### Course Outline

Pre-calculus 11 is an advanced high school mathematics course. Students will explore the following topics:

- Algebra and Number (AN)
- Trigonometry (T)
- Relations and Functions (RF)

#### Algebra and Number (AN)

Students will be expected to develop algebraic reasoning and number sense.

- demonstrate an understanding of the absolute value of real numbers.
- solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.
- solve problems that involve radical equations (limited to square roots).
- determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
- perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
- solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials, or trinomials).

#### Trigonometry (T)

Students will be expected to develop trigonometric reasoning.

- demonstrate an understanding of angles in standard position (0° to 360°).
- solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.
- solve problems, using the cosine law and sine law, including the ambiguous case.
- demonstrate an understanding of angles in standard position, expressed in degrees and radians.
- develop and apply the equation of the unit circle.

#### Relations and Functions (RF)

Students will be expected to develop algebraic and graphical reasoning through the study of relations.

- factor polynomial expressions
- graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
- analyze quadratic functions to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, x-intercept and y-intercept, and to solve problems.
- solve problems that involve quadratic equations.
- solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.
- solve problems that involve linear and quadratic inequalities in two variables.
- solve problems that involve quadratic inequalities in one variable.
- analyze arithmetic sequences and series to solve problems.
- analyze geometric sequences and series to solve problems.
- graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).

**Updated August 24, 2021**