- 2 Sections
- 6 Lessons
- 2 Quizzes
- 0m Duration
Unit 1: Foundations, Inequalities & Systems
Understanding Polynomials
Welcome to Algebra 2! This course is designed to build upon the algebraic concepts mastered in Algebra 1 and Geometry. The primary focus is the study of functions—understanding their behavior, their graphs, and their real-world applications.
By the end of this course, students will have mastered the "Language of Functions," moving beyond simple lines to analyze complex curves, logarithms, and systems. This material serves as the critical bridge to Pre-Calculus and AP Calculus.
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This course includes
Course Structure & Unit Breakdown
Semester 1: The Power of Polynomials
Unit 1: Foundations, Inequalities & Systems
Goal: Master the tools for analyzing relationships between multiple variables.
1.1 Domain & Range: Interval notation and set-builder notation.
1.2 Absolute Value Equations: Solving and graphing $|x|$.
1.3 Linear Inequalities: Compound inequalities (AND vs. OR).
1.4 Systems of Equations: Solving $2 \times 2$ and $3 \times 3$ systems (Substitution/Elimination).
1.5 Matrices: Introduction to matrix operations and solving systems via Cramer’s Rule or Inverse Matrices.
Unit 2: Quadratic Functions & Complex Numbers
Goal: Explore the parabolic path and the imaginary number system.
2.1 Complex Numbers: Definition of $i$, operations with complex numbers, and conjugates.
2.2 Factoring Strategies: Grouping, Difference of Squares, and Sum/Difference of Cubes.
2.3 Solving Quadratics: Completing the Square and the Quadratic Formula.
2.4 Parabolas as Conics: Vertex form vs. Standard form; Focus and Directrix.
2.5 Quadratic Inequalities: Solving and graphing regions.
Unit 3: Polynomial Functions
Goal: Analyze high-degree functions and their end behaviors.
3.1 Operations on Polynomials: Long Division and Synthetic Division.
3.2 The Theorems: Remainder Theorem, Factor Theorem, and Fundamental Theorem of Algebra.
3.3 Roots & Zeros: The Rational Root Theorem and finding real/imaginary zeros.
3.4 Graphing Polynomials: End behavior, turning points, and multiplicity of roots.
Semester 2: Transcendentals & Analysis
Unit 4: Radical & Inverse Functions
Goal: Understand the relationship between powers and roots.
4.1 Inverses: Finding inverse functions algebraically and graphically.
4.2 Radical Expressions: Simplifying $n$-th roots.
4.3 Rational Exponents: Converting between radical form $\sqrt[n]{x^m}$ and exponential form $x^{m/n}$.
4.4 Solving Radical Equations: Dealing with extraneous solutions.
4.5 Square Root & Cube Root Functions: Graphing and transformations.
Unit 5: Exponential & Logarithmic Functions
Goal: Model growth, decay, and scales of magnitude.
5.1 Exponential Growth & Decay: The natural base $e$ and compound interest.
5.2 Logarithms: Definition, rewriting forms, and common logs.
5.3 Properties of Logarithms: Product, Quotient, and Power rules; Change of Base formula.
5.4 Solving Equations: Solving exponential equations using logarithms.
5.5 Modeling: Real-world applications (Newton’s Law of Cooling, Richter Scale).
Unit 6: Rational Functions
Goal: Analyze functions with discontinuities and asymptotes.
Vertical Asymptotes (VA) & Holes (Removable Discontinuities).
6.1 Simplifying Rationals: Multiplying and dividing rational expressions.
6.2 Solving Rational Equations: Cross-multiplication and LCD methods.
6.3 Graphing Rationals:
Horizontal Asymptotes (HA) & Slant (Oblique) Asymptotes.
Unit 7: Data Analysis & Statistics
Goal: Interpret data distributions and probability.
7.1 Regression: Linear, Quadratic, and Exponential regression models.
7.2 Probability: Permutations, Combinations, and Independent/Dependent events.
7.3 Statistics: Measures of Central Tendency, Standard Deviation, and the Normal Distribution (Bell Curve).
Unit 8: Introduction to Trigonometry (Pre-Cal Prep)
Goal: Introduction to the unit circle and periodic functions.
8.1 The Unit Circle: Degrees vs. Radians.
8.2 Trig Ratios: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent.
8.3 Graphing Sine & Cosine: Amplitude, period, and phase shift.
Required Materials
Graphing Calculator: TI-84 Plus (or similar) or Desmos access.
Engineering Graph Paper: For precise sketching of conics and asymptotes.
Notebook: Dedicated for theorems and proofs.
Essential Question
"How can we use mathematical language to describe specific patterns of change in the physical world?"
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Key Strategy 2: Multiplying by 25
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Key Strategy 2: Cubes and Cube Roots
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