Mathematics 30-1

Unit 1: Relations and Functions

General outcome: develop algebraic and graphical reasoning through the study of relations. The algebra of functions (operations and composition), the full transformation toolkit (translations, stretches, reflections, inverses), logarithms and their laws, exponential and logarithmic functions and equations, and the graphs of polynomial, radical and rational functions.

• Operations on functions
• Composition of functions

• Horizontal and vertical translations

• Horizontal and vertical stretches

• Combining translations and stretches

• Reflections through the x- and y-axes
• Reflection through the line y = x

• Inverses of relations

• Understanding logarithms
• Product, quotient and power laws

• Graphing exponential functions
• Graphing logarithmic functions
• Solving exponential equations
• Solving logarithmic equations

• Factoring higher-degree polynomials
• Graphing polynomial functions

• Graphing radical functions
• Graphing rational functions

Unit 2: Trigonometry

General outcome: develop trigonometric reasoning. Angles in standard position in degrees and radians, the unit circle, the six trigonometric ratios, the graphs of sine, cosine and tangent, solving trigonometric equations, and proving trigonometric identities.

• Angles in standard position (degrees)
• Radian measure and conversion

• The equation of the unit circle

• Primary ratios in radians and degrees
• Reciprocal ratios: cosecant, secant, cotangent

• Graphing sine and cosine
• Graphing tangent

• First-degree trigonometric equations
• Second-degree trigonometric equations

• Reciprocal and quotient identities
• Pythagorean identities
• Sum and difference identities
• Double-angle identities

Unit 3: Permutations, Combinations and Binomial Theorem

General outcome: develop algebraic and numeric reasoning that involves combinatorics. The fundamental counting principle, permutations of n objects taken r at a time, combinations, and expanding a binomial power with the binomial theorem.

• The fundamental counting principle
• Permutations of n taken r at a time

• Combinations of n taken r at a time
• Expanding with the binomial theorem