Canada · Ontario Curriculum Expectations
Grade 11 Mathematics
This course explores the behavior of functions, trigonometric identities, and algebraic sequences. Students develop abstract reasoning skills by modeling real world phenomena through quadratic, exponential, and trigonometric lenses.
Characteristics of Functions
Students explore the definition of a function and use function notation to represent transformations and inverses. The unit emphasizes the distinction between relations and functions in various representations.
Distinguishing between functions and relations using mapping diagrams, graphs, and sets of ordered pairs.
Applying vertical and horizontal translations, stretches, and reflections to base functional forms.
Determining the inverse of a linear or quadratic function and understanding the graphical symmetry involved.
Rational and Equivalent Expressions
A deep dive into algebraic manipulation, focusing on simplifying complex rational expressions and proving identities.
Factoring polynomials to simplify ratios and identifying restrictions on variables.
Performing addition, subtraction, multiplication, and division on complex algebraic fractions.
Quadratic Functions and Equations
Expanding on grade 10 quadratics by exploring the discriminant, complex roots, and optimization problems.
Using the quadratic formula to predict the number and type of solutions for a quadratic equation.
Finding the intersection of lines and parabolas using both algebraic and graphical methods.
Exponential Functions
Investigating growth and decay models, including the properties of integer and rational exponents.
Mastering power laws and extending understanding to rational and negative exponents.
Applying exponential functions to finance, biology, and physics through half-life and doubling time.
Trigonometric Ratios and Functions
Extending trigonometry beyond right triangles to periodic functions and the unit circle.
Solving for unknown sides and angles in non-right triangles, including the ambiguous case.
Graphing sine and cosine curves and identifying amplitude, period, and phase shifts.
Sequences and Series
Exploring patterns through arithmetic and geometric progressions and their applications in finance.
Defining recursive and general formulas for patterns with constant differences or ratios.
Using series to calculate the future value of investments and the present value of loans.