PreCalculus 12

We will be using the new curriculum, which was finalized this year. The Big Ideas are

  • Using inverses is the foundation of solving equations and can be extended to relationships between functions.

  • Understanding the characteristics of families of functions allows us to model and understand relationships and to build connections between classes of functions.

  • Transformations of shapes extend to functions and relations in all of their representations.

Textbook: McAskill et al., Pre-Calculus 12, McGraw-Hill Ryerson, 2012.

Assessment will be based on unit tests, homework, quizzes, and a final exam.

Assignments 15%

Unit Tests and Quizzes 70%

Final Exam 15%

Assignments will be marked by the student and handed in. Answer keys will be provided.

Quizzes will fall throughout the course units.

Unit Tests will occur at the end of each unit.

The final exam will take place in the exam period.

Content

  • transformations of functions and relations

    • of graphs and equations of parent functions and relations (e.g., absolute value, radical, reciprocal, conics, exponential, logarithmic, trigonometric)

    • vertical and horizontal translations, stretches, and reflections

    • inverses: graphs and equations

    • extension:

      • recognizing composed functions (e.g., y =)

      • operations on functions

  • exponential functions and equations

    • graphing, including transformations

    • solving equations with same base and with different bases, including base e

    • solving problems in situational contexts

  • geometric sequences and series

    • common ratio, first term, general term

    • geometric sequences connecting to exponential functions

    • infinite geometric series

    • sigma notation

  • logarithms: operations, functions, and equations

    • applying laws of logarithms

    • evaluating with different bases

    • using common and natural logarithms

    • exploring inverse of exponential

    • graphing, including transformations

    • solving equations with same base and with different bases

    • solving problems in situational contexts

  • polynomial functions and equations

    • factoring, including the factor theorem and the remainder theorem

    • graphing and the characteristics of a graph (e.g., degree, extrema, zeros, end-behaviour)

    • solving equations algebraically and graphically

  • rational functions

    • characteristics of graphs, including asymptotes, intercepts, point discontinuities, domain, end-behaviour

  • trigonometry: functions, equations, and identities

    • examining angles in standard position in both radians and degrees

    • exploring unit circle, reference and coterminal angles, special angles

    • graphing primary trigonometric functions, including transformations and characteristics

    • solving first- and second-degree equations (over restricted domains and all real numbers)

    • solving problems in situational contexts

    • using identities to reduce complexity in expressions and solve equations (e.g., Pythagorean, quotient, double angle, reciprocal, sum and difference)