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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. area of a non-right triangle
(n-2)(180 degrees)
Lwh
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.

2. permutations of n different objects
Opposite angles formed by two intersecting lines; always congruent
(x^a)/(y^a)
x^ab
N(n-1)(n-2)...(2)(1) = n!

3. divisible by 11
A list is ordered and can have duplicates
Lwh
1098 etc
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

4. area of parallelogram
101010
At least two congruent sides; the angles opposite these sides are also congruent
(n-2)(180 degrees)
Base * height

5. regular polygon
1/x^a
(xy)^a
Opposite angles formed by two intersecting lines; always congruent
All its interior angles are congruent

6. area of triangle
1
(n-2)(180 degrees)
1/x^a
1/2 base * height

7. 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.
x^ab
2(pir^2) + 2pirh; the two bases and the side
Less affected by outliers than the mean

8. 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).
A + B - their intersection
2(pir^2) + 2pirh; the two bases and the side

9. isosceles triangle
At least two congruent sides; the angles opposite these sides are also congruent
Lwh
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
N(n-1)(n-2)...(2)(1) = n!

10. independence of two events E and F
Opposite angles formed by two intersecting lines; always congruent
101010
P(E and F) = P(E)P(F)
1 - 2 - root(3); note that this is half of an equilateral triangle

11. area of rectangle
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
The sum of the areas of the six faces: 2(lw + lh + wh)
Last two digits (taken together) are divisible by 4

12. volume of cylinder
Rules for 2 and three: even and the sum of its digits is divisible by three
Pi*r^2h
Any line connecting two points on a circle. The diameter is a chord
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

13. union of sets A and B
Side opposite the right angle
A + B - their intersection
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
(x^a)/(y^a)

14. x^-a
Three sides congruent - two sides and included angle - two angles and included side
2(pir^2) + 2pirh; the two bases and the side
1/x^a
1 - 1 - root(2)

15. how many triangles can a polygon of n sides be divided into?
P(E) + P(F) - P(E and F)
N-2
x^ab
Sum of its digits is divisible by 9

16. advantage of median
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.
Less affected by outliers than the mean
1098 etc

17. x^0
1
N!/k!(n-k)! which is also denotes as n choose k
A + B - their intersection
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

18. 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
1/x^a
x^ab
Opposite angles formed by two intersecting lines; always congruent

19. divisible by 6
x^(a-b) or a/x^(b-a)
1/2 base * height
|S|
Rules for 2 and three: even and the sum of its digits is divisible by three

20. what'S the median if there are an even number of data points?
1
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
The sum of the areas of the six faces: 2(lw + lh + wh)

21. difference between normal or population standard deviation and the sample standard deviation
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
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
P(E or F) = P(E) + P(F)

22. sum of relative frequencies in a frequency distribution
N!/k!(n-k)! which is also denotes as n choose k
Pi*r^2h
1 if decimals - 100 if percents
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

23. relationship between n choose k and n choose n-k
N!/k!(n-k)! which is also denotes as n choose k
Always equal - i.e. 9 choose 3 = 9 choose 6
Base * height
Mean of the two middle ones

24. chord
Side opposite the right angle
A + B - their intersection
Any line connecting two points on a circle. The diameter is a chord
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

25. (x^a)(x^b)
Lwh
Opposite angles formed by two intersecting lines; always congruent
Pi*r^2h
x^(a+b)

26. area of trapezoid
x^ab
|S|
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
N!/k!(n-k)! which is also denotes as n choose k

27. area of cylinder
Number of outcomes yielding E / number of total outcomes
2(pir^2) + 2pirh; the two bases and the side
N!/k!(n-k)! which is also denotes as n choose k
Side opposite the right angle

28. possible combinations of three digits allowing repeats
(xy)^a
101010
1 - 2 - root(3); note that this is half of an equilateral triangle
Number of outcomes yielding E / number of total outcomes

29. differences between a set and a list
A list is ordered and can have duplicates
(xy)^a
x^ab
Lwh

30. (x/y)^a
(x^a)/(y^a)
Mean of the two middle ones
Lwh
101010

31. sides of 30/60/90 triangle
At least two congruent sides; the angles opposite these sides are also congruent
101010
2pi*r
1 - 2 - root(3); note that this is half of an equilateral triangle

32. (x^a)^b
N(n-1)(n-2)...(2)(1) = n!
x^ab
(n-2)(180 degrees)
Any line connecting two points on a circle. The diameter is a chord

33. divisible by 8
Last three digits (taken together) are divisible by 8
(n-2)(180 degrees)
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

34. divisible by 3
Sum of its digits is divisible by 3
x^(a+b)
Pi*r^2h
(x^a)/(y^a)

35. dividing fractions
(xy)^a
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Invert the second fraction and multiply them
Last three digits (taken together) are divisible by 8

36. number of elements in set S
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(pir^2) + 2pirh; the two bases and the side
Last two digits (taken together) are divisible by 4
|S|

37. probability of an event E
Number of outcomes yielding E / number of total outcomes
All its interior angles are congruent
Always equal - i.e. 9 choose 3 = 9 choose 6
Invert the second fraction and multiply them

38. hypotenuse
Last three digits (taken together) are divisible by 8
(xy)^a
Side opposite the right angle
A + B - their intersection

39. possible combinations of three digits without allowing repeats
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
1098 etc
At least two congruent sides; the angles opposite these sides are also congruent
Pi * r^2

40. (x^a)(y^a)
1098 etc
Number of outcomes yielding E / number of total outcomes
(xy)^a
1 - 2 - root(3); note that this is half of an equilateral triangle

41. divisible by 9
Lwh
Sum of its digits is divisible by 9
N!/(n-k)!
N(n-1)(n-2)...(2)(1) = n!

42. (x^a)/(x^b)
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
Sum of its digits is divisible by 9
101010
x^(a-b) or a/x^(b-a)

43. vertical angles
Sum of its digits is divisible by 9
2(pir^2) + 2pirh; the two bases and the side
Opposite angles formed by two intersecting lines; always congruent
N-2

44. probability that either E or F occur
1 if decimals - 100 if percents
N(n-1)(n-2)...(2)(1) = n!
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) + P(F) - P(E and F)

45. congruency of triangles
1
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1/2 base * height
Three sides congruent - two sides and included angle - two angles and included side

46. divisible by 4
Last two digits (taken together) are divisible by 4
Any line connecting two points on a circle. The diameter is a chord
Opposite angles formed by two intersecting lines; always congruent
Sum of its digits is divisible by 9

47. permutations of n objects taken k at a time (order counts)
Three sides congruent - two sides and included angle - two angles and included side
N!/(n-k)!
A + B - their intersection
2pi*r

48. area of circle
A + B - their intersection
All its interior angles are congruent
Pi * r^2
Rules for 2 and three: even and the sum of its digits is divisible by three

49. circumference of circle
2pi*r
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
2(pir^2) + 2pirh; the two bases and the side
N-2

50. similar triangles
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
(xy)^a
101010