Our Curriculum › Math › 11th Grade
Algebra II
A full year of Algebra II: complex numbers, polynomials, rational and radical expressions, the unit circle and sine and cosine, exponentials and logarithms, statistical inference, and a long run of applied projects, timed practice and a capstone.
180 lessons
One a day for a school year
10 units
Each opens to its lessons
21 applied projects
Finance, sound, medicine, games & more
Standards
Common Core high school math
What's taught, unit by unit
Complex numbersDays 1–10
The imaginary unit i, adding, subtracting, multiplying and dividing complex numbers, conjugates, quadratics with complex solutions, the Fundamental Theorem of Algebra, and graphing on the complex plane.
- 1 · Welcome to Algebra II: A Year of New Number Systems
- 2 · Introducing Imaginary Numbers
- 3 · Complex Numbers: Adding and Subtracting
- 4 · Complex Numbers: Multiplying
- 5 · Complex Conjugates and Dividing Complex Numbers
- 6 · Solving Quadratics with Complex Solutions
- 7 · The Fundamental Theorem of Algebra
- 8 · Graphing Complex Numbers on the Complex Plane
- 9 · Mixed Practice: Complex Numbers
Plus 1 review day, not listed.
Polynomials, radicals & rational expressionsDays 11–25
Polynomial arithmetic and identities, factoring higher-degree polynomials, finding zeros, end behavior and graphing, rational expressions and equations, nth-root radicals and radical equations, and asymptotes of rational functions.
- 11 · Polynomial Arithmetic: Adding and Subtracting
- 12 · Multiplying Polynomials
- 13 · Polynomial Identities
- 14 · Factoring Higher-Degree Polynomials
- 15 · Finding Zeros of Polynomial Functions
- 16 · Graphing Polynomial Functions: End Behavior
- 17 · Graphing Polynomial Functions: Putting It Together
- 18 · Introducing Rational Expressions
- 19 · Multiplying and Dividing Rational Expressions
- 21 · Solving Rational Equations
- 22 · Simplifying Radical Expressions
- 23 · Solving Radical Equations
- 24 · Graphing Rational Functions: Asymptotes
- 25 · Graphing Rational Functions: Full Sketches
Plus 1 review day, not listed.
Unit circle, trig graphs, exponentials & logarithmsDays 26–40
Radians and the unit circle, sine, cosine and the Pythagorean identity, graphing them with amplitude and period, modeling cycles, then exponential functions, logarithms and their properties, solving exponential equations and inverse functions.
- 26 · Introducing the Unit Circle
- 27 · Radian Measure Formalized
- 28 · Trig Functions on the Unit Circle
- 29 · The Pythagorean Identity
- 31 · Graphing Sine and Cosine Functions
- 32 · Amplitude and Period of Trig Functions
- 33 · Modeling Periodic Phenomena with Trig Functions
- 34 · Introducing Exponential Functions Revisited
- 35 · Introducing Logarithms
- 36 · Properties of Logarithms
- 37 · Solving Exponential Equations with Logarithms
- 38 · Graphing Logarithmic Functions
- 39 · Inverse Functions
Plus 2 review days, not listed.
Transformations, modeling & statistical inferenceDays 41–53
Transforming any function family, choosing the best function to model data, multi-step modeling, then sample surveys, experiments and observational studies, the normal distribution, population estimates, margin of error and statistical significance.
- 41 · Function Transformations Generalized
- 42 · Combining Multiple Transformations
- 43 · Modeling with the Best Function Family
- 44 · Multi-Step Modeling Problems
- 46 · Introducing Statistical Inference
- 47 · Sample Surveys vs. Experiments vs. Observational Studies
- 48 · The Normal Distribution
- 49 · Population Estimates from Samples
- 51 · Sample Surveys and Margin of Error via Simulation
- 52 · Informal Statistical Significance
- 53 · Mixed Practice: Statistical Inference
Plus 2 review days, not listed.
Second pass: conics, trig models & rational functionsDays 54–75
Circles and parabolas from their equations, sound and light waves, arithmetic and geometric sequences, modeling with amplitude, midline and phase shift, rational functions with holes and slant asymptotes, and polynomial division. Conics here cover circles and parabolas only.
- 54 · Conic Sections: Circles and Parabolas from the General Form
- 55 · Modeling Sound and Light Waves with Trig Functions
- 56 · Sequences: Arithmetic Patterns
- 57 · Sequences: Geometric Patterns
- 58 · Rational Functions in Context: Concentration and Cost
- 59 · Applications of Arithmetic and Geometric Patterns
- 61 · Polynomial Zeros in Context: Volume and Optimization
- 62 · Comparing Study Designs: Case Studies
- 64 · Modeling Periodic Behavior: Amplitude and Midline
- 65 · Period and Phase Shift in Periodic Models
- 66 · Building a Complete Sinusoidal Model
- 67 · Rational Function Domain and Vertical Asymptotes
- 68 · Horizontal Asymptotes and End Behavior of Rational Functions
- 69 · Mixed Practice: Conics, Rational Functions, and Polynomials
- 71 · Holes, Slant Asymptotes, and Rate Problems
- 72 · The Remainder Theorem and Synthetic Division
- 73 · Synthesizing Function Families for Modeling
- 74 · Practicing a Comprehensive Mixed Algebra II Review Set
Plus 4 review days, not listed.
Halfway reviews & first projectsDays 76–90
An explainer on logarithms, applied projects in finance, sound, music, architecture and revenue models, mixed review sets, four cumulative reviews, a timed halfway assessment and a growth reflection.
- 76 · Explainer Project: Teaching Logarithms
- 77 · Applied Project: Algebra II in Finance
- 78 · Applied Project: Algebra II in Sound and Music
- 79 · Practicing a Comprehensive Mixed Algebra II Review Set 2
- 81 · Cumulative Review: Complex Numbers and Polynomials
- 82 · Cumulative Review: Rational Expressions and the Unit Circle
- 83 · Cumulative Review: Logarithms and Statistics
- 84 · Cumulative Review: Conics, Polynomials, and Complex Numbers
- 85 · Timed Practice Assessment: The Halfway Comprehensive
- 86 · Halfway-Year Growth Reflection
- 87 · Explainer Project: Teaching the Unit Circle
- 88 · Applied Project: Algebra II in Architecture
- 89 · Applied Project: Finding Zeros of a Revenue Model
Plus 2 review days, not listed.
Applied projects & mixed practiceDays 91–120
Applied projects in population modeling, signal processing, epidemiology, cryptography, astronomy, pH, sports, weather and genetics, plus confidence intervals and a survey project, the Rational Root Theorem, mixed review sets and timed assessments.
- 91 · Explainer Project: Teaching Statistical Inference
- 92 · Applied Project: Algebra II in Population Modeling
- 93 · Applied Project: Algebra II in Signal Processing
- 94 · Reviewing Common Errors in Logarithm Properties
- 96 · Applied Project: Algebra II in Epidemiology
- 97 · Applied Project: Algebra II in Cryptography
- 98 · Practicing a Comprehensive Mixed Algebra II Review Set 3
- 99 · Timed Practice Assessment: Trig, Logs, and Statistics
- 101 · Applied Project: Algebra II in Astronomy
- 102 · Applied Project: Algebra II in Chemistry (pH)
- 103 · Rational Root Theorem: Practice Finding All Zeros
- 104 · Practicing a Comprehensive Mixed Algebra II Review Set 4
- 106 · Confidence Intervals and Margin of Error
- 107 · Applied Project: Design a Survey and Report a Margin of Error
- 108 · Practicing a Comprehensive Mixed Algebra II Review Set 5
- 109 · Timed Practice Assessment: Conics, Polynomials, and Complex Numbers
- 111 · Applied Project: Algebra II in Sports Analytics
- 112 · Applied Project: Algebra II in Weather Prediction
- 113 · Sample Surveys, Experiments, and Observational Studies
- 114 · Practicing a Comprehensive Mixed Algebra II Review Set 6
- 116 · Applied Project: Algebra II in Genetics
- 117 · Explainer Project: Teaching Conic Sections
- 118 · Practicing a Comprehensive Mixed Algebra II Review Set 7
- 119 · Timed Practice Assessment: A Full-Year Mixed Set
Plus 6 review days, not listed.
Capstone projectDays 121–130
A multi-day project on a real-world field chosen by the student: researching the algebra behind it, solving applied problems, building visuals, writing it up and presenting.
- 121 · Capstone Prep: Choosing a Real-World Algebra Field
- 122 · Capstone: Researching Foundations
- 123 · Capstone: Solving Applied Problems
- 124 · Capstone: Building Visuals
- 126 · Capstone: Writing Up the Project
- 127 · Capstone: Presentation Prep
- 128 · Capstone: Presentation Delivery
- 129 · Practicing a Comprehensive Mixed Algebra II Review Set 8
Plus 2 review days, not listed.
Cumulative review, timed practice & projectsDays 131–170
Three-part cumulative reviews, repeated timed practice assessments, common-error days, explainer projects, applied projects such as a Ferris wheel, game physics, medicine and traffic flow, and a final project.
- 131 · Cumulative Review: Complex Numbers, Polynomials, and Rational Expressions
- 132 · Cumulative Review: Trig, Logarithms, and Exponentials
- 133 · Cumulative Review: Statistics, Conics, Polynomials, and Complex Numbers
- 134 · Explainer Project: Teaching Function Transformations
- 136 · 2 Timed Practice Assessments, Part 1: The Comprehensive Final Prep
- 137 · 2 Timed Practice Assessments, Part 2: The Comprehensive Final Prep
- 138 · Common Error Review: Algebra II's Trickiest Topics
- 139 · Final Year Reflection: My Year in Algebra II
- 141 · Applied Project: Modeling a Ferris Wheel with a Sinusoidal Function
- 142 · Applied Project: Algebra II in Video Game Physics
- 143 · Reviewing Common Errors in Statistical Inference
- 144 · Practicing a Comprehensive Mixed Algebra II Review Set 9
- 146 · Applied Project: Compound Interest and Solving for Time with Logarithms
- 147 · Explainer Project: Teaching Asymptotes and Holes in Rational Functions
- 148 · Practicing a Comprehensive Mixed Algebra II Review Set 10
- 149 · Timed Practice Assessment 2: Statistics, Rational Expressions, and Logs
- 151 · Applied Project: Optimizing a Production-Cost Model
- 152 · Applied Project: Algebra II in Medicine
- 153 · Reviewing Common Errors in Function Family Modeling
- 154 · Practicing a Comprehensive Mixed Algebra II Review Set 11
- 156 · Applied Project: Algebra II in Traffic Flow Modeling
- 157 · Explainer Project: Teaching Statistical Study Design
- 158 · Practicing a Comprehensive Mixed Algebra II Review Set 12
- 159 · Timed Practice Assessment: A Full-Year Mixed Set 2
- 161 · Full-Year Algebra II Cumulative Review, Part 1
- 162 · Full-Year Algebra II Cumulative Review, Part 2
- 163 · Full-Year Algebra II Cumulative Review, Part 3
- 164 · Timed Practice Assessment: The Comprehensive Final
- 166 · Explainer Project: Teaching Function Family Modeling
- 167 · Applied Project: Algebra II Bringing It All Together
- 168 · Practicing a Comprehensive Mixed Algebra II Review Set 13
- 169 · Looking Ahead: Precalculus Next Year
Plus 8 review days, not listed.
Final review & celebrationDays 171–180
Final reviews of the whole course, preparing and giving a year-end presentation, three celebration days, two looks ahead to Precalculus, and a final reflection.
- 171 · Final Review: Complex Numbers, Polynomials, and Rational Functions
- 172 · Final Review: Trig, Logs, Statistics, Conics, Function Transformations, and Inverse Functions
- 173 · Preparing Your Year-End Math Presentation
- 174 · Delivering Your Year-End Math Presentation
- 175 · Celebration Day: Reflecting on a Year of Algebra II!
- 176 · Celebration Day: A Favorite Problem Challenge
- 177 · Celebration Day: Algebra All Around You
- 178 · Looking Ahead: Precalculus Next Year, Part 2
- 179 · Final Reflection: My Year in Algebra II
- 180 · Congratulations! You Completed Algebra II!
By the end of the year, your child can
- Add, multiply and divide complex numbers and solve quadratics with complex solutions
- Factor and graph polynomials, find their zeros and simplify and solve rational equations
- Use the unit circle and sine and cosine graphs to model repeating patterns
- Solve exponential and logarithmic equations and use them in growth and decay problems
- Choose a function family to model real data and explain why it fits
- Explain what margin of error and different study designs tell us about survey results
Other 11th Grade subjects: English 11: Literature · English 11: Composition & Grammar · Physics · US Government & Civics