Principles of Mathematics 12 Math-U-See
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| A: Problem Solving It is expected that students will use a variety of methods to solve real-life, practical, technical, and theoretical problems. It is expected that students will: |
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| √ | A1. solve problems that involve a specific content area such as, geometry, algebra, trigonometry, statistics, probability, etc. A2. solve problems that involve more than one content area A3. Solve problems that involve mathematics within other disciplines A4. analyze problems and identify the significant elements A5. develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following:
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| √ | A6. Demonstrate the ability to work individually and co-operatively to solve problems A7. Determine that their solutions are correct and reasonable A8. Clearly communicate a solution to a problem and the process used to solve it A9. use appropriate technology to assist in problem solving |
| B: Patterns and Relations (Patterns) It is expected that students will generate and analyse exponential patterns. It is expected that students will: |
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| √ | B1. Derive and apply expressions to represent general terms and sums for geometric growth and to solve problems B2. Connect geometric sequences to exponential functions over the natural numbers B3. estimate values of expressions for infinite geometric processes |
| C: Patterns and Relations (Variables and Equations) It is expected that students will solve exponential, logarithmic and trigonometric equations and identities. It is expected that students will: |
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| √ | C1. Solve exponential equations having bases that are powers of one another C2. Solve and verify exponential and logarithmic equations and identities C3. Distinguish between degree and radian measure, and solve problems using both C4. Determine the exact and the approximate values of trigonometric ratios for any multiples of 0°, 30°, 45°, 60° and 90° and  radC5. Solve first and second degree trigonometric equations over a domain of length  :
C7. analyze trigonometric identities:
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| D: Patterns and Relations (Relations and Functions) It is expected that students will represent & analyse exponential and logarithmic functions, using technology appropriate. It is expected that students will: |
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| √ | D1. Model, graph, and apply exponential functions to solve problems D2. Change functions from exponential form to logarithmic form and vice versa D3. Model, graph, and apply logarithmic functions to solve problems D4. Explain the relationship between the laws of logarithms and the laws of exponents D5. Describe the three primary trigonometric functions as circular functions with reference to the unit circle and an angle in standard position D6. draw (using technology), sketch, and analyze the graphs of sine, cosine, and tangent functions, for:
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| E: Shape and Space (Measurement) It is expected that students will classify conic sections, using their shapes and equations. It is expected that students will: |
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| √ | E1 . classify conic sections according to shape E2. Classify conic sections according to a given equation in general or standard (completed square) form (vertical or horizontal axis of symmetry only) E3. convert a given equation of a conic section from general to standard form and vice versa |
| F: Shape and Space (Transformations) It is expected that students will perform, analyse and create transformations of functions and relations that are described by equations or graphs. It is expected that students will: |
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| √ | F1. Describe how various translations of functions affect graphs and their related equations: |
| Graph a variety of functions, Not always with function notation | |
| √ | F2. Describe how various stretches of functions (compressions and expansions) affect graphs and their related equations: |
| √ | F3 . Describe how reflections of functions in both axes and in the line  affect graphs and their related equations:
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| √ | F4. using the graph and/or the equation of  describe and sketch  F5. Using the graph and/or the equation of  describe and sketch  F6. Describe and perform single transformations and combinations of transformations on functions and relations |
| G: Statistics and Probability (Chance and Uncertainty) It is expected that students will: |
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| Honors | G1. find the standard deviation of a data set or a probability distribution, using technology G2. Use z-scores and the normal distribution to solve problems G3. Use the normal approximation to the binomial distribution to solve problems involving probability calculations for large samples (where npq>10) G4. Solve pathway problems, interpreting and applying any constraints G5. Use the fundamental counting principle to determine the number of different ways to perform multistep operations G6. Determine the number of permutations of n different objects taken r at a time, and use this to solve problems G7. Determine the number of combinations of n different objects taken r at a time, and use this to solve problems G8. Solve problems, using the binomial theorem where N belongs to the set of natural numbers G9. construct a sample space for two or three events G10. Classify events as independent or dependent G11. Solve problems, using the probabilities of mutually exclusive and complementary events G12. Determine the conditional probability of two events G13. Solve probability problems involving permutations, and combinations and conditional probability |
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