Mathematics 3200

Unit 1: Logarithms

The relationship between logarithms and exponents, and the laws of logarithms.

• Logarithms and exponents
• Exact and estimated log values
• The laws of logarithms

Unit 2: Polynomial Functions and the Binomial Theorem

Dividing and factoring polynomials, graphing polynomial functions, and expanding binomials.

• Polynomial and synthetic division
• Remainder and factor theorems

• Graphs of polynomial functions
• Sketching and modelling polynomials
• Zeros and multiplicity

• Pascal's triangle and coefficients
• The binomial theorem

Unit 3: Functions, Transformations, Exponentials and Logarithms

Inverses, radical functions, the transformation toolkit, and exponential and logarithmic functions and equations.

• Relations, functions, and inverses
• Sketching inverse relations
• Equations of inverse functions

• Domain and range of a radical function
• Graphing radical functions
• Solving radical equations graphically

• Translations of functions
• Stretches of functions
• Combined transformations
• Reflections of functions

• Solving exponential equations
• Solving logarithmic equations
• Graphs of exponential and log functions
• Exponential growth and decay
• Logarithmic scales
• Graphs of logarithmic functions

Unit 4: Trigonometry

Radian measure and the unit circle, exact values and equations, sinusoidal and tangent graphs, and identities.

• Angles in standard position
• Radian and degree measure
• Coterminal angles and arc length
• The unit circle and trig ratios

• Exact trig values
• Solving trigonometric equations
• Angles from a trig ratio

• Sine and cosine graphs
• Effects of the sinusoidal parameters
• Transforming sinusoidal functions
• Modelling with sinusoidal functions
• The tangent graph

• Identities vs equations
• Proving and using identities

Unit 5: Permutations and Combinations

Counting with the fundamental counting principle, permutations, and combinations.

• The fundamental counting principle
• Permutations
• Permutations with constraints

• Combinations