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Volume of an Ellipsoid:. 4. V = r 1 r 2 r 3. 3. Distance from a point to a line. |am + bn + c| . d = . a 2 + b 2. Area of an ellipse. A = r 1 r 2. # of integral divisors if a n b m c p = #. (n+1)(m+1)(p+1). # of relatively prime numbers a n b m c p = #. 1. 1.
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Volume of an Ellipsoid: 4 V= r1r2r3 3
Distance from a point to a line |am + bn + c| d = a2 + b2
Area of an ellipse A = r1r2
# of integral divisors if anbmcp = # (n+1)(m+1)(p+1)
# of relatively prime numbersanbmcp = # 1 1 n(1- )(1- ) Prime factor Prime factor
Sum of integral divisors if anbmcp = # (a0+a1+a2…)(b0+b1+b2…)(c0+c1+c2…)
Arithmetic mean of two numbers x + y 2
Harmonic mean of two numbers 2xy x + y
Area of any polygon given the vertices Shoelace theorem
The internal diagonal is 6, what is the side of the cube? 6 3
The side of a cube is 3, what is the length of the internal diagonal? 3 3
The hypotenuse of a 30-60-90 triangle is 18, what is the length of the shorter side of the triangle? 9
Doing a job together xy x + y
Pythagorean Theorem a2 + b2 = c2
Domain x values
A B C D E Which one is the Median? C
A B C D E Which one is the Lower Extreme? A
A B C D E Which one is the Upper Extreme? E
A B C D E Which one is the Upper Quartile? D
A B C D E Which one is the Lower Quartile? B
Degree of an angle with hour hand H and minute hand M 1 | (60H – 11M)| 2
In a box and Whiskers graph how do you find the lower boundary? Lower quartile – 1.5 x IQR
In a box and Whiskers graph how you find the IQR? Upper quartile – Lower quartile
Range y values
The short side of a 30-60-90 triangle is 12, what is the length of the hypotenuse of the triangle? 24
Order doesn’t matter combinations
The short side of a 30-60-90 triangle is 12, what is the length of the longer side of the triangle? 12 3
Sin opposite hypotenuse
CSC hypotenuse opposite
Cos adjacent hypotenuse
Sec hypotenuse adjacent
Tan opposite adjacent
Cot adjacent opposite
Law of Sines Sin A Sin C Sin B = = a c b
Order matter permutation
Largest unattainable sum mn – (m+n)
Slope of a line given two points y1 – y2 x1 – x2
Combinations formula n! r!(n-r)!
permutations formula n! (n-r)!