Math Flashcards
degrees in a triangle (if you add all three angles)
180
How to recognize a multiple of 3
Sum of all the digits is a multiple of 3
How to recognize a multiple of 4
Last 2 digits are a multiple of 4
How to recognize a multiple of 9
Sum of all the digits is a multiple of 9
Mean, Median, Mode
Mean = average
Median = middle number
Mode = most common number
Trick for finding mean of consecutive numbers
Find mean (or average) of the lowest and highest numbers
Trick for finding sum of consecutive numbers
Remember that the average is the sum divided by number of terms (so sum is average times number of terms)
Use average of lowest and highest numbers to find average of the whole set
Number of terms is (high-low+1)
Factor this into 2 binomials:
a(squared) + 2ab + b(squared)
(a + b) (squared)
Factor this into 2 binomials:
a(squared) - 2ab + b(squared)
(a - b) (squared)
Factor this into 2 binomials:
a(squared) - b(squared)
(a - b) (a + b)
How many degrees along a straight line (if you add up all the angles)?
180
Area of a triangle
1/2 (base) (height)
Isosceles triangle
2 sides are the same (which means that 2 angles are also the same)
Equilateral triangle
All 3 sides are the same, and each angle is 60 degrees
Similar triangles
In 2 “similar triangles”, their angles are identical and the sides are proportional
(Ex: If you double one side to produce the 2nd triangle, you’ll double each of the other sides too)
Pythagorean theorem (for right triangles)
a(squared) + b(squared) = c(squared)
Special right triangles:
Sides 3:4:__
or
Sides 5:12:__
Sides 3:4:5
or
Sides 5:12:13
Special right triangles: Trick for finding sides of a triangle with angles 30:60:90 degrees
If short leg is x…
Long leg is x(square root of 3)
Hypotenuse is 2x
Special right triangles: Trick for finding sides of a triangle with angles 45:45:90 degrees
If each leg is x…
Hypotenuse is x(square root of 2)
Area of a parallelogram
Area = (base) (height)
Area of a trapezoid
Area = (average of parallel sides) (height)
Circumference of a circle
2(pi)(r)
Area of a circle
(pi)(r squared)
Slope of a line
Rise / Run
Simple interest formula
Interest = Principle(r)(t)
Compound interest formula
Final balance = (Principle) x (1 + interest rate/c) (exponent t times c)
(c is number of times the interest is compounded annually)
Combined work formula
(ex: If I work at this speed and you work at this speed, how long does it take with both of us working on it?)
(1/my time) + (1/your time) = (1/our time)
Overlapping data sets
(Ex: __ students studying spanish, __ studying french, __ studying neither; how many studying both?)
Group 1 + Group 2 + neither - both = Total
4!
4 x 3 x 2 x 1
0!
1
Permutation vs. Combination
Order matters in a permutation; use logic to multiply out the number of possible outcomes
(Ex: how many possibilities of runners coming in first, second, and third in a race)
A combination is just pulling a subgroup from a larger group, and order doesn’t matter; use the combination formula
(Ex: how many possible groups of 3 staff members to be on a committee)
Combination formula
C = n! / (k! (n-k)!)
N is number in the larger group
K is number you’re choosing
Standard deviation
Measure of how much the numbers in a set deviate from the mean
0 raised to an exponent
0
x raised to the exponent 1/2
square root of x
Side lengths of a 30-60-90 triangle
x, x times square root of 3, 2x
Side lengths of a 45-45-90 triangle
x, x, x times square root of 2
Sum of angles in a polygon
(n-2)(180)
n is number of sides
Sum of angles in a triangle
180
Congruent vs similar shapes
Congruent shapes have the same side lengths and angles (they can be mapped onto each other with just rotating, reflection, and/or translation)
Similar shapes have the same angles but can be different sizes (dilation is also allowed when trying to map them onto each other)
Area of a parallelogram
A = base (height)
Area of a trapezoid
A = (average length of the two parallel lines) (height)
Value of pi
About 3.14 (or to get closer, can use fraction 22/7)
Volume of a cylindar
V = pi (r squared) (height)
