NC.M3: Math 3

Math 3

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Math 3 extends algebraic and function work to polynomial, rational, and trigonometric models, with students interpreting, building, and transforming a wider family of functions. Geometric content focuses on congruence, proof, circles, and modeling with geometry, supported by coordinate methods. Statistics centers on inference: using sample data to draw and justify conclusions about populations.

NC.M3.A-APRAlgebra: Arithmetic with Polynomial and Rational ExpressionsNC.M3.A-CEDAlgebra: Creating EquationsNC.M3.A-REIAlgebra: Reasoning with Equations and InequalitiesNC.M3.A-SSEAlgebra: Seeing Structure in ExpressionsNC.M3.F-BFFunctions: Building FunctionsNC.M3.F-IFFunctions: Interpreting FunctionsNC.M3.F-LEFunctions: Linear, Quadratic, and Exponential ModelsNC.M3.F-TFFunctions: Trigonometric FunctionsNC.M3.G-CGeometry: CirclesNC.M3.G-COGeometry: CongruenceNC.M3.G-GMDGeometry: Geometric Measurement & DimensionNC.M3.G-GPEGeometry: Expressing Geometric Properties with EquationsNC.M3.G-MGGeometry: Modeling with GeometryNC.M3.N-CNNumber and Quantity: The Complex Number SystemNC.M3.S-ICStatistics and Probability: Making Inference and Justifying Conclusions
Example Problems
Consider the following rational division:


What is the quotient in lowest terms?
It takes 12 hours and $250 to paint a single-family home, and it takes 80 hours and $600 to paint a commercial building.

A painting company has less than
$70000 to paint these properties, and it wants to spend at most 900 hours to do so.

Let
denote the number of single-family homes they paint and the number of commercial buildings they paint.

Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
Solve for x:
Is the expression equivalent to 1?
What is the inverse of the function?
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