Education and Early Childhood Learning

General Learning Outcome: Develop trigonometric reasoning.

• 12P.T.1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
  [C, CN, ME, R, V]

• 12P.T.2. Develop and apply the equation of the unit circle.
  [CN, R, V]

• 12P.T.3. Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
  [C, ME, PS, R, T, V]

• 12P.T.4. Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
  [C, CN, PS, T, V]

• 12P.T.5. Solve, algebraically and graphically, first- and second-degree trigonometric equations with the domain expressed in degrees and radians.
  [C, CN, PS, R, T, V]

  Learners should be able to solve first-degree sine, cosine, and tangent double-angle trigonometric equations.

• 12P.T.6. 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)

  [C, R, T, V]

General Learning Outcome: Develop algebraic and graphical reasoning through the study of relations.

• 12P.R.1. Demonstrate an understanding of operations on, and compositions of, functions.
  [CN, R, T, V]

• 12P.R.2. Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
  [C, CN, R, V]

• 12P.R.3. Demonstrate an understanding of the effects of horizontal and vertical compressions and stretches on the graphs of functions and their related equations.
  [C, CN, R, V]

  A compression by a factor of $a$ is the same as a stretch by a factor of $\frac{1}{a}$.

• 12P.R.4. Apply translations, compressions, and stretches to the graphs and equations of functions.
  [C, CN, R, V]

• 12P.R.5. Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the

  • x-axis
  • y-axis
  • line $y=x$

  [C, CN, R, V]

• 12P.R.6. Demonstrate an understanding of inverses of relations.
  [C, CN, R, V]

• 12P.R.7. Demonstrate an understanding of logarithms.
  [C, CN, ME, R]

• 12P.R.8. Demonstrate an understanding of the product, quotient, and power laws of logarithms.
  [C, CN, R, T]

• 12P.R.9. Graph and analyze exponential and logarithmic functions.
  [C, CN, T, V]

  It is intended that students will be able to work with logarithms of any base, $b>1$, including base $e$.

• 12P.R.10. Solve problems that involve exponential and logarithmic equations.
  [C, CN, PS, R]

• 12P.R.11. Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
  [C, CN, ME]

• 12P.R.12. Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5).
  [C, CN, PS, T, V]

• 12P.R.13. Graph and analyze radical functions (limited to functions involving one radical).
  [C, CN, R, T, V]

• 12P.R.14. Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials, or trinomials).
  [C, CN, R, T, V]

General Learning Outcome: Develop algebraic and numeric reasoning that involves combinatorics.

• 12P.P.1. Apply the fundamental counting principle to solve problems.
  [C, CN, PS, R, V]

• 12P.P.2. Determine the number of permutations of n elements taken r at a time to solve problems.
  [C, PS, R, V]

  Learners should be able to use strategies such as cases or grouping objects together to solve a contextual problem. Also, it is intended that circular permutations not be included.

• 12P.P.3. Determine the number of combinations of n different elements taken r at a time to solve problems.
  [C, PS, R, V]

• 12P.P.4. Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
  [C, CN, R, V]