| Trigonometry |
Permutations, Combinations and Binomial Theorem |
Relations and Functions |
General Outcome
Develop trigonometric reasoning. |
General Outcome
Develop algebraic and numeric reasoning that involves combinatorics. |
General Outcome
Develop algebraic and graphical reasoning through the study of relations. |
Specific Outcome
It is expected that students will: |
Specific Outcome
It is expected that students will: |
Specific Outcome
It is expected that students will: |
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12P.T.1.
- Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
[CN, ME, R, V]
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12P.P.1
- Apply the fundamental counting principle to solve problems.
[C, PS, R, V]
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12P.R.1.
- Demonstrate an understanding of operations on, and compositions of, functions.
[CN, R, T, V]
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12P.T.2.
- Develop and apply the equation of the unit circle.
[CN, R, V]
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12P.P.2.
- Determine the number of permutations of n elements taken r at a time to solve problems.
[C, PS, R, V]
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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]
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12P.T.3.
- Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
[ME, PS, R, T, V]
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12P.P.3.
- Determine the number of combinations of n different elements taken r at a time to solve problems.
[C, PS, R, V]
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12P.R.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]
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12P.T.4.
- Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
[CN, PS, T, V]
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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).
[CN, R, V]
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12P.R.4.
- Apply translations and stretches to the graphs and equations of functions.
[C, CN, R, V]
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12P.T.5.
- Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.
[CN, PS, R, T, V]
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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]
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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).
[R, T, V]
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12P.R.6.
- Demonstrate an understanding of inverses of relations.
[C, CN, R, V]
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12P.R.7.
- Demonstrate an understanding of logarithms.
[CN, ME, R]
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12P.R.8.
- Demonstrate an understanding of the product, quotient and power laws of logarithms.
[C, CN, R, T]
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12P.R.9.
- Graph and analyze exponential and logarithmic functions.
[C, CN, T, V]
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12P.R.10.
- Solve problems that involve exponential and logarithmic equations.
[C, CN, PS, R]
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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]
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12P.R.12.
- Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5).
[C, CN, T, V]
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12P.R.13.
- Graph and analyze radical functions (limited to functions involving one radical).
[CN, R, T, V]
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12P.R.14.
- Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).
[CN, R, T, V]
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