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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. congruency of triangles
All its interior angles are congruent
1
Sum of its digits is divisible by 3
Three sides congruent - two sides and included angle - two angles and included side

2. sum of measures of interior angles of a polygon with n sides
2(pir^2) + 2pirh; the two bases and the side
Lwh
Pi * r^2
(n-2)(180 degrees)

3. x^0
A + B - their intersection
1
Any line connecting two points on a circle. The diameter is a chord
P(E and F) = P(E)P(F)

4. area of cylinder
P(E and F) = P(E)P(F)
2(pir^2) + 2pirh; the two bases and the side
P(E) + P(F) - P(E and F)
Invert the second fraction and multiply them

5. union of sets A and B
Last two digits (taken together) are divisible by 4
Less affected by outliers than the mean
A + B - their intersection
(x^a)/(y^a)

6. similar triangles
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Less affected by outliers than the mean
(n-2)(180 degrees)
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

7. x^-a
Base * height
Lwh
1/x^a
Sum of its digits is divisible by 9

8. volume of cylinder
1098 etc
The sum of the areas of the six faces: 2(lw + lh + wh)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi*r^2h

9. (x/y)^a
Three sides congruent - two sides and included angle - two angles and included side
Always equal - i.e. 9 choose 3 = 9 choose 6
A + B - their intersection
(x^a)/(y^a)

10. dividing fractions
Invert the second fraction and multiply them
1
Pi * r^2
N-2

11. (x^a)(x^b)
Lwh
|S|
x^(a+b)
1/x^a

12. how many triangles can a polygon of n sides be divided into?
1 - 2 - root(3); note that this is half of an equilateral triangle
Lwh
1/2 base * height
N-2

13. divisible by 8
Last three digits (taken together) are divisible by 8
A list is ordered and can have duplicates
Less affected by outliers than the mean
P(E or F) = P(E) + P(F)

14. what'S the median if there are an even number of data points?
1/x^a
2pi*r
Mean of the two middle ones
Opposite angles formed by two intersecting lines; always congruent

15. 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
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
N!/(n-k)!

16. divisible by 11
Side opposite the right angle
P(E or F) = P(E) + P(F)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
N-2

17. 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.
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1/2 base * height
(n-2)(180 degrees)

18. possible combinations of three digits allowing repeats
(n-2)(180 degrees)
101010
Pi * r^2
(xy)^a

19. number of elements in set S
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
|S|
Mean of the two middle ones
At least two congruent sides; the angles opposite these sides are also congruent

20. area of rectangle
N(n-1)(n-2)...(2)(1) = n!
Lwh
The sum of the areas of the six faces: 2(lw + lh + wh)
Subtract the mean from each value and divide by the standard deviation

21. permutations of n different objects
Any line connecting two points on a circle. The diameter is a chord
Last two digits (taken together) are divisible by 4
N(n-1)(n-2)...(2)(1) = n!
1 - 1 - root(2)

22. permutations of n objects taken k at a time (order counts)
Last three digits (taken together) are divisible by 8
101010
N!/k!(n-k)! which is also denotes as n choose k
N!/(n-k)!

23. sides of isoceles right triangle
1098 etc
Last three digits (taken together) are divisible by 8
1 - 1 - root(2)
Mean of the two middle ones

24. possible combinations of three digits without allowing repeats
N(n-1)(n-2)...(2)(1) = n!
1098 etc
P(E and F) = P(E)P(F)
x^ab

25. relationship between n choose k and n choose n-k
Pi*r^2h
Always equal - i.e. 9 choose 3 = 9 choose 6
(x^a)/(y^a)
(n-2)(180 degrees)

26. independence of two events E and F
Last three digits (taken together) are divisible by 8
(xy)^a
1
P(E and F) = P(E)P(F)

27. advantage of median
1
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Less affected by outliers than the mean
Mean of the two middle ones

28. regular polygon
Invert the second fraction and multiply them
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
x^(a-b) or a/x^(b-a)
All its interior angles are congruent

29. length of arc of circle
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Subtract the mean from each value and divide by the standard deviation
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
x^(a-b) or a/x^(b-a)

30. divisible by 3
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
1 if decimals - 100 if percents
Sum of its digits is divisible by 3
N-2

31. vertical angles
1/x^a
1
Opposite angles formed by two intersecting lines; always congruent
N!/k!(n-k)! which is also denotes as n choose k

32. (x^a)/(x^b)
101010
x^(a-b) or a/x^(b-a)
1
Base * height

33. divisible by 6
(xy)^a
P(E) + P(F) - P(E and F)
Mean of the two middle ones
Rules for 2 and three: even and the sum of its digits is divisible by three

34. chord
2(pir^2) + 2pirh; the two bases and the side
Side opposite the right angle
Any line connecting two points on a circle. The diameter is a chord
A list is ordered and can have duplicates

35. mutually exclusive
2(pir^2) + 2pirh; the two bases and the side
P(E or F) = P(E) + P(F)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

36. divisible by 9
Sum of its digits is divisible by 9
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
Base * height

37. how to tell if something is prime
1 if decimals - 100 if percents
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
At least two congruent sides; the angles opposite these sides are also congruent
Mean of the two middle ones

38. area of parallelogram
2pi*r
Invert the second fraction and multiply them
Base * height
|S|

39. sides of 30/60/90 triangle
P(E) + P(F) - P(E and F)
N!/k!(n-k)! which is also denotes as n choose k
1098 etc
1 - 2 - root(3); note that this is half of an equilateral triangle

40. 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.
x^(a-b) or a/x^(b-a)
2(pir^2) + 2pirh; the two bases and the side
|S|

41. (x^a)(y^a)
(xy)^a
Number of outcomes yielding E / number of total outcomes
P(E or F) = P(E) + P(F)
Pi * r^2

42. area of trapezoid
P(E and F) = P(E)P(F)
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.
Always equal - i.e. 9 choose 3 = 9 choose 6

43. sum of relative frequencies in a frequency distribution
Any line connecting two points on a circle. The diameter is a chord
Always equal - i.e. 9 choose 3 = 9 choose 6
Three sides congruent - two sides and included angle - two angles and included side
1 if decimals - 100 if percents

44. circumference of circle
2pi*r
Sum of its digits is divisible by 9
Any line connecting two points on a circle. The diameter is a chord
Base * height

45. differences between a set and a list
P(E or F) = P(E) + P(F)
A list is ordered and can have duplicates
The sum of the areas of the six faces: 2(lw + lh + wh)
Pi * r^2

46. hypotenuse
Sum of its digits is divisible by 3
1 - 2 - root(3); note that this is half of an equilateral triangle
1 if decimals - 100 if percents
Side opposite the right angle

47. divisible by 4
Last two digits (taken together) are divisible by 4
Less affected by outliers than the mean
1/x^a
Base * height

48. volume of rectangle
Lwh
(x^a)/(y^a)
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
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

49. isosceles triangle
Pi * r^2
Subtract the mean from each value and divide by the standard deviation
1/2 base * height
At least two congruent sides; the angles opposite these sides are also congruent

50. standardization/normalization
Sum of its digits is divisible by 9
Pi*r^2h
Subtract the mean from each value and divide by the standard deviation
101010