Pre-Calculus Mathematics, Grade 12 (40S)

Unit 1: Trigonometry

Angles in standard position in radians, the unit circle, the six trigonometric ratios, trigonometric functions and their graphs, trigonometric equations, and proving identities.

• Sketching and converting angles
• Coterminal angles and arc length

• The equation of the unit circle
• Exact trigonometric ratios
• Solving with trigonometric ratios

• Graphs of sine, cosine, and tangent
• Transforming trigonometric graphs
• Solving trigonometric equations
• General solutions and identities in equations

• Proving with reciprocal, quotient, and Pythagorean identities
• Sum, difference, and double-angle identities

Unit 2: Relations and Functions

Operations and compositions of functions, the full family of transformations, inverses, logarithms and their laws, and the analysis of exponential, logarithmic, polynomial, radical, and rational functions.

• Operations on functions
• Compositions of functions

• Translations of graphs
• Compressions and stretches
• Combining transformations
• Reflections of graphs
• Inverses of relations

• Understanding logarithms
• Laws of logarithms

• Graphing exponential functions
• Graphing logarithmic functions
• Solving exponential and logarithmic equations
• Applications of exponential and logarithmic equations

• Long and synthetic division of polynomials
• The remainder and factor theorems
• Graphing polynomial functions
• Radical functions
• Rational functions

Unit 3: Permutations, Combinations and Binomial Theorem

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

• The fundamental counting principle
• Permutations
• Combinations

• Pascal's triangle and binomial patterns
• Expanding with the binomial theorem