Alberta

T Trigonometry

• T.1 Develop trigonometric reasoning.

  • T.1.1 Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

    • Convert between radians and degrees (12-N.1)

  • T.1.2 Develop and apply the equation of the unit circle.

  • T.1.3 Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.

    • Find trigonometric ratios using right triangles (12-N.5)
    • Find trigonometric ratios using the unit circle (12-N.6)

  • T.1.4 Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.

    • Graph sine functions (12-O.4)
    • Graph cosine functions (12-O.8)

  • T.1.5 Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.

    • Solve trigonometric equations (12-N.9)

  • T.1.6 Prove trigonometric identities, using:

    • T.1.6.a reciprocal identities.

      • Trigonometric identities I (12-P.3)
      • Trigonometric identities II (12-P.4)

    • T.1.6.b quotient identities.

    • T.1.6.c Pythagorean identities.

      • Trigonometric identities I (12-P.3)
      • Trigonometric identities II (12-P.4)

    • T.1.6.d sum or difference identities (restricted to sine, cosine and tangent).

    • T.1.6.e double-angle identities (restricted to sine, cosine and tangent).

RF Relations and Functions

• RF.1 Develop algebraic and graphical reasoning through the study of relations.

  • RF.1.1 Demonstrate an understanding of operations on, and compositions of, functions.

    • Add, subtract, multiply and divide functions (12-A.10)
    • Composition of functions (12-A.11)

  • RF.1.2 Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.

    • Translations of functions (12-B.1)

  • RF.1.3 Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.

    • Dilations of functions (12-B.3)

  • RF.1.4 Apply translations and stretches to the graphs and equations of functions.

  • RF.1.5 Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the:

    • RF.1.5.a x-axis.

      • Reflections of functions (12-B.2)

    • RF.1.5.b y-axis.

      • Reflections of functions (12-B.2)

    • RF.1.5.c line y = x.

  • RF.1.6 Demonstrate an understanding of inverses of relations.

    • Identify inverse functions (12-A.12)
    • Find values of inverse functions from tables (12-A.13)
    • Find values of inverse functions from graphs (12-A.14)
    • Find inverse functions and relations (12-A.15)

  • RF.1.7 Demonstrate an understanding of logarithms.

    • Convert between exponential and logarithmic form: rational bases (12-F.1)
    • Evaluate logarithms (12-F.2)

  • RF.1.8 Demonstrate an understanding of the product, quotient and power laws of logarithms.

    • Identify properties of logarithms (12-F.4)
    • Product property of logarithms (12-F.5)
    • Quotient property of logarithms (12-F.6)
    • Power property of logarithms (12-F.7)
    • Properties of logarithms: mixed review (12-F.8)

  • RF.1.9 Graph and analyze exponential and logarithmic functions.

    • Domain and range of exponential and logarithmic functions (12-G.1)
    • Match exponential functions and graphs (12-G.3)

  • RF.1.10 Solve problems that involve exponential and logarithmic equations.

    • Solve exponential equations by rewriting the base (12-G.4)
    • Solve exponential equations using common logarithms (12-G.5)
    • Solve logarithmic equations I (12-G.6)
    • Solve logarithmic equations II (12-G.7)
    • Exponential growth and decay: word problems (12-G.11)
    • Compound interest: word problems (12-G.12)
    • Continuously compounded interest: word problems (12-G.13)

  • RF.1.11 Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

    • Factor sums and differences of cubes (12-D.10)
    • Factor using a quadratic pattern (12-D.12)

  • RF.1.12 Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5).

    • Match polynomials and graphs (12-D.9)

  • RF.1.13 Graph and analyze radical functions (limited to functions involving one radical).

    • Domain and range of radical functions (12-H.1)

  • RF.1.14 Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

    • Rational functions: asymptotes and excluded values (12-E.1)

PCB Permutations, Combinations and Binomial Theorem

• PCB.1 Develop algebraic and numeric reasoning that involves combinatorics.

  • PCB.1.1 Apply the fundamental counting principle to solve problems.

    • Counting principle (11-Y.4)

  • PCB.1.2 Determine the number of permutations of n elements taken r at a time to solve problems.

    • Combinations and permutations (12-Y.3)

  • PCB.1.3 Determine the number of combinations of n different elements taken r at a time to solve problems.

    • Combinations and permutations (12-Y.3)

  • PCB.1.4 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).

    • Pascal's triangle (12-D.14)
    • Pascal's triangle and the Binomial Theorem (12-D.15)
    • Binomial Theorem I (12-D.16)
    • Binomial Theorem II (12-D.17)