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]

## MATHEMATICS 30-1

[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation

[PS] Problem Solving
[R] Reasoning
[T] Technology
[V] Visualization

### 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]
1. Develop and apply the equation of the unit circle.
[CN, R, V]
1. Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
[ME, PS, R, T, V]
[ICT: C6–4.1]
1. Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
[CN, PS, T, V]
[ICT: C6–4.1, C6–4.3]
1. 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]
1. 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]
1. Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
[C, CN, R, V]
1. Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.
[C, CN, R, V]
1. Apply translations and stretches to the graphs and equations of functions.
[C, CN, R, V]
1. 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]
1. Demonstrate an understanding of inverses of relations.
[C, CN, R, V]
1. Demonstrate an understanding of logarithms.
[CN, ME, R]
1. Demonstrate an understanding of the product, quotient and power laws of logarithms.
[C, CN, ME, R, T]
[ICT: C6–4.1]
1. Graph and analyze exponential and logarithmic functions.
[C, CN, T, V]
[ICT: C6–4.3, C6–4.4, F1–4.2]
1. Solve problems that involve exponential and logarithmic equations.
[C, CN, PS, R]
1. Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
[C, CN, ME]
1. Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
[C, CN, T, V]
[ICT: C6–4.3, C6–4.4]
1. Graph and analyze radical functions (limited to functions involving one radical).
[CN, R, T, V]
[ICT: C6–4.1, C6–4.3]
1. 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]
1. Determine the number of permutations of n elements taken r at a time to solve problems.
[C, PS, R, V]
1. Determine the number of combinations of n different elements taken r at a time to solve problems.
[C, PS, R, V]
1. 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]

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