Pre-Calculus (first semester)

Curriculum-Map

Focus: - The study of functions and their applications in the world.

Broad-based Concept: Functions Generalizations: In our world we find relationships which can be modeled by functions.

Unit One

Introduction of Trigonometric Functions

Unit Two

Graphing of Trigonometric Functions and their Inverses

Unit Three

Using Properties of Trigonometric Functions to Solve Equations

Concepts:

Functions

Periodic Functions

Measurement of Rotation

Definition of Trigonometric Functions

Approximate Values of Trigonometric Functions

Concepts:

Graphs of the six Trigonometric Functions and their characteristics

Graphs of the Inverse Trigonometric Functions

Trigonometric Functions as Math Models

Graphs of Trigonometric Functions

Basic Transformations

Concepts:

Trigonometric Properties

Simplification using Trigonometric Properties

Solving equations using Trigonometric Properties

Enduring Understandings:

The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, radical, exponential, logarithmic, trigonometric, and piecewise-defined functions. 01

Enduring Understandings:

The student interprets the meaning of the symbolic representations of functions and operations on functions within a context. 02

The student uses functions and their properties to model and solve real –life problems. 03

Enduring Understandings:

The student interprets the meaning of the symbolic representations of functions and operations on functions within a context. 02

Guiding Questions:

Essential TEKS Questions:

1. Can you describe parent functions symbolically and graphically, including

01A

Essential TEKS Questions:

1. Can you apply basic transformations, including

to the parent functions? 02A

2. Can you perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically? 02B

3. Can you use functions such as logarithmic, exponential, trigonometric, polynomial, etc, to model real live data. 03A

4. Can you determine the domain and range of functions using graphs, tables, and symbols?) 01B

5. Can you describe symmetry of graphs of even and odd functions? 01C

6. Can you recognize and use connections among significant points of a function (roots, maximum points, and minimum points), the graph of a function, and the symbolic representation of a function? 01D

7. Can you investigate continuity, end behavior, vertical and horizontal asymptotes, and limits and connect these characteristics to the graph of a function. 01E

Essential TEKS Questions:

1. Can you investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties? 02C

Unit Four

Triangles and Vectors

Concepts:

Laws of Sines and Cosines

Solving Triangle Problems

Vectors

Enduring Understandings:

The Student uses vectors to model physical situations 06

The student uses functions and their properties to model and solve real-life problems. 03

Guiding Questions:

Essential TEKS Questions:

1. Can you use the concepts of vectors to model situations defined by magnitude and direction? 06A

2. Can you analyze and solve vector problems generated by real-life situations. 06B

3. Can you solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas.