Grade 11: Mathematics

Here is a comprehensive contents outline for Grade 11 Mathematics, aligned with the British Columbia (BC) curriculum in Canada.

The BC Grade 11 math curriculum offers several pathways to cater to students’ different interests and post-secondary goals. The main courses are:

1. Foundations of Mathematics 11: Focused on logical reasoning, financial literacy, and mathematical modeling for students interested in the humanities, social sciences, or direct entry into the workforce.

2. Pre-Calculus 11: Focused on abstract reasoning, algebraic skills, and problem-solving for students interested in pursuing STEM fields (Science, Technology, Engineering, and Mathematics) at the university level.

The following outlines break down the content for these two distinct pathways.

Pathway 1: Foundations of Mathematics 11

Big Ideas of the Course:

• Logical reasoning helps us discover and describe mathematical truths.

• Statistical analysis allows us to explore, understand, and communicate data.

• Financial literacy promotes understanding of financial decisions and their effects.

Unit 1: Logical Reasoning and Set Theory

• Key Concepts:

  • Inductive and Deductive Reasoning: Making conjectures and drawing conclusions based on patterns and logic.

  • Set Theory: Sets, subsets, universal sets, Venn diagrams, and set notation (union, intersection, complement).

  • Solving Problems with Venn Diagrams: Applying set theory to solve real-world counting problems.

Unit 2: Probability and Statistics

• Key Concepts:

  • Statistics: Measures of central tendency (mean, median, mode) and spread (range, standard deviation, interquartile range).

  • Statistical Analysis: Using standard deviation to analyze data sets. Understanding the normal distribution and the Empirical Rule (68-95-99.7).

  • Probability: Odds and probability, mutually exclusive events, independent and dependent events, conditional probability.

Unit 3: Financial Mathematics

• Key Concepts:

  • Compound Interest: Understanding and calculating compound interest, comparing different compounding periods.

  • Loans and Investments: Analyzing and comparing simple and compound interest scenarios for loans and investments.

  • Credit Cards and Debt: Understanding how credit card interest works and the implications of carrying a balance.

  • Budgeting: Creating and analyzing a budget.

Unit 4: Geometry and Measurement

• Key Concepts:

  • Scale Diagrams and Similarity: Using scale factors to solve problems involving similar 2D shapes and 3D objects.

  • Sine and Cosine Laws: Solving problems involving acute and obtuse triangles in 2D and 3D contexts.

Unit 5: Mathematical Modeling

• Key Concepts:

  • Relations and Functions: Representing relations in different ways (graphs, equations, words, mapping notation).

  • Linear and Quadratic Functions: Modeling real-world situations with linear and quadratic equations and interpreting the meaning of the slope, vertex, and intercepts in context.

Pathway 2: Pre-Calculus 11

Big Ideas of the Course:

• Algebra allows us to generalize relationships through abstract analysis.

• Relationships can be described and generalizations made through mathematical modeling.

• Proportional reasoning is used to make sense of multiplicative relationships.

Unit 1: Absolute Value and Reciprocal Functions

• Key Concepts:

  • Absolute Value: Solving absolute value equations and graphing absolute value functions (e.g., $y=|x|$, $y=|2x-1|$).

  • Reciprocal Functions: Graphing and analyzing functions of the form y=1f(x)y=f(x)1​, particularly where $f(x)$ is linear or quadratic. Identifying asymptotes and invariant points.

Unit 2: Radical Expressions and Equations

• Key Concepts:

  • Operations with Radicals: Simplifying, adding, subtracting, multiplying, and dividing square root expressions (radicals).

  • Rationalizing the Denominator: Simplifying radical expressions by removing the radical from the denominator.

  • Solving Radical Equations: Algebraically solving equations that involve square roots, and identifying extraneous roots.

  • Graphing Radical Functions: Analyzing the graphs of functions like y=xy=x​.

Unit 3: Quadratic Functions and Equations

• Key Concepts:

  • Factoring Review and Extension: Factoring complex trinomials and polynomials of the form ax2+bx+cax2+bx+c.

  • Completing the Square: Converting a quadratic equation from standard form to vertex form, y=a(x−p)2+qy=a(x−p)2+q.

  • The Quadratic Formula: Using the formula x=−b±b2−4ac2ax=2a−b±b2−4ac​​ to solve any quadratic equation.

  • Analyzing Quadratic Functions: Graphing parabolas, identifying the vertex, axis of symmetry, domain, range, and intercepts.

  • The Discriminant: Using b2−4acb2−4ac to determine the nature of the roots (real, equal, imaginary).

Unit 4: Rational Expressions and Equations

• Key Concepts:

  • Operations with Rational Expressions: Simplifying, multiplying, dividing, adding, and subtracting algebraic fractions.

  • Non-Permissible Values: Identifying values for which a rational expression is undefined.

  • Solving Rational Equations: Algebraically solving equations involving fractions with polynomials in the numerator and denominator.

Unit 5: Trigonometry

• Key Concepts:

  • The Sine and Cosine Laws: Solving problems involving acute and obtuse triangles.

  • Angles in Standard Position: Understanding angles greater than 90° and their related acute angles.

  • The Three Primary Trig Ratios for Any Angle: Extending sine, cosine, and tangent to all quadrants.

  • The Sine Law – The Ambiguous Case: Recognizing and solving situations where two triangles are possible (SSA).

Additional Potential Topics (Varies by School/Teacher)

• Foundations 11: May include project-based units on statistics or financial planning.

• Pre-Calculus 11: May include a more in-depth unit on sequences and series (arithmetic and geometric).

Curricular Competencies (The “Doing” of Mathematics)

Throughout all units, students will be expected to develop these skills:

• Reasoning and Analyzing

• Understanding and Solving

• Communicating and Representing

• Connecting and Reflecting

This outline provides a solid foundation for what a student can expect to learn in BC’s Grade 11 math courses. The choice between Foundations and Pre-Calculus is critical and should be based on a student’s future academic and career plans.