Program of Studies: [Math 10C] [Math 10-3] [Math 10-4] [Math 20-1] [Math 20-2] [Math 20-3] [Math 20-4] [Math 30-1] [Math 30-2] [Math 30-3]

Trigonometry

General Outcome: Develop trigonometric reasoning.

Specific Outcomes: It is expected that students will:

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

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

3. Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
   [ME, PS, R, T, V]
   [ICT: C6–4.1]

4. Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
   [CN, PS, T, V]
   [ICT: C6–4.1, C6–4.3]

5. Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.
   [CN, PS, R, T, V]
   [ICT: C6–4.1, C6–4.4]

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).
  [R, T, V]
  [ICT: C6–4.1, C6–4.4]

Relations and Functions

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

Specific Outcomes: It is expected that students will:

1. Demonstrate an understanding of operations on, and compositions of, functions.
   [CN, R, T, V]
   [ICT: C6–4.1]

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]
   

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

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

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]

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

7. Demonstrate an understanding of logarithms.
   [CN, ME, R]

8. Demonstrate an understanding of the product, quotient and power laws of logarithms.
   [C, CN, ME, R, T]
   [ICT: C6–4.1]
   

9. Graph and analyze exponential and logarithmic functions.
   [C, CN, T, V]
   [ICT: C6–4.3, C6–4.4, F1–4.2]

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

12. Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
    [C, CN, T, V]
    [ICT: C6–4.3, C6–4.4]

13. Graph and analyze radical functions (limited to functions involving one radical).
    [CN, R, T, V]
    [ICT: C6–4.1, C6–4.3]

14. Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).
    [CN, R, T, V]
    [ICT: C6–4.1, C6–4.3, C6–4.4]
    

Permutations, Combinations and Binomial Theorem

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

Specific Outcomes: It is expected that students will:

1. Apply the fundamental counting principle to solve problems.
   [C, PS, R, V]
   [ICT: C6–2.3]
   

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

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

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

March, 2008 http://www.education.alberta.ca/media/655889/math10to12.pdf

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf

Authorized Resources: http://www.education.alberta.ca/teachers/program/math/educator/resources.aspx