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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. how many triangles can a polygon of n sides be divided into?
Base * height
(xy)^a
N(n-1)(n-2)...(2)(1) = n!
N-2

2. 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
Always equal - i.e. 9 choose 3 = 9 choose 6
N!/(n-k)!
Number of outcomes yielding E / number of total outcomes

3. mutually exclusive
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
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
N!/k!(n-k)! which is also denotes as n choose k

4. probability that either E or F occur
P(E) + P(F) - P(E and F)
1 - 2 - root(3); note that this is half of an equilateral triangle
Sum of its digits is divisible by 3
101010

5. area of rectangle
The sum of the areas of the six faces: 2(lw + lh + wh)
Three sides congruent - two sides and included angle - two angles and included side
A + B - their intersection
2pi*r

6. (x^a)^b
(n-2)(180 degrees)
1098 etc
Always equal - i.e. 9 choose 3 = 9 choose 6
x^ab

7. isosceles triangle
(xy)^a
Pi*r^2h
1
At least two congruent sides; the angles opposite these sides are also congruent

8. probability of an event E
N-2
P(E and F) = P(E)P(F)
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

9. volume of cylinder
Mean of the two middle ones
Pi*r^2h
All its interior angles are congruent
1098 etc

10. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
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.
1/2 base * height

11. (x/y)^a
(x^a)/(y^a)
1 - 2 - root(3); note that this is half of an equilateral triangle
2pi*r
At least two congruent sides; the angles opposite these sides are also congruent

12. area of sector of circle
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
N!/(n-k)!
Subtract the mean from each value and divide by the standard deviation
1 - 2 - root(3); note that this is half of an equilateral triangle

13. divisible by 4
Side opposite the right angle
Number of outcomes yielding E / number of total outcomes
Last two digits (taken together) are divisible by 4
A list is ordered and can have duplicates

14. difference between normal or population standard deviation and the sample standard deviation
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
Three sides congruent - two sides and included angle - two angles and included side
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

15. area of circle
Invert the second fraction and multiply them
(n-2)(180 degrees)
1098 etc
Pi * r^2

16. permutations of n objects taken k at a time (order counts)
1/x^a
N!/(n-k)!
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!

17. independence of two events E and F
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
2pi*r
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).

18. number of elements in set S
All its interior angles are congruent
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
|S|
Rules for 2 and three: even and the sum of its digits is divisible by three

19. sum of relative frequencies in a frequency distribution
1 if decimals - 100 if percents
Number of outcomes yielding E / number of total outcomes
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

20. union of sets A and B
Invert the second fraction and multiply them
N(n-1)(n-2)...(2)(1) = n!
1098 etc
A + B - their intersection

21. length of arc of circle
Sum of its digits is divisible by 3
1 if decimals - 100 if percents
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.

22. divisible by 11
(x^a)/(y^a)
The sum of the areas of the six faces: 2(lw + lh + wh)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
P(E) + P(F) - P(E and F)

23. differences between a set and a list
Side opposite the right angle
Sum of its digits is divisible by 9
x^(a+b)
A list is ordered and can have duplicates

24. permutations of n different objects
101010
Three sides congruent - two sides and included angle - two angles and included side
N(n-1)(n-2)...(2)(1) = n!
P(E) + P(F) - P(E and F)

25. divisible by 8
N!/(n-k)!
Last three digits (taken together) are divisible by 8
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
x^ab

26. divisible by 6
The sum of the areas of the six faces: 2(lw + lh + wh)
2(pir^2) + 2pirh; the two bases and the side
Lwh
Rules for 2 and three: even and the sum of its digits is divisible by three

27. regular polygon
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N!/(n-k)!
All its interior angles are congruent
A + B - their intersection

28. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
Number of outcomes yielding E / number of total outcomes
P(E and F) = P(E)P(F)
101010

29. possible combinations of three digits allowing repeats
x^ab
N!/(n-k)!
101010
Invert the second fraction and multiply them

30. sides of isoceles right triangle
P(E and F) = P(E)P(F)
x^(a+b)
A + B - their intersection
1 - 1 - root(2)

31. congruency of triangles
1098 etc
A list is ordered and can have duplicates
Three sides congruent - two sides and included angle - two angles and included side
x^(a-b) or a/x^(b-a)

32. area of trapezoid
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Less affected by outliers than the mean
Opposite angles formed by two intersecting lines; always congruent

33. area of a non-right triangle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Invert the second fraction and multiply them
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
A + B - their intersection

34. possible combinations of three digits without allowing repeats
1098 etc
x^(a+b)
2pi*r
101010

35. (x^a)(x^b)
The sum of the areas of the six faces: 2(lw + lh + wh)
101010
x^(a+b)
Any line connecting two points on a circle. The diameter is a chord

36. dividing fractions
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
Invert the second fraction and multiply them
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

37. volume of rectangle
Lwh
1/2 base * height
x^ab
Sum of its digits is divisible by 9

38. divisible by 3
Sum of its digits is divisible by 3
Lwh
Last three digits (taken together) are divisible by 8
2(pir^2) + 2pirh; the two bases and the side

39. area of parallelogram
Base * height
N(n-1)(n-2)...(2)(1) = n!
The sum of the areas of the six faces: 2(lw + lh + wh)
1098 etc

40. hypotenuse
Lwh
Number of outcomes yielding E / number of total outcomes
A + B - their intersection
Side opposite the right angle

41. (x^a)(y^a)
All its interior angles are congruent
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
(xy)^a
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

42. x^0
N-2
1
Lwh
Sum of its digits is divisible by 3

43. x^-a
A list is ordered and can have duplicates
101010
1/x^a
P(E or F) = P(E) + P(F)

44. sides of 30/60/90 triangle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Any line connecting two points on a circle. The diameter is a chord
1 - 2 - root(3); note that this is half of an equilateral triangle
(xy)^a

45. relationship between n choose k and n choose n-k
Always equal - i.e. 9 choose 3 = 9 choose 6
|S|
Three sides congruent - two sides and included angle - two angles and included side
P(E) + P(F) - P(E and F)

46. divisible by 9
2pi*r
Side opposite the right angle
Last three digits (taken together) are divisible by 8
Sum of its digits is divisible by 9

47. circumference of circle
Base * height
Any line connecting two points on a circle. The diameter is a chord
2pi*r
At least two congruent sides; the angles opposite these sides are also congruent

48. how to tell if something is prime
P(E) + P(F) - P(E and F)
(x^a)/(y^a)
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

49. advantage of median
Subtract the mean from each value and divide by the standard deviation
All its interior angles are congruent
Less affected by outliers than the mean
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

50. chord
Last three digits (taken together) are divisible by 8
1 if decimals - 100 if percents
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Any line connecting two points on a circle. The diameter is a chord