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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. divisible by 11
x^(a+b)
1098 etc
Number of outcomes yielding E / number of total outcomes
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

2. probability of an event E
Number of outcomes yielding E / number of total outcomes
1 - 2 - root(3); note that this is half of an equilateral triangle
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

3. sides of isoceles right triangle
(n-2)(180 degrees)
1 - 1 - root(2)
Invert the second fraction and multiply them
N(n-1)(n-2)...(2)(1) = n!

4. possible combinations of three digits without allowing repeats
Three sides congruent - two sides and included angle - two angles and included side
Number of outcomes yielding E / number of total outcomes
1098 etc
1 - 2 - root(3); note that this is half of an equilateral triangle

5. area of sector of circle
1 if decimals - 100 if percents
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.
(xy)^a

6. independence of two events E and F
Sum of its digits is divisible by 3
P(E and F) = P(E)P(F)
All its interior angles are congruent
Mean of the two middle ones

7. area of cylinder
x^(a+b)
N!/k!(n-k)! which is also denotes as n choose k
2(pir^2) + 2pirh; the two bases and the side
Less affected by outliers than the mean

8. isosceles triangle
P(E) + P(F) - P(E and F)
At least two congruent sides; the angles opposite these sides are also congruent
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

9. area of rectangle
The sum of the areas of the six faces: 2(lw + lh + wh)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
1 - 2 - root(3); note that this is half of an equilateral triangle
x^ab

10. volume of rectangle
(n-2)(180 degrees)
x^(a+b)
Lwh
All its interior angles are congruent

11. mutually exclusive
Last three digits (taken together) are divisible by 8
|S|
P(E or F) = P(E) + P(F)
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

12. length of arc of circle
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.
|S|
1 if decimals - 100 if percents

13. (x^a)^b
(xy)^a
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
x^ab
Invert the second fraction and multiply them

14. how many triangles can a polygon of n sides be divided into?
N-2
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
Pi * r^2

15. divisible by 3
1 if decimals - 100 if percents
1 - 1 - root(2)
Always equal - i.e. 9 choose 3 = 9 choose 6
Sum of its digits is divisible by 3

16. circumference of circle
2pi*r
1098 etc
x^(a+b)
N!/k!(n-k)! which is also denotes as n choose k

17. area of parallelogram
Pi * r^2
Base * height
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

18. number of elements in set S
Always equal - i.e. 9 choose 3 = 9 choose 6
|S|
Opposite angles formed by two intersecting lines; always congruent
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

19. standardization/normalization
P(E and F) = P(E)P(F)
N(n-1)(n-2)...(2)(1) = n!
Opposite angles formed by two intersecting lines; always congruent
Subtract the mean from each value and divide by the standard deviation

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

21. advantage of median
Pi*r^2h
Lwh
Less affected by outliers than the mean
(n-2)(180 degrees)

22. (x^a)(y^a)
Any line connecting two points on a circle. The diameter is a chord
x^(a+b)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
(xy)^a

23. permutations of n different objects
N(n-1)(n-2)...(2)(1) = n!
x^ab
At least two congruent sides; the angles opposite these sides are also congruent
2pi*r

24. dividing fractions
Invert the second fraction and multiply them
At least two congruent sides; the angles opposite these sides are also congruent
Base * height
x^(a+b)

25. difference between normal or population standard deviation and the sample standard deviation
Mean of the two middle ones
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
Base * height
All its interior angles are congruent

26. combinations of n objects taken k at a time (order doesn'T count)
Opposite angles formed by two intersecting lines; always congruent
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
1098 etc
N!/k!(n-k)! which is also denotes as n choose k

27. how to tell if something is prime
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
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

28. vertical angles
x^ab
Opposite angles formed by two intersecting lines; always congruent
Number of outcomes yielding E / number of total outcomes
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

29. (x/y)^a
(x^a)/(y^a)
At least two congruent sides; the angles opposite these sides are also congruent
2pi*r
N(n-1)(n-2)...(2)(1) = n!

30. relationship between n choose k and n choose n-k
Lwh
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Always equal - i.e. 9 choose 3 = 9 choose 6
Pi * r^2

31. divisible by 9
N!/(n-k)!
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Sum of its digits is divisible by 9
Subtract the mean from each value and divide by the standard deviation

32. x^0
Three sides congruent - two sides and included angle - two angles and included side
Sum of its digits is divisible by 9
Rules for 2 and three: even and the sum of its digits is divisible by three
1

33. sides of 30/60/90 triangle
At least two congruent sides; the angles opposite these sides are also congruent
Rules for 2 and three: even and the sum of its digits is divisible by three
1 - 2 - root(3); note that this is half of an equilateral triangle
1

34. divisible by 6
Rules for 2 and three: even and the sum of its digits is divisible by three
1 if decimals - 100 if percents
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

35. possible combinations of three digits allowing repeats
101010
N(n-1)(n-2)...(2)(1) = n!
Number of outcomes yielding E / number of total outcomes
P(E) + P(F) - P(E and F)

36. divisible by 4
Last two digits (taken together) are divisible by 4
1 - 1 - root(2)
x^(a-b) or a/x^(b-a)
All its interior angles are congruent

37. area of triangle
The sum of the areas of the six faces: 2(lw + lh + wh)
Invert the second fraction and multiply them
1/2 base * height
Mean of the two middle ones

38. what'S the median if there are an even number of data points?
A + B - their intersection
Mean of the two middle ones
2pi*r
N!/k!(n-k)! which is also denotes as n choose k

39. union of sets A and B
1098 etc
Sum of its digits is divisible by 9
A + B - their intersection
Lwh

40. chord
Number of outcomes yielding E / number of total outcomes
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Any line connecting two points on a circle. The diameter is a chord
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

41. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
A list is ordered and can have duplicates
1/x^a
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

42. x^-a
1/x^a
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
(x^a)/(y^a)

43. sum of relative frequencies in a frequency distribution
Any line connecting two points on a circle. The diameter is a chord
Base * height
1 if decimals - 100 if percents
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

44. differences between a set and a list
101010
A list is ordered and can have duplicates
x^ab
1/2 base * height

45. volume of cylinder
Subtract the mean from each value and divide by the standard deviation
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
Pi*r^2h

46. 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.
P(E and F) = P(E)P(F)
Pi*r^2h
x^ab

47. congruency of triangles
P(E and F) = P(E)P(F)
Any line connecting two points on a circle. The diameter is a chord
(x^a)/(y^a)
Three sides congruent - two sides and included angle - two angles and included side

48. divisible by 8
2pi*r
Last three digits (taken together) are divisible by 8
1/x^a
Opposite angles formed by two intersecting lines; always congruent

49. sum of measures of interior angles of a polygon with n sides
N!/k!(n-k)! which is also denotes as n choose k
Invert the second fraction and multiply them
Pi * r^2
(n-2)(180 degrees)

50. probability that either E or F occur
The sum of the areas of the six faces: 2(lw + lh + wh)
A + B - their intersection
P(E) + P(F) - P(E and F)
Three sides congruent - two sides and included angle - two angles and included side