## Course title

MATH## Pre-requisite

Pre-calculus or Algebra 2 with instructor permission## Course description

Physics (This course has significant math content and can satisfy a 4th year math credit)

The goal of this course is to understand and apply the scientific process; as well as to understand the physical processes of the universe and how they apply to our daily lives. Students will be able to apply mathematics in order to use formulas and equations to explain natural phenomena. In order to practice these concepts; students will complete assignments; conduct prepared laboratory activities; design and conduct their own experiments and demonstrate this knowledge on examinations. During Semester 1; we will focus on forces and motion; forces in fluids; work; power; and machines; energy; and thermal energy and heat. During Semester 2; we will focus on mechanical waves and sound; the electromagnetic spectrum; electricity; and magnetism; and nuclear physics. During both semesters; we will apply the general physical concepts we learn in class to astronomical observations and phenomena. Math Content: Precalculus with Physical Applications (Physics): Arizona Math Standards

ÔøºN-RN: The Real Number System

HS.N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Example: Use the rational exponent (1/2) instead of a square root when typing in velocity formulas into a graphing calculator.

N-Q: Quantities

HS.N-Q.A.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Example: Use unit analysis when deriving physical formulas such as centripetal acceleration. HS.N-Q.A.2. Define appropriate quantities for the purpose of descriptive modeling.

Example: Using meters to estimate and measure distance; comparing Joules (SI unit) with known energy outputs.

HS.N-Q.A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Example: Using significant figures to appropriately round answers based on the accuracy of data provided by the problem or experiment.

N-CN: The Complex Number System

HS.N-CN.C.7. Solve quadratic equations with real coefficients that have complex solutions. Example: Solving the distance equation when modeling parabolic motion: x(t) = -(1/2)gt^2 + vt + x0.

N-VM: Vector and Matrix Quantities

HS.N-VM.A.1. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments; and use appropriate symbols for vectors and their magnitudes (e.g.; v; |v|; ||v||; v).

Example: Calculate the resultant force of two objects using the vector quantities for each; where the difference of sign implies different directions of motion.

HS.N-VM.A.2. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

ÔøºÔøºÔøºÔøº

ÔøºExample: Calculate the net electric force on a test charge placed in between two objects of the same charge.

HS.N-VM.A.3. Solve problems involving velocity and other quantities that can be represented by vectors.

Example: Calculate the velocity of a projectile object with an initial velocity of 4.5 m/s after it has been in the air for 3 seconds. In which direction is it moving?

HS.N-VM.B.4. Add and subtract vectors.

Example: Calculate the velocity of an airplane traveling 650 km/h E with a 200 km/h headwind.

A-SSE: Seeing Structure in Expressions

HS.A-SSE.A.1. Interpret expressions that represent a quantity in terms of its context.

Example: Calculate the total work done by multiplying the net force by the distance traveled; and express this amount in energy (joules).

HS.A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Example: Show how Kinetic Energy and Potential Energy are equal to each other based on the Law of Conservation of Energy; and use this property to solve for the total amount of Kinetic energy for an object that has fallen 50 meters.

A-CED: Creating Equations

HS.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions; and simple rational and exponential functions.

Example: Using the equations for the y-position of an projectile object; and x-position of a projectile object; both based on time; rewrite the equation to solve for the y-position of an object based on time; inputing x-position having been rewritten for time.

HS.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Example: Use Newton‚Äôs Universal Law of Gravitation to compare the Gravitational force between two objects by comparing how an increase in mass directly increases the force; and an increase in distance between the objects decreases the force by the square of the distance.

ÔøºÔøº

ÔøºHS.A-CED.A.4. Rearrange formulas to highlight a quantity of interest; using the same reasoning as in solving equations.

Example: Rearrange Ohm‚Äôs law V = IR to highlight resistance R.

A-REI: Reasoning with Equations and Inequalities

HS.A-REI.A.2. Solve simple rational and radical equations in one variable; and give examples showing how extraneous solutions may arise.

Example: Solve for the distance between two objects in space that both have a mass of 50 kg and a gravitational force between them of 0.0004 N.

HS.A-REI.B.3. Solve linear equations and inequalities in one variable; including equations with coefficients represented by letters.

Example:

HS.A-REI.B.4. Solve quadratic equations in one variable.

Example: Find for the acceleration of an object based on its initial velocity and time in the air.

F-IF: Interpreting Functions

HS.F-IF.A.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain; then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Example: Understand that for most equations involving magnitude values; the domain of the functions is {x | x ‚àà R; x
HS.F-IF.B.4. For a function that models a relationship between two quantities; interpret key features of graphs and tables in terms of the quantities; and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing; decreasing; positive; or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Example: Based on the time of an object; sketch the graph of the height of an object in the air with an initial velocity of 10 m/s and launch angle of 25 Ãä.

HS.F-IF.B.5. Relate the domain of a function to its graph and; where applicable; to the quantitative relationship it describes. For example; if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory; then the positive integers would be an appropriate domain for the function.

ÔøºÔøº

Example: If v(t) is the velocity of an object after t seconds; an appropriate domain for v(t) would be positive rational values; since time cannot be negative.

HS.F-IF.B.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Example: Calculate the average acceleration for a vehicle that starts at 25 m/s and comes to a stop.

F-TF: Trigonometric Functions

HS.F-TF.A.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Example: Calculate the angular velocity of a wheel that rotates 5 radians in 3 seconds. How far has a point on the edge of the wheel moved in this time?

HS.F-TF.A.4. Use the units circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Example: Explain how a boat‚Äôs motion near the shore - rising and falling with the incoming waves - can be modeled with both a sine wave as well as a circle.

HS.F-TF.B.5. Choose trigonometric functions to model periodic phenomena with specified amplitude; frequency; and midline.

Example: Create a periodic function to describe the height of a wave after t seconds with a wave height of 3 m and wavelength of 25 m.

## School country

United States## School state

Arizona## School city

Phoenix## High school

Metropolitan Arts Institute## School / district Address

1700 N. 7th Ave.## School zip code

85007## Requested competency code

Math## Date submitted

## Approved

Yes## Approved competency code

- LPHY
- Physics