TMSCA Calculator Formulas

Geometric Mean

√ab

Harmonic Mean

1/((1/a + 1/b . .)/n)

Arithmic Mean

(a + b . . )/n

Combinations

n!/(n! - R)!(R!)

Permutations

n!/(n-R)!

Compound Interest

A=Principle(1+rate/number)∧number*time

Simple Interest

I = Principleratetime

Sum of roots of a Quadratic Equation

S = -b/a

Product of roots of a Quadratic Equation

P = c/a

Discriminate of a Quadratic Equation

b² - 4ac

Slope Formula

(y₂-y₁)/(x₂-x₁)

Distance Formula

d=√(x₂-x₁)²+(y₂-y₁)²

Area of a polygon

A = perimeter²/(tan(180/n))4n

Longest diagonal of a polygon (even sides)

Length/sin(180/n)

Longest diagonal of a polygon (odd sides)

Length/2sin(90/n)

Linear pair

x + y = 180

mid-range

(a+b)/2

a gross

144

baker's dozen

13

leap year

366 days

triangular number

n(n+1)/2

hexagonal number

n(2n-1)

pentagonal number

n(3n-1)/2

Inner diagonal of a cube

s√3

Inner diagonal of a rectangular prism

√l²+w²+h²

Area of ellipse

π(major axis/2)(minor axis/2)

Area of annulus

πR²-πr²

Surface area of a tetrahedron

√3 * e²

Surface area of a cube using inner diagonal

2d²

Volume of a cube using inner diagonal

(√3*d³)/9

Surface area of a sphere

4πr²

Area of rhombus using diagonals

(d₁*d₂)/2

Area of regular hexagon using edge

(3√3)/2 * e²

Area of an equilateral triangle using height

(h²√3)/3

Area of a sector

(θ/360)πr²

area of a scalene triangle with two sides and one angle

(1/2)a*b(SinC)

Area of a scalene triangle with three sides

s = (a+b+c)/2, and then √s(s-a)(s-b)(s-c)

Law of Cosines (to find angle X using three sides)

c²=a²+b²-2ab(cos C)

Law of Sines

sin∠A/a=sin∠B/b=sin∠C/c

inclusive

includes the starting and ending point of a set of numbers

exclusive

includes all numbers between the starting and ending point of a set of numbers (does not include starting and ending point)

weighted average

= (Gr1 avg*#)+(Gr2 avg*#)÷Gr1#+Gr2#

percentage on acid solution questions

%(1st) * %(2nd) = %(1st + 2nd)

additive inverse

the value when added to its original, results in zero. Ex. -7+7=10

reciprocal

the number by which another number can be multiplied to produce 1, if you have a fraction its reciprocal is that fraction turned upside down

amount of square feet in a square yard

9 ft

amount of square inches in a square foot

144 in

Calculating final temperature of a mixture

(m1T1+m2T2)/(m1+m2)

Diagonal of a Cube

s√3

30-60-90 triangle special rules

shorter leg: x longer leg: x√3 hypotenuse: 2x

45-45-90 triangle special rules

two congruent legs: x hypotenuse: x√2

Distinct diagonals in a polygon

n(n-3)/2

vertex of a quadratic

-b/2a

speed

s=d/t

Root Mean Square

1. Square all the values

2. Find the mean of all the squared values

3. Square root the mean

Interior angles of a polygon

180(n-2)

Inverse Variation (Seesaw Problems)

y * x = y * x

Direct Variation

y/x = y/x

finding fulcrum of a seesaw

w*d = (total distance-d)*w

speed

s = d/t

distance

d = s*t

time

t = d/s

amount of cubic inches in a gallon

231 in³ = 1 gal

frustum of a cone volume

πh/3 (r²+R²+r*R)

quadratic equation

x=(-b±√b²-4ac)/2a

quadratic function

ax²+bx+c=0

Overflow problems

1. enter exponent

2. enter base number

3. LOG base number

4. multiply exponent and LOGbasenum together

5. gold key, show (digits before the decimal is your exponent, write this down)

6. Enter exponent digits

7. subtract

8. gold key, 10^x (your new base number) new base number x 10^new exponent !WHEN YOU FIND YOUR NEW BASE NUMBER, THE EXPONENT SHOULD SAY ZERO Ex. 1.39 E 0

product of the least common multiple and the greatest common factor

The product of the LCM and the GCF is always the product of the two numbers

Volume of a Frustum of a Cone

1/3(h)(B₁+B₂+√B₁B₂)

Surface Area of a Cone

πr(slant height) + πr²

isoceles triangle

3 sides, two equal sides

equilateral triangle

has three equal sides, each of the angles measures 60°

oblique pyramid

pyramid

base not parallel to ground. Usually calculate the base with 3 sided scalene triangle formula: s = (a+b+c)/2, √s(s-a)(s-b)(s-c)

squares and right triangles

a²+b²+(a)(b)

SOH CAH TOA stands for

SOH = sinθ, opposite/hypotenuse CAH = cosθ, adjacent/hypotenuse TOA = tanθ, opposite/adjacent

How to find feet cubed in a gallon

(231 in³ * gallons) / 12³

How to turn degrees into radians

degrees x (π/180)

How to turn radians into degrees

radians x (180/π)

Fibbonacci Sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

What's the great circle of a sphere

The circle that divides a sphere into two hemispheres