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Grade 12 Advanced Mathematics I learners will study any four chosen topics from a list of thirteen–seven of which have specific learning outcomes. The core topics are complex numbers and polar coordinates, statistics, number theory, matrices and systems of equations, 3-dimensional geometry, vectors, and conic sections. The additional topics are fractal geometry, calculus topics to extend beyond Introduction to Calculus content, history of mathematics, applications of mathematics to computer science and combinatorics extending beyond permutations and combinations, and interdisciplinary project. The flexibility of the course allows teachers to choose the topics and encourages the input of learners; however, the topics chosen must be different for each half credit.
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 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.
Topic: Complex Numbers and Polar Coordinates
AM.1.1. Define and perform operations on complex numbers.
AM.1.2. Make connections between complex numbers and quadratic equation solutions.
AM.1.3. Demonstrate an understanding of polar coordinates and their graphs.
AM.1.4. Make connections between complex numbers and polar coordinates.
Topic: Statistics
AM.2.1. Demonstrate an understanding of the concepts of measures of central tendency and spread.
AM.2.2. Demonstrate an understanding of probability distributions including the binomial distribution.
AM.2.3. Develop and apply the properties of a normal distribution.
Topic: Number Theory
AM.3.1. Apply proof techniques to prove mathematical theorems or statements.
AM.3.2. Explore, develop, and apply the properties of integers.
AM.3.3. Represent numbers in different bases.
Topic: Matrices and Systems of Equations
AM.4.1. Demonstrate an understanding of matrices.
AM.4.2. Perform operations on matrices.
AM.4.3. Solve systems of equations using matrices.
Topic: 3-Dimensional Geometry
AM.5.1. Demonstrate an understanding of 3-space.
AM.5.2. Represent and analyze lines, planes, and surfaces algebraically and graphically in 3-space.
Topic: Vectors
AM.6.1. Develop an understanding of vectors and perform basic vector operations.
AM.6.2. Demonstrate an understanding of the dot product and cross product of vectors to solve problems.
AM.6.3. Develop and apply the vector equation of a line.
Topic: Conic Sections
AM.7.1. Represent and analyze conic sections algebraically and geometrically.
AM.7.2. Demonstrate an understanding of focal points in a conic section.
AM.7.3. Analyze a conic section in terms of its eccentricity.
Grade 12 Pre-Calculus Mathematics - Curriculum Implementation Resources: Web Pages
Grade 12 Pre-Calculus Mathematics - Curriculum Implementation Resources: Multimedia
Grade 12 Pre-Calculus Mathematics - Curriculum Implementation Resources: Documents
