Homeschool · Diploma track · Grades 10-11

Algebra 2: free lessons and course outline

A full year of Algebra 2 on the California traditional pathway, built to be the student's whole course in the subject rather than a supplement to one. Algebra 2 is where the function concept stops being one idea among many and becomes the organizing principle of the subject: every family studied here is introduced the same way, by what it does, what its graph looks like, how it transforms, and what kind of equation it solves. Eleven units take the year from functions and transformations through quadratics and complex numbers, polynomials, rational and radical functions, exponentials and logarithms, sequences and series, trigonometry, and a closing unit on statistics and inference. Every solution is worked line by line, and every extraneous solution is checked rather than assumed away.

DIPLOMA TRACK CA CCSS MATH TRADITIONAL PATHWAY MODEL ANSWERS 75 LESSONS 880 PRACTICE PROBLEMS Algebra 1 and Geometry. This is a complete course in Algebra 2 and does not assume other instruction in the subject.

Algebra 2 is the course that decides whether a student can take Precalculus and then calculus. It is also the course where the subject changes character: Algebra 1 asks you to solve, and Algebra 2 asks you to recognize what kind of object you are looking at before you do anything to it. The eleven units follow the California traditional pathway, and they are ordered so that each function family arrives with the algebra it needs already in place. Unit 1 sets up functions, transformations, composition and inverses, because every later unit is an application of those four ideas to a new family. Units 2 through 5 work through the algebraic families in order of the arithmetic they require: quadratics and the complex numbers that complete them, polynomials, rational expressions, then radicals and rational exponents. Units 6 and 7 introduce exponential and logarithmic functions as inverses of each other, which is why they sit adjacent. Unit 8 covers sequences and series, Units 9 and 10 trigonometry as a function rather than as triangle measurement, and Unit 11 closes on statistics, sampling and inference, which the standards place in this course and which most textbooks bury at the back. Every lesson opens with the method, names the specific error that costs the marks, works an example in full, and then gives ten practice problems with complete solutions.

U1Unit 1: Functions, Transformations and Inverses7 lessons
U2Unit 2: Quadratic Functions and Complex Numbers7 lessons
U3Unit 3: Polynomial Functions7 lessons
U4Unit 4: Rational Expressions and Functions7 lessons
U5Unit 5: Radicals, Rational Exponents and Radical Functions7 lessons
U6Unit 6: Exponential Functions and Modeling7 lessons
U7Unit 7: Logarithmic Functions7 lessons
U8Unit 8: Sequences and Series7 lessons
U9Unit 9: Trigonometric Functions7 lessons
U10Unit 10: Trigonometric Identities and Equations6 lessons
U11Unit 11: Statistics, Sampling and Inference6 lessons

Every lesson, unit by unit

U1 is free to read below. The other units open with a free month or a paid plan.

U1 Unit 1: Functions, Transformations and InversesFREE

U2 Unit 2: Quadratic Functions and Complex Numbers

2.1 The three forms of a quadratic
2.2 Completing the square
2.3 The quadratic formula
2.4 The discriminant
2.5 Complex numbers
2.6 Complex roots and conjugate pairs
2.7 Quadratic inequalities and modeling

U3 Unit 3: Polynomial Functions

3.1 Polynomial vocabulary and end behavior
3.2 Operations with polynomials
3.3 Long division and synthetic division
3.4 The remainder and factor theorems
3.5 Factoring higher-degree polynomials
3.6 The rational root theorem
3.7 Graphing polynomial functions

U4 Unit 4: Rational Expressions and Functions

4.1 Simplifying rational expressions
4.2 Multiplying and dividing rational expressions
4.3 Adding and subtracting rational expressions
4.4 Complex fractions
4.5 Solving rational equations
4.6 Asymptotes, holes and graphs
4.7 Modeling with rational functions

U5 Unit 5: Radicals, Rational Exponents and Radical Functions

5.1 Rational exponents
5.2 Simplifying radicals
5.3 Operations with radicals
5.4 Rationalizing denominators
5.5 Solving radical equations
5.6 Graphing radical functions
5.7 Powers and roots as inverses

U6 Unit 6: Exponential Functions and Modeling

6.1 Exponential functions and their graphs
6.2 Writing an exponential model
6.3 Compound interest and the number e
6.4 Transformations of exponential functions
6.5 Comparing growth types
6.6 Half-life and doubling time
6.7 Fitting a model and knowing its limits

U7 Unit 7: Logarithmic Functions

7.1 Logarithms defined
7.2 Graphs of logarithmic functions
7.3 Properties of logarithms
7.4 The change of base formula
7.5 Solving exponential equations
7.6 Solving logarithmic equations
7.7 Logarithmic scales in use

U8 Unit 8: Sequences and Series

8.1 Sequences, explicit and recursive
8.2 Arithmetic sequences
8.3 Arithmetic series
8.4 Geometric sequences
8.5 Geometric series
8.6 Infinite geometric series
8.7 The binomial theorem

U9 Unit 9: Trigonometric Functions

9.1 Angles, radians and arc length
9.2 The unit circle
9.3 The six trigonometric functions
9.4 Reference angles and signs
9.5 Graphing sine and cosine
9.6 Phase shift and vertical shift
9.7 Modeling periodic phenomena

U10 Unit 10: Trigonometric Identities and Equations

10.1 The Pythagorean identities
10.2 Proving an identity
10.3 Sum and difference formulas
10.4 Double angle formulas
10.5 Solving trigonometric equations
10.6 Inverse trigonometric functions

U11 Unit 11: Statistics, Sampling and Inference

11.1 Summarizing a distribution
11.2 The normal distribution and z-scores
11.3 The empirical rule and normal probabilities
11.4 Sampling and study design
11.5 What each study design can conclude
11.6 Margin of error and evaluating a claim

Keep going in the full Algebra 2 course

All of U1 (Unit 1: Functions, Transformations and Inverses) is free to everyone, with no account. The course has 75 lessons, each with worked examples and practice problems that come with full solutions. A free account can also start a free month of the whole course, with no card.

Open this lesson in the course See the whole course