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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. x^0
(n-2)(180 degrees)
x^ab
(xy)^a
1

2. sum of relative frequencies in a frequency distribution
Rules for 2 and three: even and the sum of its digits is divisible by three
Opposite angles formed by two intersecting lines; always congruent
1 if decimals - 100 if percents
1 - 1 - root(2)

3. divisible by 6
A + B - their intersection
1/x^a
1 if decimals - 100 if percents
Rules for 2 and three: even and the sum of its digits is divisible by three

4. x^-a
x^ab
A + B - their intersection
1 - 2 - root(3); note that this is half of an equilateral triangle
1/x^a

5. (x^a)(y^a)
Base * height
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
A + B - their intersection
(xy)^a

6. probability of an event E
x^ab
Always equal - i.e. 9 choose 3 = 9 choose 6
(xy)^a
Number of outcomes yielding E / number of total outcomes

7. (x^a)^b
(x^a)/(y^a)
x^ab
101010
A + B - their intersection

8. hypotenuse
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Side opposite the right angle
|S|
Pi * r^2

9. divisible by 11
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
x^(a-b) or a/x^(b-a)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Number of outcomes yielding E / number of total outcomes

10. dividing fractions
(x^a)/(y^a)
Invert the second fraction and multiply them
Pi*r^2h
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

11. 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.
Pi * r^2
1 - 1 - root(2)

12. difference between normal or population standard deviation and the sample standard deviation
P(E and F) = P(E)P(F)
2pi*r
(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

13. independence of two events E and F
Side opposite the right angle
x^(a+b)
P(E or F) = P(E) + P(F)
P(E and F) = P(E)P(F)

14. volume of rectangle
Lwh
Mean of the two middle ones
P(E or F) = P(E) + P(F)
Base * height

15. length of arc of circle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
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
Rules for 2 and three: even and the sum of its digits is divisible by three

16. divisible by 3
P(E and F) = P(E)P(F)
1 if decimals - 100 if percents
Sum of its digits is divisible by 3
101010

17. how many triangles can a polygon of n sides be divided into?
N-2
Always equal - i.e. 9 choose 3 = 9 choose 6
Last two digits (taken together) are divisible by 4
Mean of the two middle ones

18. possible combinations of three digits without allowing repeats
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
101010
1098 etc
A + B - their intersection

19. (x/y)^a
Sum of its digits is divisible by 3
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
(x^a)/(y^a)
Less affected by outliers than the mean

20. congruency of triangles
A + B - their intersection
Three sides congruent - two sides and included angle - two angles and included side
Last two digits (taken together) are divisible by 4
Base * height

21. area of circle
1 if decimals - 100 if percents
A list is ordered and can have duplicates
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Pi * r^2

22. union of sets A and B
1
At least two congruent sides; the angles opposite these sides are also congruent
x^(a+b)
A + B - their intersection

23. possible combinations of three digits allowing repeats
N(n-1)(n-2)...(2)(1) = n!
101010
2pi*r
(n-2)(180 degrees)

24. differences between a set and a list
1 - 2 - root(3); note that this is half of an equilateral triangle
Sum of its digits is divisible by 9
N!/(n-k)!
A list is ordered and can have duplicates

25. permutations of n different objects
2pi*r
1 if decimals - 100 if percents
N(n-1)(n-2)...(2)(1) = n!
A list is ordered and can have duplicates

26. area of sector of circle
A + B - their intersection
(xy)^a
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

27. sides of isoceles right triangle
Last two digits (taken together) are divisible by 4
1 - 1 - root(2)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1 if decimals - 100 if percents

28. isosceles triangle
(n-2)(180 degrees)
101010
Sum of its digits is divisible by 3
At least two congruent sides; the angles opposite these sides are also congruent

29. number of elements in set S
Last two digits (taken together) are divisible by 4
|S|
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Less affected by outliers than the mean

30. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
Opposite angles formed by two intersecting lines; always congruent
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
(n-2)(180 degrees)

31. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
(xy)^a
N!/(n-k)!
Any line connecting two points on a circle. The diameter is a chord

32. area of parallelogram
Base * height
Pi*r^2h
1 if decimals - 100 if percents
Rules for 2 and three: even and the sum of its digits is divisible by three

33. mutually exclusive
Lwh
1/2 base * height
P(E or F) = P(E) + P(F)
Last two digits (taken together) are divisible by 4

34. 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
1 if decimals - 100 if percents
Subtract the mean from each value and divide by the standard deviation

35. 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.
1098 etc
101010
The sum of the areas of the six faces: 2(lw + lh + wh)

36. advantage of median
Less affected by outliers than the mean
2pi*r
P(E and F) = P(E)P(F)
At least two congruent sides; the angles opposite these sides are also congruent

37. divisible by 9
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
N!/(n-k)!
Sum of its digits is divisible by 9

38. sides of 30/60/90 triangle
N!/(n-k)!
x^(a-b) or a/x^(b-a)
1 - 2 - root(3); note that this is half of an equilateral triangle
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

39. what'S the median if there are an even number of data points?
Mean of the two middle ones
1 if decimals - 100 if percents
|S|
Last two digits (taken together) are divisible by 4

40. area of trapezoid
2pi*r
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
1098 etc

41. (x^a)/(x^b)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Last two digits (taken together) are divisible by 4
x^(a-b) or a/x^(b-a)

42. sum of measures of interior angles of a polygon with n sides
(n-2)(180 degrees)
N(n-1)(n-2)...(2)(1) = n!
Sum of its digits is divisible by 9
Opposite angles formed by two intersecting lines; always congruent

43. probability that either E or F occur
(x^a)/(y^a)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
2pi*r
P(E) + P(F) - P(E and F)

44. volume of cylinder
A list is ordered and can have duplicates
Pi*r^2h
(x^a)/(y^a)
101010

45. divisible by 4
A list is ordered and can have duplicates
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1098 etc
Last two digits (taken together) are divisible by 4

46. (x^a)(x^b)
1 - 1 - root(2)
N(n-1)(n-2)...(2)(1) = n!
A + B - their intersection
x^(a+b)

47. area of triangle
1/2 base * height
Base * height
Sum of its digits is divisible by 3
Number of outcomes yielding E / number of total outcomes

48. vertical angles
N-2
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Opposite angles formed by two intersecting lines; always congruent
Mean of the two middle ones

49. similar triangles
N-2
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
All its interior angles are congruent

50. chord
Sum of its digits is divisible by 9
Any line connecting two points on a circle. The diameter is a chord
Opposite angles formed by two intersecting lines; always congruent
Pi*r^2h