Pre-Calculus 120B

Unit 1: Relations and Functions

Arithmetic and geometric sequences and series, factoring and graphing higher-degree polynomials, reciprocal and rational functions, and operations on and compositions of functions.

• Arithmetic sequences
• Arithmetic series

• Geometric sequences
• Geometric and infinite geometric series

• Factoring higher-degree polynomials
• Factoring sums and differences of cubes
• Graphing polynomial functions
• Analyzing polynomial characteristics

• Graphing reciprocal functions
• Reciprocal of a quadratic function
• Graphing rational functions
• Solving rational equations

• Operations on functions
• Composition of functions
• A function toolkit: comparing function types
• Choosing a function to model a situation

Unit 2: Permutations, Combinations and Binomial Theorem

The fundamental counting principle, permutations and combinations, and expanding binomial powers with the binomial theorem.

• The fundamental counting principle
• Permutations of n objects taken r at a time
• Permutations with repetition and identical objects

• Combinations of n objects taken r at a time
• Combination problems with cases and conditions
• Expanding binomials with the binomial theorem
• Finding a specific term of a binomial expansion

Unit 3: Limits

The limit of a function at a point graphically and analytically, one-sided limits, continuity, and limits involving infinity — the bridge into calculus.

• Limits from a graph
• Limits analytically
• One-sided limits

• Continuity of a function
• Continuity on an interval and making a function continuous
• Limits involving infinity
• Indeterminate forms at infinity