Pre-Calculus 12

Unit 1: Permutations, Combinations and Binomial Theorem

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

• Counting principle and permutations
• Combinations
• The binomial theorem
• A specific term of a binomial expansion

Unit 2: Relations and Functions

Operations and compositions of functions, transformations, inverses, logarithms and their laws, and graphing exponential, logarithmic, polynomial, radical, and rational functions.

• Operations on functions
• Composition of functions

• Translations of graphs
• Stretches of graphs
• Applying translations and stretches
• Transformed equations
• Reflections in the axes
• Reflection in the line y = x
• Inverses of relations

• Understanding logarithms
• The product, quotient and power laws
• The power law and change of base
• Graphing exponential functions
• Graphing logarithmic functions
• Exponential equations
• Logarithmic equations

• Factoring higher-degree polynomials
• Graphing polynomial functions
• Roots and intercepts of polynomials
• Graphing radical functions
• Graphing rational functions
• Sketching rational functions

Unit 3: Trigonometry

Angles in standard position, the unit circle, the six trigonometric ratios, graphing trigonometric functions, solving trigonometric equations, and proving identities.

• Angles in standard position
• The unit circle

• The six trigonometric ratios
• Reciprocal trigonometric ratios
• Graphing sine and cosine
• Graphing tangent

• Solving trigonometric equations
• Second-degree trigonometric equations
• Reciprocal, quotient and Pythagorean identities
• Sum and difference identities
• Double-angle identities