Mathematics 20 Individual Units
[The order of the units described here does not necesarily match the textbook, or the order in which they will be taught].
Unit 1: Systems of Equations
- Graphing review
- Overview; solving systems graphically
- Practical problems
- Algebraic methods:
- Substitution
- Comparison
- Elimination
- Review and practice
- More problems
- Three variable systems
- Non-linear systems
- Unit review and test
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Unit 2: Linear Inequalities
- Review (linear equalities)
- Problem solving and calculator solutions
- Linear inequalities and graphing
- Two variable solutions and graphing
- Problem solving
- Solving systems of linear inequalities
- Unit review and test
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Unit 3: Quadratic Functions
- Review, including calculator use
- Transformations
- Translations
- Shape change
- Problem solving
- Completing the Square
- More graphing
- Practical problems
- Unit review and test
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Unit 4A: Quadratic Equations
- Review (graphing, and calculator use)
- Review (solving directly)
- Review (factoring)
- Supplemental factoring review
- Problem solving
- The Quadratic Formula
- Complex answers (intro to complex numbers)
- The Discriminant
- 'Backwards' problems
- Unit review and test
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Unit 4B: Polynomial Equations
- Overview and examples
- Remainder Theorem
- Factor Theorem
- Integral and Rational Zero Theorems
- Equation solving
- Problem solving
- Graphing
- Finding roots of all kinds (inc. irrational and imaginary)
- Regression
- Unit review and test
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Unit 5: Functions
- Review
- Operations
- Composition of functions
- Inverse functions
- Problem solving
- Using a calculator
- Inequalities (quadratic and polynomial only)
- Absolute value (equations: simpler ones only)
- Rational functions, equations, and inequations
- Radical functions, equations (simpler ones only), and inequations
- Unit review and test
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Unit 6: Logical Reasoning & Proofs
- Deductive reasoning
- Analyzing statements
- Direct proofs
- Connections with geometry facts
- Unit review and test
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Unit 7: The Circle
- Properties of the circle
- Proofs
- Angles in a circle
- Cyclic quadrilaterals
- Tangents
- Proofs (reference trig methods)
- Arc length and sector area
- Polygons
- Unit review and test
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Unit 8: Coordinate Geometry & Trig
- Connecting coordinate geometry to plane geometry
- Review: midpoint, distance formulas
- Distance from a point to a line
- Equation of a circle
- Lines and circles
- Trigonometry review, inc. sin and cos laws
- Practice
- Unit Review and test
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Unit 9: Personal Finance
- Earnings
- Net income
- Interest and annuities
- Effective annual interest rate
- Consumer credit, mortgages
- Financial statements
- Unit review and test
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