GRE Math Flashcards
0!
1
First ten prime numbers
2 3 5 7 11
13 17 19 23 29
Percent increase or decrease
% change = delta/initial
then convert to a percent
Is 0 even or odd?
Even
Interest equation
I = prt
principle * rate * time
Work rate equation
1/(rate a) + 1/(rate b) = 1/(rate combined)
Permutation equation (no repetition)
P(n,r) = n!/(n-r)!
order matters
Combination equation
No repetition
C(n,r) = n!/r!(n-r)!
order doesn’t matter
Alternate angles
Inside of Z shape. Aka alternate interior angles.
Independent successive choices equation
Just multiply
Find the standard deviation (5 steps)
- Find the mean.
- For each data point, square the difference between the point and the mean.
- Find the sum of all step 2s.
- Variance = step 3 / number of data points.
- Standard deviation = square root of variance.
Divisibility rules for 3 4 6 9
3: sum of digits is divisible by 3
4: last two digits is divisible by 4
6: is divisible by 2 and 3
9: sum of digits is divisible by 9
x^2 - y^2 =
x^2 - y^2 = (x+y)(x-y)
(x+y)(x-y) =
(x+y)(x-y) = x^2 - y^2
Sum of positive integers from 1 through n
= n(n+1) / 2
Numbers to test in quantitative comparisons
0 1 2 -2 1/2
Congruent shapes vs. similar shapes
Congruent shapes: same shape, may be rotated
Similar shapes: same shape, may be different size
Vertical angles
Opposite each other, and are congruent.
Corresponding angles
Are congruent, in same location on two parallel lines.
Interior angles
On the same side as the transversal, are supplementary.
Complementary angles
Sum = 90
Supplementary angles
Sum = 180
Area of circle
A = pi * r^2
Circumference of circle
C = 2 * pi * r
Area of a sector of a circle
A = (sector angle/360) * (A of circle)
Ratio of sides in a 45-45-90 isosceles right triangle
1 : 1 : sqrt(2)
Ratio of sides in a 30-60-90 right triangle
1 : sqrt(3) : 2
Area of a parallelogram
A = bh
Area of a trapezoid
A = 1/2 * (b1 + b2) * h
Sum of a polygon’s interior angles
= 180*(n-2)
sqrt(x) * sqrt(y) =
sqrt(x) * sqrt(y) = sqrt(xy)
sqrt(xy) =
sqrt(xy) = sqrt(x) * sqrt(y)
sqrt(x) / sqrt(y) =
sqrt(x) / sqrt(y) = sqrt(x/y)
sqrt(x/y) =
sqrt(x/y) = sqrt(x) / sqrt(y)
Length of a triangle side compared to the other two sides
Difference of other two < L < sum of other two
Distance formula
d = sqrt[ (x-a)^2 + (y-b)^2 ]
Midpoint formula
M = [ (x+a)/2 , (y+b)/2 ]
Either-or probabilities
Just add (as long as events are independent)
Geometric probability
Desired area / total area
Definition of standard deviation
How much the numbers in a set vary from the set’s mean
Permutation with repetition formula
P(n,r) = n^r
Steps for approaching permutation/combination problems
- Permutation or combination?
- Repetitions allowed?
- Indistinguishable objects in base set?
Permutations with k indistinguishable objects
P / k!
P / (k! m!)
Solving absolute value inequalities
|x|>y
x>y
or
x<(-y)
x^a • x^b =
x^a • x^b = x^(a+b)
(x^a)^b =
(x^a)^b = x^(ab)
(xy)^a =
(xy)^a = x^a • y^a
(x/y)^a =
(x/y)^a = (x^a)/(y^a)
Solving higher order inequalities
For what values of x is x^2>-6x-5
- Replace > or < with =
- Solve for x. Those are the places on the number line where the expression changes sign.
- Test values in those intervals.
- Convert this to an inequality.
Sqrt(2)
1.4
Sqrt(3)
1.7
Normal distribution/ bell curve
Within 1 SD: 68%
Within 2 SD: 96%
(2% 14% 34% 34% 14% 2%)
