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