(F)
1 - 1 - root(2)
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

3. possible combinations of three digits allowing repeats
101010
P(E and F) = P(E)P(F)
Mean of the two middle ones
Less affected by outliers than the mean

4. 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.
x^(a-b) or a/x^(b-a)
Mean of the two middle ones
2pi*r

5. what'S the median if there are an even number of data points?
1 - 1 - root(2)
Side opposite the right angle
Mean of the two middle ones
Pi*r^2h

6. divisible by 3
Mean of the two middle ones
Sum of its digits is divisible by 3
P(E) + P(F) - P(E and F)
Last two digits (taken together) are divisible by 4

7. (x^a)(y^a)
Sum of its digits is divisible by 3
Last three digits (taken together) are divisible by 8
(xy)^a
Pi*r^2h

8. x^0
x^(a-b) or a/x^(b-a)
1/x^a
A list is ordered and can have duplicates
1

9. (x/y)^a
Pi*r^2h
(x^a)/(y^a)
P(E) + P(F) - P(E and F)
Base * height

10. (x^a)/(x^b)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Last three digits (taken together) are divisible by 8
1
x^(a-b) or a/x^(b-a)

11. circumference of circle
2pi*r
1 if decimals - 100 if percents
Last two digits (taken together) are divisible by 4
Side opposite the right angle

12. area of parallelogram
1 - 1 - root(2)
N!/(n-k)!
Opposite angles formed by two intersecting lines; always congruent
Base * height

13. permutations of n different objects
Any line connecting two points on a circle. The diameter is a chord
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N(n-1)(n-2)...(2)(1) = n!

14. number of elements in set S
1
|S|
Lwh
N-2

15. x^-a
1/x^a
P(E and F) = P(E)P(F)
Sum of its digits is divisible by 9
Any line connecting two points on a circle. The diameter is a chord

16. differences between a set and a list
Subtract the mean from each value and divide by the standard deviation
Sum of its digits is divisible by 3
2(pir^2) + 2pirh; the two bases and the side
A list is ordered and can have duplicates

17. vertical angles
Mean of the two middle ones
Opposite angles formed by two intersecting lines; always congruent
Rules for 2 and three: even and the sum of its digits is divisible by three
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

18. congruency of triangles
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Subtract the mean from each value and divide by the standard deviation
Pi * r^2
Three sides congruent - two sides and included angle - two angles and included side

19. how many triangles can a polygon of n sides be divided into?
Always equal - i.e. 9 choose 3 = 9 choose 6
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
P(E) + P(F) - P(E and F)

20. mutually exclusive
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Rules for 2 and three: even and the sum of its digits is divisible by three
P(E and F) = P(E)P(F)
P(E or F) = P(E) + P(F)

21. divisible by 8
Last three digits (taken together) are divisible by 8
N!/k!(n-k)! which is also denotes as n choose k
1 if decimals - 100 if percents
A list is ordered and can have duplicates

22. divisible by 6
Rules for 2 and three: even and the sum of its digits is divisible by three
2(pir^2) + 2pirh; the two bases and the side
(n-2)(180 degrees)
Number of outcomes yielding E / number of total outcomes

23. how to tell if something is prime
Opposite angles formed by two intersecting lines; always congruent
Any line connecting two points on a circle. The diameter is a chord
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
The sum of the areas of the six faces: 2(lw + lh + wh)

24. (x^a)^b
N(n-1)(n-2)...(2)(1) = n!
1/x^a
(n-2)(180 degrees)
x^ab

25. length of arc of circle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
P(E and F) = P(E)P(F)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
N!/(n-k)!

26. sum of measures of interior angles of a polygon with n sides
x^(a+b)
(n-2)(180 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
Less affected by outliers than the mean

27. dividing fractions
Invert the second fraction and multiply them
1/2 base * height
N!/k!(n-k)! which is also denotes as n choose k
Pi * r^2

28. area of trapezoid
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.
(x^a)/(y^a)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

29. isosceles triangle
At least two congruent sides; the angles opposite these sides are also congruent
Base * height
1098 etc
|S|

30. area of circle
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
(x^a)/(y^a)
At least two congruent sides; the angles opposite these sides are also congruent
Pi * r^2

31. divisible by 4
Last two digits (taken together) are divisible by 4
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Always equal - i.e. 9 choose 3 = 9 choose 6
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

32. advantage of median
Less affected by outliers than the mean
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Last two digits (taken together) are divisible by 4
N(n-1)(n-2)...(2)(1) = n!

33. sum of relative frequencies in a frequency distribution
1 if decimals - 100 if percents
Always equal - i.e. 9 choose 3 = 9 choose 6
N-2
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

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

35. (x^a)(x^b)
At least two congruent sides; the angles opposite these sides are also congruent
Number of outcomes yielding E / number of total outcomes
x^(a+b)
A list is ordered and can have duplicates

36. divisible by 9
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Sum of its digits is divisible by 9
Three sides congruent - two sides and included angle - two angles and included side
Subtract the mean from each value and divide by the standard deviation

37. sides of isoceles right triangle
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
|S|
1 - 1 - root(2)
At least two congruent sides; the angles opposite these sides are also congruent

38. volume of cylinder
Number of outcomes yielding E / number of total outcomes
1 - 2 - root(3); note that this is half of an equilateral triangle
All its interior angles are congruent
Pi*r^2h

39. probability that either E or F occur
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Opposite angles formed by two intersecting lines; always congruent
The sum of the areas of the six faces: 2(lw + lh + wh)
P(E) + P(F) - P(E and F)

40. possible combinations of three digits without allowing repeats
101010
The sum of the areas of the six faces: 2(lw + lh + wh)
1098 etc
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

41. standardization/normalization
Sum of its digits is divisible by 9
N-2
Subtract the mean from each value and divide by the standard deviation
Sum of its digits is divisible by 3

42. combinations of n objects taken k at a time (order doesn'T count)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6

43. 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
1
P(E) + P(F) - P(E and F)
P(E and F) = P(E)P(F)

44. similar triangles
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
N!/k!(n-k)! which is also denotes as n choose k
Three sides congruent - two sides and included angle - two angles and included side

45. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
Pi * r^2
N-2
x^(a-b) or a/x^(b-a)

46. area of triangle
1/2 base * height
At least two congruent sides; the angles opposite these sides are also congruent
Opposite angles formed by two intersecting lines; always congruent
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

47. divisible by 11
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.
N-2
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

48. regular polygon
All its interior angles are congruent
P(E and F) = P(E)P(F)
101010
x^ab

49. permutations of n objects taken k at a time (order counts)
Last two digits (taken together) are divisible by 4
2(pir^2) + 2pirh; the two bases and the side
N!/(n-k)!
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

50. chord
Any line connecting two points on a circle. The diameter is a chord
Mean of the two middle ones
1 - 2 - root(3); note that this is half of an equilateral triangle
(n-2)(180 degrees)