Foundations of Mathematics 20

Unit 1: Reasoning and Proof

A research inquiry project, and inductive and deductive reasoning including conjectures, proof, validity, and puzzles and games.

• Investigating and presenting a mathematics topic

• Inductive reasoning and conjectures
• Deductive proof and validity
• Puzzles and games

Unit 2: Proportional Reasoning and Geometry

Proportional reasoning with rates and scale, and properties of angles, triangles, and the sine and cosine laws.

• Rates
• Scale diagrams and scale factor
• Scale factor, area, and volume

• Angle relationships and proofs
• Solving angle and triangle problems

• Applying the sine and cosine laws
• The ambiguous case

Unit 3: Statistics

Normal distribution with standard deviation and z-scores, and the interpretation of statistical data using confidence intervals and margin of error.

• The normal curve and standard deviation
• Z-scores

• Confidence intervals and margin of error

Unit 4: Inequalities and Quadratic Modelling

Systems of linear inequalities with optimization, and quadratic functions used to model situations.

• Graphing systems of linear inequalities
• Linear programming and optimization

• Intercepts and zeros of quadratics
• Vertex and axis of symmetry
• Domain, range, and graphing quadratics