Test your basic knowledge |

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 rectangle
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
Sum of its digits is divisible by 9
The sum of the areas of the six faces: 2(lw + lh + wh)

2. divisible by 3
101010
Sum of its digits is divisible by 3
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
1 - 1 - root(2)

3. area of parallelogram
x^(a+b)
Base * height
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
(x^a)/(y^a)

4. area of trapezoid
Number of outcomes yielding E / number of total outcomes
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
All its interior angles are congruent

5. independence of two events E and F
|S|
At least two congruent sides; the angles opposite these sides are also congruent
P(E and F) = P(E)P(F)
(x^a)/(y^a)

6. (x^a)^b
|S|
P(E) + P(F) - P(E and F)
x^(a-b) or a/x^(b-a)
x^ab

7. circumference of circle
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
(n-2)(180 degrees)
1 - 1 - root(2)

8. regular polygon
2(pir^2) + 2pirh; the two bases and the side
All its interior angles are congruent
Base * height
101010

9. sum of relative frequencies in a frequency distribution
P(E or F) = P(E) + P(F)
At least two congruent sides; the angles opposite these sides are also congruent
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1 if decimals - 100 if percents

10. advantage of median
A list is ordered and can have duplicates
2(pir^2) + 2pirh; the two bases and the side
1/x^a
Less affected by outliers than the mean

11. chord
|S|
Last two digits (taken together) are divisible by 4
N!/k!(n-k)! which is also denotes as n choose k
Any line connecting two points on a circle. The diameter is a chord

12. dividing fractions
A list is ordered and can have duplicates
Number of outcomes yielding E / number of total outcomes
P(E and F) = P(E)P(F)
Invert the second fraction and multiply them

13. x^-a
Number of outcomes yielding E / number of total outcomes
1/x^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

14. x^0
101010
1
|S|
N!/k!(n-k)! which is also denotes as n choose k

15. what'S the median if there are an even number of data points?
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
Less affected by outliers than the mean
Mean of the two middle ones

16. volume of rectangle
N!/(n-k)!
Lwh
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Number of outcomes yielding E / number of total outcomes

17. vertical angles
Last two digits (taken together) are divisible by 4
P(E) + P(F) - P(E and F)
Less affected by outliers than the mean
Opposite angles formed by two intersecting lines; always congruent

18. divisible by 9
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
P(E and F) = P(E)P(F)
1
Sum of its digits is divisible by 9

19. permutations of n different objects
Less affected by outliers than the mean
N-2
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
N(n-1)(n-2)...(2)(1) = n!

20. how many triangles can a polygon of n sides be divided into?
All its interior angles are congruent
2pi*r
1098 etc
N-2

21. divisible by 6
Three sides congruent - two sides and included angle - two angles and included side
Rules for 2 and three: even and the sum of its digits is divisible by three
(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

22. hypotenuse
Any line connecting two points on a circle. The diameter is a chord
|S|
Side opposite the right angle
x^ab

23. sum of measures of interior angles of a polygon with n sides
Sum of its digits is divisible by 9
N!/k!(n-k)! which is also denotes as n choose k
(n-2)(180 degrees)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

24. (x^a)(x^b)
N!/(n-k)!
x^(a+b)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
|S|

25. divisible by 11
Pi * r^2
Base * height
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

26. area of triangle
Rules for 2 and three: even and the sum of its digits is divisible by three
1
Any line connecting two points on a circle. The diameter is a chord
1/2 base * height

27. area of a non-right triangle
x^ab
P(E or F) = P(E) + P(F)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

28. possible combinations of three digits without allowing repeats
Any line connecting two points on a circle. The diameter is a chord
2(pir^2) + 2pirh; the two bases and the side
1098 etc
Rules for 2 and three: even and the sum of its digits is divisible by three

29. how to tell if something is prime
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1
1/x^a

30. relationship between n choose k and n choose n-k
Rules for 2 and three: even and the sum of its digits is divisible by three
Always equal - i.e. 9 choose 3 = 9 choose 6
N-2
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

31. sides of 30/60/90 triangle
1 - 2 - root(3); note that this is half of an equilateral triangle
P(E) + P(F) - P(E and F)
x^(a-b) or a/x^(b-a)
2pi*r

32. area of cylinder
Pi*r^2h
x^(a+b)
Sum of its digits is divisible by 3
2(pir^2) + 2pirh; the two bases and the side

33. volume of cylinder
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Pi * r^2
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi*r^2h

34. divisible by 8
Last three digits (taken together) are divisible by 8
2pi*r
(n-2)(180 degrees)
Any line connecting two points on a circle. The diameter is a chord

35. probability that either E or F occur
1098 etc
Side opposite the right angle
P(E) + P(F) - P(E and F)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

36. divisible by 4
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
A list is ordered and can have duplicates
Last two digits (taken together) are divisible by 4

37. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
P(E) + P(F) - P(E and F)
1 - 2 - root(3); note that this is half of an equilateral triangle
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

38. similar triangles
1 if decimals - 100 if percents
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
Opposite angles formed by two intersecting lines; always congruent

39. differences between a set and a list
A list is ordered and can have duplicates
(n-2)(180 degrees)
Last two digits (taken together) are divisible by 4
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

40. number of elements in set S
P(E) + P(F) - P(E and F)
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
|S|

41. possible combinations of three digits allowing repeats
2(pir^2) + 2pirh; the two bases and the side
2pi*r
1/2 base * height
101010

42. sides of isoceles right triangle
101010
P(E and F) = P(E)P(F)
1 - 1 - root(2)
P(E) + P(F) - P(E and F)

43. isosceles triangle
Sum of its digits is divisible by 3
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
101010
At least two congruent sides; the angles opposite these sides are also congruent

44. area of circle
2pi*r
1 if decimals - 100 if percents
Pi * r^2
(n-2)(180 degrees)

45. probability of an event E
Pi*r^2h
Number of outcomes yielding E / number of total outcomes
(n-2)(180 degrees)
N!/k!(n-k)! which is also denotes as n choose k

46. length of arc of circle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Last three digits (taken together) are divisible by 8
1098 etc
Invert the second fraction and multiply them

47. congruency of triangles
Invert the second fraction and multiply them
Three sides congruent - two sides and included angle - two angles and included side
At least two congruent sides; the angles opposite these sides are also congruent
Sum of its digits is divisible by 3

48. area of sector of circle
Any line connecting two points on a circle. The diameter is a chord
x^(a-b) or a/x^(b-a)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
1 - 2 - root(3); note that this is half of an equilateral triangle

49. combinations of n objects taken k at a time (order doesn'T count)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N!/k!(n-k)! which is also denotes as n choose k
Mean of the two middle ones
1 - 2 - root(3); note that this is half of an equilateral triangle

50. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
Base * height
Less affected by outliers than the mean
A + B - their intersection