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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. length of arc of circle
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)
N(n-1)(n-2)...(2)(1) = n!
Mean of the two middle ones

2. divisible by 4
At least two congruent sides; the angles opposite these sides are also congruent
Last two digits (taken together) are divisible by 4
P(E and F) = P(E)P(F)
Subtract the mean from each value and divide by the standard deviation

3. permutations of n different objects
Pi*r^2h
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Pi * r^2
N(n-1)(n-2)...(2)(1) = n!

4. (x^a)^b
2(pir^2) + 2pirh; the two bases and the side
x^ab
Lwh
Subtract the mean from each value and divide by the standard deviation

5. difference between normal or population standard deviation and the sample standard deviation
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
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

6. sides of 30/60/90 triangle
1 - 2 - root(3); note that this is half of an equilateral triangle
Always equal - i.e. 9 choose 3 = 9 choose 6
Opposite angles formed by two intersecting lines; always congruent
2(pir^2) + 2pirh; the two bases and the side

7. how many triangles can a polygon of n sides be divided into?
Side opposite the right angle
N-2
x^ab
N(n-1)(n-2)...(2)(1) = n!

8. possible combinations of three digits without allowing repeats
1098 etc
N!/(n-k)!
(xy)^a
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

9. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
P(E) + P(F) - P(E and F)
Pi * r^2
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

10. isosceles triangle
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)
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.

11. volume of rectangle
P(E) + P(F) - P(E and F)
Lwh
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.

12. relationship between n choose k and n choose n-k
A + B - their intersection
2pi*r
1 - 1 - root(2)
Always equal - i.e. 9 choose 3 = 9 choose 6

13. independence of two events E and F
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
Any line connecting two points on a circle. The diameter is a chord
P(E and F) = P(E)P(F)

14. possible combinations of three digits allowing repeats
Three sides congruent - two sides and included angle - two angles and included side
2pi*r
101010
A + B - their intersection

15. divisible by 9
Sum of its digits is divisible by 9
A + B - their intersection
Mean of the two middle ones
Always equal - i.e. 9 choose 3 = 9 choose 6

16. volume of cylinder
Sum of its digits is divisible by 9
2(pir^2) + 2pirh; the two bases and the side
At least two congruent sides; the angles opposite these sides are also congruent
Pi*r^2h

17. (x^a)(x^b)
Last two digits (taken together) are divisible by 4
N-2
Invert the second fraction and multiply them
x^(a+b)

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

19. dividing fractions
Invert the second fraction and multiply them
Sum of its digits is divisible by 9
1/x^a
Side opposite the right angle

20. chord
Any line connecting two points on a circle. The diameter is a chord
Last three digits (taken together) are divisible by 8
(x^a)/(y^a)
1098 etc

21. area of rectangle
The sum of the areas of the six faces: 2(lw + lh + wh)
Invert the second fraction and multiply them
Less affected by outliers than the mean
(x^a)/(y^a)

22. (x/y)^a
(x^a)/(y^a)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
2(pir^2) + 2pirh; the two bases and the side
The sum of the areas of the six faces: 2(lw + lh + wh)

23. area of sector of circle
1/x^a
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
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.

24. divisible by 11
1
A + B - their intersection
Always equal - i.e. 9 choose 3 = 9 choose 6
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

25. divisible by 6
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
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
P(E and F) = P(E)P(F)

26. probability of an event E
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
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

27. probability that either E or F occur
1098 etc
(n-2)(180 degrees)
P(E) + P(F) - P(E and F)
Three sides congruent - two sides and included angle - two angles and included side

28. differences between a set and a list
x^(a+b)
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
N!/k!(n-k)! which is also denotes as n choose k

29. regular polygon
Pi*r^2h
All its interior angles are congruent
(xy)^a
N-2

30. sum of relative frequencies in a frequency distribution
1 if decimals - 100 if percents
All its interior angles are congruent
(x^a)/(y^a)
A list is ordered and can have duplicates

31. (x^a)/(x^b)
P(E) + P(F) - P(E and F)
Subtract the mean from each value and divide by the standard deviation
N!/(n-k)!
x^(a-b) or a/x^(b-a)

32. similar triangles
Less affected by outliers than the mean
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Rules for 2 and three: even and the sum of its digits is divisible by three
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

33. area of trapezoid
Pi * r^2
x^(a-b) or a/x^(b-a)
1/x^a
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

34. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
2pi*r
N-2
Pi * r^2

35. divisible by 3
Sum of its digits is divisible by 3
1 if decimals - 100 if percents
1 - 2 - root(3); note that this is half of an equilateral triangle
101010

36. sides of isoceles right triangle
A list is ordered and can have duplicates
x^ab
Sum of its digits is divisible by 9
1 - 1 - root(2)

37. sum of measures of interior angles of a polygon with n sides
Base * height
(n-2)(180 degrees)
Last three digits (taken together) are divisible by 8
Number of outcomes yielding E / number of total outcomes

38. advantage of median
x^(a-b) or a/x^(b-a)
The sum of the areas of the six faces: 2(lw + lh + wh)
Less affected by outliers than the mean
1 - 2 - root(3); note that this is half of an equilateral triangle

39. number of elements in set S
Pi * r^2
|S|
Rules for 2 and three: even and the sum of its digits is divisible by three
The sum of the areas of the six faces: 2(lw + lh + wh)

40. hypotenuse
Side opposite the right angle
A list is ordered and can have duplicates
P(E) + P(F) - P(E and F)
Base * height

41. x^-a
1/x^a
Opposite angles formed by two intersecting lines; always congruent
x^(a+b)
Last three digits (taken together) are divisible by 8

42. vertical angles
1/2 base * height
1 - 2 - root(3); note that this is half of an equilateral triangle
Less affected by outliers than the mean
Opposite angles formed by two intersecting lines; always congruent

43. x^0
1
Opposite angles formed by two intersecting lines; always congruent
P(E and F) = P(E)P(F)
Mean of the two middle ones

44. what'S the median if there are an even number of data points?
(xy)^a
Mean of the two middle ones
2pi*r
Less affected by outliers than the mean

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

46. area of triangle
Lwh
P(E or F) = P(E) + P(F)
101010
1/2 base * height

47. permutations of n objects taken k at a time (order counts)
At least two congruent sides; the angles opposite these sides are also congruent
N!/(n-k)!
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
1 if decimals - 100 if percents

48. area of parallelogram
1/2 base * height
N!/(n-k)!
P(E or F) = P(E) + P(F)
Base * height

49. area of circle
P(E and F) = P(E)P(F)
Sum of its digits is divisible by 9
Pi * r^2
x^(a-b) or a/x^(b-a)

50. mutually exclusive
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
P(E or F) = P(E) + P(F)
At least two congruent sides; the angles opposite these sides are also congruent
Opposite angles formed by two intersecting lines; always congruent