## Pre-Calculus 12

### Course Outline

Pre-calculus 12 is an advanced high school mathematics course. Students will explore the following topics:

• Trigonometry
• Relations and Functions:
• Permutations, Combinations, and Binomial Theorem

#### Trigonometry (T):

Students will be expected to develop trigonometric reasoning.

• Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
• Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
• Solve, algebraically and graphically, first- and second-degree trigonometric equations with the domain expressed in degrees and radians.
• Prove trigonometric identities, using:
- reciprocal identities,
- quotient identities,
- Pythagorean identities,
- sum or difference identities (restricted to sine, cosine, and tangent),
- double-angle identities (restricted to sine, cosine, and tangent)

#### Relations and Functions (RF):

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

• Demonstrate an understanding of operations on, and compositions of, functions.
• Understand the effects of horizontal and vertical translations on the graphs of functions and their related equations.
• The effects of horizontal and vertical stretches on the graphs of functions and their related equations.
• Apply translations and stretches to the graphs and equations of functions.
• Understand the effects of reflections on the graphs of functions and their related equations, including reflections in the x-axis, y-axis, and line y = x.
• Understand inverses of relations.
• Demonstrate an understanding of logarithms.
• Demonstrate an understanding of the product, quotient, and power laws of logarithms.
• Graph and analyze exponential and logarithmic functions.
• Solve problems that involve exponential and logarithmic equations.
• Understand factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
• Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
• Graph and analyze radical functions (limited to functions involving one radical).
• Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials, or trinomials).

#### Permutations, Combinations, and Binomial Theorem (PCB):

Students will be expected to develop algebraic and numeric reasoning that involves combinatorics.

• Apply the fundamental counting principle to solve problems.
• Determine the number of permutations of n elements taken r at a time to solve problems.
• Determine the number of combinations of n different elements taken r at a time to solve problems.
• Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).

Updated August 24, 2021