Math Made Easy’s algebra 2 lessons cover all 20 chapters, from complex numbers to statistical experiments and simulation. Every algebra 2 lesson is free and aligned to the Common Core high school standards. Mathbot, our blue robot coach, guides eleventh graders extending their algebra and function skills through worked examples first.
What the algebra 2 lessons teach
- Real and Complex Numbers
- Polynomial Division and the Remainder Theorem
- Function Operations, Composition and Inverses
- Sequences and Series
- Data, Normal Distributions and Statistical Inference
Work in order: read a lesson such as Real and Complex Numbers, solve the matching worksheet, check it against the answer key, take the chapter test, and finish with the 10-question quiz. Logarithms are introduced as the inverse of exponentials, so students see why the product and change-of-base rules hold.
Graph every new function family by hand once before relying on technology. Domains covered by the algebra 2 lessons: The Complex Number System, Arithmetic with Polynomials & Rational Expressions, Trigonometric Functions, Interpreting Categorical & Quantitative Data, and Making Inferences.
Chapter 1 · Algebra 2 · N-RN.A.1, N-RN.A.2, N-CN.A.1, N-CN.A.2
Real and Complex Numbers: Working with i
Sort numbers into natural, integer, rational, irrational, and real sets, then meet the imaginary unit i with i^2 = -1. You will add, subtract, and multiply complex numbers, such as (2 + 3i)(1 - i) = 5 + i. Read the lesson on complex numbers, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Number sets
- Imaginary unit
- Complex arithmetic
Chapter 2 · Algebra 2 · N-CN.C.7, A-REI.B.4b
Quadratics with Complex Solutions
Solve quadratics whose solutions are not real, using the quadratic formula with i, and let the discriminant predict the type of roots. For x^2 + 4x + 13 = 0 the solutions are -2 plus or minus 3i. Work through the complex solutions lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Quadratic formula
- Discriminant
- Complex roots
Chapter 3 · Algebra 2 · N-RN.A.1, N-RN.A.2, A-REI.A.2
Radicals and Rational Exponents Made Clear
Work with nth roots, convert between radical and rational-exponent forms, simplify radical expressions, and solve radical equations, rejecting extraneous solutions. Solving square root of (x + 2) = x shows why checking matters. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your radicals skills.
- nth roots
- Radical equations
- Extraneous solutions
Chapter 4 · Algebra 2 · F-IF.C.7c, A-APR.B.3, F-IF.B.4
Polynomial Functions: Zeros, Ends, and Graphs
Read degree, leading coefficient, and end behavior, find zeros and multiplicity from factored form, and sketch graphs with turning points. A cubic like (x + 1)(x - 2)^2 touches the axis at 2 and crosses at -1. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where polynomial functions points were earned.
- End behavior
- Zeros and multiplicity
- Sketching graphs
Chapter 5 · Algebra 2 · A-APR.B.2, A-APR.D.6, A-APR.C.4
Dividing Polynomials: Remainder and Factor Theorems
Divide polynomials by long division and synthetic division, then apply the Remainder and Factor Theorems. Dividing x^3 - 2x^2 - 5x + 6 by x - 3 shows a remainder of 0, so x - 3 is a factor. Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on polynomial division, and the test comes with a scoring guide.
- Synthetic division
- Remainder theorem
- Factor theorem
Chapter 6 · Algebra 2 · A-APR.D.6, A-APR.D.7, A-REI.A.2
Rational Expressions and Equations Step by Step
Simplify, multiply, divide, add, and subtract rational expressions, then solve rational equations and discard extraneous values. A work-rate story, where one pipe fills a tank in 3 hours and another in 6, leads to 1/3 + 1/6. Learn rational expressions in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Operations on fractions
- Rational equations
- Work problems
Chapter 7 · Algebra 2 · F-IF.C.7d, F-IF.B.4
Rational Functions: Asymptotes, Holes, and Graphs
Find vertical and horizontal asymptotes and holes, state the domain, and graph y = a/(x - h) + k. Inverse variation appears when travel time shrinks as speed grows, like t = 120/r. After the lesson, the worksheet and answer key let you fix errors in rational functions before you attempt the quiz and the test.
- Asymptotes
- Holes and domain
- Inverse variation
Chapter 8 · Algebra 2 · F-BF.B.3, F-IF.C.7b
Transformations of Functions and Their Graphs
Apply f(x) + k, f(x + k), kf(x), and f(kx) to quadratic, absolute value, root, and exponential parents, and test for even and odd symmetry. Shifting y = square root of x three units left gives square root of (x + 3). Take the quiz first to see what you know about transformations, then study the lesson, finish the worksheet, and use the test scoring guide.
- Shifts and reflections
- Stretches
- Even and odd
Chapter 9 · Algebra 2 · F-BF.A.1b, F-BF.A.1c, F-BF.B.4a
Combining and Inverting Functions
Add, subtract, multiply, and compose functions, then find inverses and verify them by composition. For f(x) = 2x + 3 the inverse is (x - 3)/2, and its graph is the reflection of f over y = x. Do the lesson, then the worksheet and answer key, then the scored test on function operations; the short quiz gives a fast check on the way.
- Composition
- Finding inverses
- Inverse graphs
Chapter 10 · Algebra 2 · F-IF.C.8b, F-LE.A.4, F-LE.B.5
Exponential Models: Growth, Decay, and Interest
Model growth and decay with percent rates, compound interest several times a year and continuously with e, and half-life or doubling time. Investing $1,000 at 5% compounded continuously for 10 years gives about $1,648. Lesson first, worksheet next: the answer key confirms each exponential models result, and the quiz and test with scoring guide close the chapter.
- Compound interest
- The number e
- Half-life
Chapter 11 · Algebra 2 · F-LE.A.4, F-BF.B.4a, F-IF.C.7e
Logarithms: The Inverse of Exponents
Define a logarithm as the inverse of an exponential, work with common and natural logs, graph log functions, and use the product, quotient, power, and change-of-base rules. For example, log2 of 32 equals 5. Read the lesson on logarithms, solve the worksheet and check it with the answer key, then take the quiz and the test.
- Log definition
- Log properties
- Change of base
Chapter 12 · Algebra 2 · F-LE.A.4, A-SSE.B.3c
Using Logs to Solve Exponent Equations
Solve a b^(ct) = d with logarithms and handle logarithmic equations, then apply both to populations, interest, pH, decibels, and half-life. A culture doubling every 3 hours reaching 1,000 cells takes a computable time. Work through the exponential and log equations lesson, test yourself on the worksheet with its answer key, and finish with the quiz and the scored test.
- Solving with logs
- Log equations
- Applications
Chapter 13 · Algebra 2 · A-SSE.B.4, F-BF.A.2, F-IF.A.3
Sequences and Series: Patterns That Add Up
Write arithmetic and geometric sequences explicitly and recursively, use sigma notation, and sum finite series. Saving $50 more each month than the last month is arithmetic, and a loan balance is geometric. Mathbot suggests the lesson first, then the worksheet with answer key, and finally the quiz and test to prove your series skills.
- Sigma notation
- Arithmetic series
- Geometric series
Chapter 14 · Algebra 2 · F-TF.A.1, F-TF.A.2, F-TF.C.8
Radians and the Unit Circle Explained
Measure angles in radians, read coordinates off the unit circle, and find sine, cosine, and tangent of any angle with sin^2 + cos^2 = 1. If sin x = 3/5 in quadrant II, then cos x = -4/5. Every page pairs a lesson with a worksheet and answer key, plus a quiz and a test whose scoring guide shows where the unit circle points were earned.
- Radians
- Unit circle
- Pythagorean identity
Chapter 15 · Algebra 2 · F-TF.B.5, F-IF.C.7e
Graphing Waves: Sine and Cosine Models
Graph sine and cosine with amplitude, period, midline, and phase shift, then fit them to periodic data. A Ferris wheel with radius 20 feet and a 4-minute turn gives a height curve you can write down. Read, solve the worksheet, grade it with the answer key; the quiz is a quick check on trig graphs, and the test comes with a scoring guide.
- Amplitude and period
- Phase shift
- Periodic models
Chapter 16 · Algebra 2 · S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7
Probability Rules and Conditional Events
Describe events as subsets, apply the addition rule, test independence, and compute conditional probability P(A|B) from two-way tables. In a class of 30 with 12 in band, you can compare P(band) with P(band | choir). Learn probability rules in the lesson, build speed on the worksheet, correct mistakes with the answer key, and confirm mastery with the quiz and test.
- Addition rule
- Independence
- Conditional probability
Chapter 17 · Algebra 2 · S-ID.A.4, S-IC.A.1, S-IC.B.3, S-IC.B.4
Normal Curves, z-Scores and Study Design
Summarize data with mean and standard deviation, use the 68-95-99.7 rule and z-scores on a normal curve, and separate surveys, experiments, and observational studies. A score 1.5 standard deviations above the mean has z = 1.5. After the lesson, the worksheet and answer key let you fix errors in normal distributions before you attempt the quiz and the test.
- Z-scores
- Normal curve
- Study types
Chapter 18 · Algebra 2 · A-SSE.A.1, A-SSE.A.2, A-CED.A.1, A-CED.A.2, A-CED.A.3, A-CED.A.4, A-REI.D.11, A-APR.C.5, N-CN.C.8, N-CN.C.9
Structure, Identities and Modeling with Equations
Rewrite polynomial, rational, and exponential expressions to reveal structure, such as x^4 - y^4 as a difference of squares, and create equations and inequalities in one or two variables. A rectangle with a perimeter limit is a typical model. Take the quiz first to see what you know about expressions and models, then study the lesson, finish the worksheet, and use the test scoring guide.
- Rewriting structure
- Creating equations
- Modeling
Chapter 19 · Algebra 2 · F-IF.B.4, F-IF.B.5, F-IF.B.6, F-IF.C.8a, F-IF.C.9
Interpreting and Comparing Functions in Context
Read key features of polynomial, rational, exponential, logarithmic, and trigonometric functions in context, relate domain to the situation, and compare average rates of change. Temperature curves over two intervals make a clear case. Do the lesson, then the worksheet and answer key, then the scored test on function features; the short quiz gives a fast check on the way.
- Key features
- Context and domain
- Rate of change
Chapter 20 · Algebra 2 · S-IC.A.2, S-IC.B.5, S-IC.B.6, S-MD.B.6, S-MD.B.7
Experiments, Simulation and Smart Decisions
Decide whether a simulation supports a model, and compare two treatments in a randomized experiment to judge if a difference is significant. If a coin lands heads 38 of 50 times, ask whether a fair-coin model still fits. Lesson first, worksheet next: the answer key confirms each statistical decisions result, and the quiz and test with scoring guide close the chapter.
- Simulation
- Randomized experiments
- Significance
Grade 11 Algebra 2 Lessons: frequently asked questions
Are the algebra 2 lessons free?
Yes. All 20 algebra 2 lessons are free to read, with no account needed. Each algebra 2 lesson points ahead to its worksheet, test and quiz.
Which standards do the algebra 2 lessons follow?
They follow the Common Core high school standards for Algebra, Functions, and Statistics & Probability, which organizes the course into The Complex Number System, Arithmetic with Polynomials & Rational Expressions, Trigonometric Functions, Interpreting Categorical & Quantitative Data, and Making Inferences. Each algebra 2 lesson is tagged with codes such as N-CN.C.7, F-LE.A.4 and F-TF.A.1.
What should I know before starting algebra 2?
Students should be fluent with linear and quadratic functions, factoring and systems from Algebra 1, plus the basic ideas from Geometry. If a gap shows up, begin with the lesson on complex numbers.
How are the algebra 2 lessons organized?
Number systems and polynomials lead off, then rational, exponential, logarithmic and trigonometric functions, and finally probability and inference. The algebra 2 chapters can be read in order or picked by topic.
What comes after algebra 2?
Precalculus follows for students heading toward calculus, while others move into statistics or a college algebra course. Finishing the 20 chapters on complex numbers through statistical experiments and simulation leaves students ready for that step.