Algebra 2
The bridge to precalculus and beyond. Extend the function family to polynomials, rationals, exponentials, logarithms, and trigonometry, with rigorous algebraic technique throughout.
10 units and 51 lessons, for Grade 10 to Grade 11. Free on Slate.
Unit 1: Review: Linear, Quadratic & Complex Numbers
Re-establish mastery of quadratics and introduce complex numbers as a natural extension.
- Functions: Domain, Range, and Transformations Review (10 min)
- Quadratic Functions Review (10 min)
- Complex Numbers (10 min)
- Quadratic Inequalities (10 min)
Unit 2: Polynomial Functions
Analyze, graph, and solve higher-degree polynomials with the full toolkit of algebra.
Unit 3: Radical Functions & Rational Exponents
Unify radical and exponent notation and explore radical and inverse functions.
- Rational Exponents (10 min)
- Radical Functions and Their Graphs (10 min)
- Solving Radical Equations (10 min)
- Inverse Functions (10 min)
Unit 4: Exponential & Logarithmic Functions
Master the inverse relationship between exponentials and logarithms and apply to growth, decay, and data modeling.
- Exponential Functions Review and Extension (10 min)
- Logarithms: Definition and Conversion (10 min)
- Properties of Logarithms (10 min)
- Solving Exponential Equations (10 min)
- Solving Logarithmic Equations (10 min)
- Applications: Compound Interest, Half-Life, Population (10 min)
Unit 5: Rational Functions
Analyze the behavior of ratios of polynomials, including asymptotes, holes, and domain restrictions.
- Rational Expressions: Simplifying (10 min)
- Operations with Rational Expressions (10 min)
- Graphing Rational Functions (10 min)
- Solving Rational Equations (10 min)
- Inverse Variation (10 min)
Unit 6: Systems, Matrices & Linear Programming
Extend systems of equations to three variables and introduce matrix methods and optimization.
- Systems with Three Variables (10 min)
- Matrix Operations (10 min)
- Matrix Equations and Inverse Matrices (10 min)
- Linear Programming (10 min)
- Nonlinear Systems of Equations (10 min)
Unit 7: Conic Sections
Study the four conic sections as slices of a double cone and as locus definitions: the parabola, circle, ellipse, and hyperbola.
- Introduction to Conic Sections (10 min)
- Parabolas: Focus, Directrix, and Standard Forms (10 min)
- Ellipses (10 min)
- Hyperbolas (10 min)
- Identifying and Graphing Conics from General Form (10 min)
Unit 8: Sequences, Series & Probability
Count, sum, and compute probabilities rigorously: essential skills for statistics and discrete math.
- Arithmetic Sequences and Series (10 min)
- Geometric Sequences and Series (10 min)
- Infinite Geometric Series (10 min)
- The Binomial Theorem (10 min)
- Permutations and Combinations (10 min)
- Probability: Multiplication and Addition Rules (10 min)
- Conditional Probability and Independence (10 min)
Unit 9: Introduction to Trigonometry
Extend trigonometry beyond right triangles to the full unit circle and periodic graphs.
- Radian Measure and the Unit Circle (10 min)
- The Six Trigonometric Functions (10 min)
- Graphs of Sine and Cosine (10 min)
- Graphs of Tangent, Cotangent, Secant, and Cosecant (10 min)
- Inverse Trigonometric Functions (10 min)
Unit 10: Statistics and Data Analysis
Apply statistical reasoning to describe, compare, and draw inferences from data.
- The Normal Distribution and Empirical Rule (10 min)
- Z-Scores and Percentiles (10 min)
- Sampling Methods and Survey Design (10 min)
- Introduction to Hypothesis Testing (10 min)