Pre-Calculus 20

Unit 1: Absolute Value and Radicals

Absolute value of real numbers and functions, and radical expressions and equations with numerical and variable radicands.

• Absolute value of real numbers
• Graphing y = |f(x)|
• Solving absolute value equations

• Mixed and entire radicals and simplifying
• Rationalizing denominators
• Radical equations and extraneous roots

Unit 2: Rational Expressions

Equivalent rational expressions, operations on them, and solving rational equations with non-permissible values.

• Equivalent forms and simplifying
• Operations on rational expressions
• Solving rational equations

Unit 3: Trigonometry

The primary trigonometric ratios using reference angles and exact values, and the sine and cosine laws including the ambiguous case.

• Standard position and reference angles
• Trig ratios from a point on the terminal arm
• Exact values for special angles

• Sine and cosine laws
• The ambiguous case

Unit 4: Quadratic Functions and Equations

Factoring polynomial expressions, quadratic functions and their graphs, and quadratic equations and systems.

• Factoring advanced polynomial expressions

• Transformations and vertex form
• Completing the square
• Graphing and characteristics

• Solving quadratic equations
• The discriminant
• Linear-quadratic and quadratic-quadratic systems

Unit 5: Inequalities, Sequences, and Reciprocals

Quadratic and two-variable inequalities, arithmetic and geometric sequences and series, and reciprocal functions.

• Two-variable inequalities
• One-variable quadratic inequalities

• Arithmetic sequences and series
• Geometric sequences and series
• Infinite geometric series

• Graphing reciprocal functions