Foundations of Mathematics 110

Unit 1: Logical Reasoning

Inductive and deductive reasoning to make and prove conjectures, analyze the validity of arguments, and use numerical-reasoning strategies to solve puzzles and games.

• Making conjectures by inductive reasoning
• Proving conjectures deductively
• Finding the error in a false proof

• Finding a strategy in a number puzzle or game
• Justifying a puzzle solution

Unit 2: Geometry

Deriving proofs about the properties of angles and triangles, solving angle and triangle problems, and solving oblique triangles with the sine law and cosine law, including the ambiguous case.

• Proving angle relationships
• Proving triangle properties
• Structuring a formal geometric proof

• Solving angle problems
• Solving triangle problems
• Multi-step angle and triangle problems in context

• Solving triangles with the sine law
• Solving triangles with the cosine law
• The ambiguous case of the sine law

Unit 3: Relations and Functions

Modelling and solving problems with systems of linear inequalities in two variables, and analyzing the characteristics of quadratic functions.

• Graphing a single linear inequality
• Solving a system of linear inequalities
• Modelling a real situation with inequalities

• Vertex and axis of symmetry
• Intercepts and roots
• Domain and range
• Modelling with quadratic functions

Unit 4: Number

Financial decision-making: comparing the costs and benefits of renting, leasing and buying; analyzing an investment portfolio; and solving problems that involve personal budgets.

• Comparing the costs of renting, leasing and buying
• Justifying a rent-lease-buy decision

• Interest rate, rate of return, and total return
• Evaluating a portfolio's performance
• Diversifying a portfolio

• Building a personal budget
• Adjusting a budget to meet a goal