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Grade 12 Pre-Calculus Mathematics learners will develop trigonometric reasoning by demonstrating an understanding of angles in standard position, developing and applying the equation of the unit circle, and using the six trigonometric ratios for angles. They will represent graphically and analyze trigonometric functions, solve algebraically and graphically trigonometric equations, and prove trigonometric identities. Learners will develop algebraic and graphical reasoning through the study of relations by demonstrating an understanding of the effect of different transformations on graphs of functions and their related equation. They will also demonstrate an understanding of inverses of relations, of logarithms, and of graphing and analyzing a variety of functions. They will develop algebraic and graphical reasoning that involves combinatorics by applying the counting principles, determining the number of permutations and combinations, as well as expanding the powers of a binomial in a variety of ways.
The Guiding Principles of Designing Learning Experiences and Assessment Practices in the French Immersion program provide guidance to all Manitoba educators as they design learning experiences and classroom assessments to strengthen, extend and expand student learning. Planning with the learner, the context, and the curricula in mind creates opportunities for the co-construction of inclusive learning experiences and assessment practices where the diverse learning needs, abilities and interests of each learner are met.
Assessment for and as learning involve learners in the process and support learner reflection; assessment of learning (commonly known as summative evaluation) measures final outcomes. All aspects, when done well, contribute to informed teaching and reliable judgment of learner progress.
The Guiding Principles of Designing Learning Experiences and Assessment Practices outlined below in the French Immersion Program in Manitoba provide guidance to all Manitoba educators as they design learning and assessment experiences to strengthen, extend and expand student learning. Planning with the learner, the context and the curricula in mind creates opportunities for the co-construction of inclusive learning experiences and assessment practices where the diverse learning needs, abilities and interests of each learner are met.
The Guiding Principles for Evaluation and Reporting are currently still under development and not yet available. When completed, a notification will be added to the Manitoba Framework for Learning “What’s New?” page on the website.
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]
12P.T.6. Prove trigonometric identities, using
[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]
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
[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]
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]
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]
Grade 12 Pre-Calculus Mathematics - Curriculum Implementation Resources: Web Pages
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