Foundations of Mathematics 11

Unit 1: Geometry

Deriving proofs about angles and triangles, solving angle and triangle problems, and the cosine and sine laws.

• Deriving angle-property proofs
• Deriving triangle-property proofs
• Building and presenting geometric proofs

• Solving angle-property problems
• Solving triangle-property problems
• Congruent-triangle problems

• The cosine law
• The sine law
• Choosing between the sine and cosine laws

Unit 2: Logical Reasoning

Inductive and deductive reasoning to analyse and prove conjectures, and spatial-reasoning puzzles and games.

• Inductive reasoning and conjectures
• Deductive reasoning and proof
• Analysing reasoning and finding errors

• Strategies for spatial puzzles
• Analysing why a strategy wins

Unit 3: Measurement

Rates, scale diagrams, and the relationships between scale factors and the areas of 2-D shapes and 3-D objects.

• Understanding and computing rates
• Solving problems with rates

• Reading scale diagrams
• Creating scale diagrams
• Solving scale-diagram problems

• Scale factor and length
• Scale factor and area
• Scale factor on 3-D objects

Unit 4: Relations and Functions

Systems of linear inequalities in two variables, and the characteristics of quadratic functions.

• Graphing a linear inequality
• Solving systems of linear inequalities
• Modelling problems with inequality systems

• The vertex of a quadratic function
• Intercepts of a quadratic function
• Domain and range of a quadratic function
• Axis of symmetry of a quadratic function