## Course title

Pre-Calculus## Pre-requisite

Algebra 3-4## Course description

**1. Reasoning with Functions and Relations **involves students understanding functions and the reasoning of functions beyond Algebra 2. It provides students with opportunities to extend the behavior of functions and relations by using multiple representations and covariational reasoning to investigate and explore quantities; their relationships; and how these relationships change.¬† Reasoning with functions and relations provides students with the algebraic tools necessary to analyze a variety of function types and the understanding of these functions in real-world situations.

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**2**. **Reasoning with Trigonometry** involves students extending their trigonometric reasoning beyond the skills learned in Geometry and Algebra 2. Students should deepen their reasoning of relationships in right triangles from using the mnemonic *SohCahToa* to being able to interpret the meaning of the trigonometric ratios as multiplicative comparisons of the appropriate sides of a right triangle. Trigonometric reasoning will be used in situations where students are finding unknown sides and/or angles of right triangles. Students will have the opportunity to extend their reasoning with trigonometric reasoning to non-right triangles and make sense of the Law of Sines and Law of Cosines. ¬†Students will use the Law of Sines and the Law of Cosines to solve problems and to make connections to formulas for the area of a triangle.¬†¬† Furthermore; students will become fluent with the Unit Circle.¬† The Unit Circle should be used to explain the symmetry and periodicity of trigonometric functions. ¬†Students should have the opportunity to model real-world situations with trigonometry including inverse trigonometric functions and periodic functions.¬† Trigonometric expressions; like algebraic expressions; can be manipulated from one form to another using mathematical rules and properties.¬†¬† Students should have opportunities to identify ways to rewrite an expression in order to simplify or produce an equivalent expression to explain properties or solve trigonometric equations; including inverse trigonometric functions; utilizing real-world context.¬†¬† When solving trigonometric equations; students should be able to evaluate and interpret the solution in terms of context. Finally; students will extend their knowledge of trigonometry to the Polar Coordinate system. Students should have the opportunity to graph; analyze; and interpret polar equations; and solve problems in real-world context with and without technology; as appropriate.

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**3. Reasoning with Vectors **involves recognizing that a vector consists of both magnitude and direction. ¬†Students should understand that motion in space; such as velocity; can be represented by a vector. ¬†Students should be proficient using appropriate symbols to represent vectors and their magnitudes.¬† Furthermore; students should be able to determine a vector from its initial point and terminal point; add and subtract vectors; and multiply a vector by a scalar.

**4. Reasoning with Matrices** involves using matrices to represent and manipulate data and as a tool to create transformations or calculate area of geometric figures. Students should have learning opportunities with matrices that allow them to make connections to the real numbers. Students will explore the roles and properties of matrices to solve systems of linear equations.

## School country

United States## School state

Arizona## School city

Phoenix## School / district Address

4502 N. Central Ave## School zip code

85012## Requested competency code

Math## Date submitted

## Approved

Yes## Approved competency code

- MTHA
- 4 years of Math