Applied Mathematics Created by: Alex Miller Texas Ranger and, yours truly, Slade Smith

Operations Addition: examples; 1+1=2, 4+7=11 Subtraction: examples; 6-2=4, 8-5=3 Multiplication: examples; 2x8=16, 9x1=9 Division: examples; 27/9=3, 30/3=10

Fractions, Decimals, and Percentages ¼=.25=25% 1/10=.1=10% 3/6=.5=50% 1/1=1=100%

Geometry A square has 4 equal sides with 90 degree angles A triangle has 3 sides and can have varying angles A circle has no sides and round

Trigonometry Functions include Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent. Used to find/analyze lengths and degrees. ((A^2)+(B^2))=(C^2)

Weight Weight=M(mass)xGravity Weight is the force an object applies solely due to gravity.

Measurements 1 mile=5280 feet or kilometers 1 pound= grams 1 kilometer=1000 meters 1 meter=100 centimeters 1 centimeter=10 millimeters

Area Area is the amount of 2 dimensional space. Area of a rectangle=length times height Area of a circle=pi times (radius^2)

Volume Volume is the measure of 3 dimensional space an object occupies. Volume of a rectangle is calculated by length times width times height. Volume of a sphere is four-thirds times pi times the radius cubed.

Scales Scales are in the form of ratios. Example; 1”=5’ o This means, for every 1 inch measured on the model/drawing, that represents 5 feet in reality.

Pitch Pitch is a measurement of steepness. It may also be called: o Gradient o Incline o Angle o Slope

Rise, Run, and Slope Rise is the amount of vertical change between two points. Run is the amount of horizontal change between two points. Slope is the change in two points based upon the rise and run.

Practice 1) What is the length of leg A if leg B is 3 and the Hypotenuse is 5? 2) Interpret the following: 1/16”=1’ 3) What is the area of a rectangle with sides equal to 7 and 9? 4) If the area of a circle is 10, what is the radius of said circle? 5) Find the volume of a sphere with a radius of.3

Practice 6) What is the slope increment of a rise of 3 and a run of 2? 7) What does pitch measure? 8) Convert 5123 centimeters to kilometers 9) True or False: a scale is used to measure weight 10) What is the perimeter 1x1 square?

Answers 1) 4 2) Every 1/16” on a model represents 1’ in full scale 3) 63 4) ) ) 1.5 per unit run 7) Steepness 8).05123km 9) false 10) 4