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Classroom: Precalculus

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This course includes the study of functions, polynomial functions, rational equations, radical equations, exponential and logarithmic equations, conics, matrices, and introduction to linear programming and non-linear systems.
Course objectives:


Include, but not limited to:

1: Identify various functions, including square root, cubic, and piecewise-defined functions, and perform transformations and operations on known functions to create new functions. Construct mathematical models from real-world word problems.



2: Identify quadratic, polynomial, and rational functions and analyze their graphs. Solve polynomial and rational inequalities. Evaluate real-world problems using rational function models.



3: Find the real zeros of polynomial functions using various theorems.



4: Identify one-to-one functions and find their inverses. Explore exponential and logarithmic functions and use their properties to model and solve real-world problems involving compound interest and uninhibited growth/decay.



5: Explore angles and their measure. Establish the value of trigonometric functions using right triangle trigonometry. Analyze properties of the graphs of trigonometric functions and apply transformations and shifts to sinusoidal graphs.



6: Explore inverse trigonometric functions. Prove identities involving trigonometric functions and use them to solve trigonometric equations.



7: Solve real-world applications by creating right triangles and using trigonometric and inverse trigonometric functions.





LessonLesson 1: Basic Definitions and Notations.

LessonLesson 2: Composite and Inverse Functions.

LessonLesson 3: Transformation of Graph.

LessonLesson 4: Linear Equations and Inequalities in one Variable

LessonLesson 5: Linear Equations and Inequalities with Absolute Value

LessonLesson 6: Equations of Straight Lines. Parallel and Perpendicular Lines.

LessonLesson 7: Systems of Linear Equations with three Variables. Determinants of Order 3.

LessonLesson 8: Roots of Polynomial Equations. The Remainder Theorem.

LessonLesson 9: Graphing Rational Functions. Zeros and Asymptotes of Graphs.

LessonLesson 10: Definition and properties of Logarithms.

LessonLesson 11: Graphs of Exponential and Logarithmic Functions.

LessonLesson 12: Solving Exponential and Logarithmic Equations. Applications.

LessonLesson 13: Angles and their Measure.

LessonLesson 14: The Trigonometric Functions of an Angle.

LessonLesson 15: Solving Triangles. The law of Cosines. The law of Sines. Applications.

LessonLesson 16: The Sine and Cosine Functions. General Trigonometry.

LessonLesson 17: Trigonometric Equations.