Mathematics 2201 (Academic)

Unit 1: Radical Expressions and Equations

Simplifying and operating with radical expressions, rationalizing denominators, and solving radical equations including extraneous roots.

• Mixed and entire radicals
• Comparing and operating with radicals
• Rationalizing a denominator

• Solving radical equations algebraically
• Verifying roots and extraneous solutions

Unit 2: Inductive and Deductive Reasoning

Making and testing conjectures, deductive proof, counterexamples, and analyzing arguments - reasoning taught as its own content, not woven away.

• Making conjectures inductively
• Counterexamples

• Proving with deductive reasoning
• Comparing reasoning and finding proof errors

Unit 3: Quadratic Functions and Equations

Quadratic functions as modelling tools: characteristics, intercepts and zeros, the vertex and axis of symmetry, graphing, and solving quadratic equations by factoring and the quadratic formula.

• Roots, zeros and intercepts
• Solving quadratics by factoring
• Solving with the quadratic formula

• Characteristics of a quadratic function
• Vertex and axis of symmetry
• Sketching from standard and vertex form

Unit 4: Angles, Triangles and Proof

Angle relationships from parallel lines and transversals, angle sums in polygons, triangle congruence, and geometric proof by inductive and deductive reasoning.

• Angle relationships from transversals
• Proving angle properties

• Proving triangles congruent
• Solving angle problems and checking solutions

Unit 5: Proportional Reasoning: Scale and Rates

Scale diagrams and models of 2-D and 3-D objects, the effect of scale factor on area and volume, and rates and unit rates in real contexts.

• Scale factor and 2-D dimensions
• Scale factor and area

• Scale diagrams of 3-D objects
• Scale factor, surface area and volume

• Interpreting and comparing rates
• Graphing rates and slope
• Solving rate problems

Unit 6: Acute Triangle Trigonometry

The sine law and the cosine law used to solve non-right (acute) triangles and multi-triangle measurement problems.

• Applying the sine and cosine laws
• Problems with more than one triangle

Unit 7: Statistical Reasoning

Collecting and assessing data, standard deviation and dispersion, the normal distribution and z-scores, and confidence intervals and margin of error in a research project.

• Collecting and assessing data
• Standard deviation and dispersion

• Properties of the normal curve
• z-scores and normal problems

• Confidence intervals and margin of error
• Statistics in the media