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.

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)