Homeschool · Diploma track · Grades 8-9

Algebra 1: free lessons and course outline

A full year of Algebra 1 on the California traditional pathway, built to be the student's whole course in the subject rather than a supplement to one. Algebra 1 is the course everything after it depends on: Geometry, Algebra 2, Precalculus, Chemistry and Physics all assume you can solve, rearrange, factor and graph without stopping to think about it. Eleven units take the year from the structure of an expression through linear equations, functions, systems, exponentials, polynomials, quadratics, radicals and rational expressions, ending in the statistics California puts in this course. Every problem is worked line by line, because a student who can state a rule but cannot carry a calculation through has learned the wrong half.

DIPLOMA TRACK CA CCSS MATH TRADITIONAL PATHWAY MODEL ANSWERS 75 LESSONS 880 PRACTICE PROBLEMS Grade 8 mathematics. This is a complete course in Algebra 1 and does not assume other instruction in the subject.

Algebra 1 is the gateway course. Nearly every mathematics and science course a student takes afterward assumes it, and the students who struggle in Algebra 2 or Chemistry are almost always students for whom some piece of Algebra 1 never became automatic. This course is built for that. The eleven units follow the California traditional pathway in the order the standards set out, because the skills genuinely have to be built in sequence: you cannot factor before you can multiply polynomials, and you cannot solve a quadratic before you can factor. The year opens with the structure of expressions and the properties that justify every step of equation solving, then moves through linear equations and inequalities, functions and their notation, linear graphs, systems, sequences and exponential growth, polynomials and factoring, quadratic functions, solving quadratics by every available method, radicals and rational expressions, and finally the descriptive statistics California places in this course. Every worked example shows every line, and the four errors that cost Algebra 1 students the most marks are named where they arise rather than saved for a list. Every lesson ends with ten problems, every unit with a ten-problem review, and the year with six pieces of mathematical writing that have full model responses.

U1Unit 1: Expressions, Quantities and the Properties Behind Algebra7 lessons
U2Unit 2: Linear Equations and Inequalities in One Variable7 lessons
U3Unit 3: Functions and Function Notation7 lessons
U4Unit 4: Linear Functions and Their Graphs7 lessons
U5Unit 5: Systems of Equations and Inequalities7 lessons
U6Unit 6: Sequences and Exponential Functions7 lessons
U7Unit 7: Polynomials and Factoring7 lessons
U8Unit 8: Quadratic Functions7 lessons
U9Unit 9: Solving Quadratic Equations7 lessons
U10Unit 10: Radicals and Rational Expressions6 lessons
U11Unit 11: Descriptive Statistics and Bivariate Data6 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: Expressions, Quantities and the Properties Behind AlgebraFREE

U2 Unit 2: Linear Equations and Inequalities in One Variable

2.1 One and two step equations
2.2 Variables on both sides
2.3 Equations with fractions and decimals
2.4 No solution and infinitely many
2.5 Rearranging formulas
2.6 Linear inequalities in one variable
2.7 Compound inequalities and absolute value

U3 Unit 3: Functions and Function Notation

3.1 Relations, functions and the vertical line test
3.2 Function notation and evaluation
3.3 Domain and range
3.4 Reading a graph
3.5 Average rate of change
3.6 Piecewise functions
3.7 Absolute value functions

U4 Unit 4: Linear Functions and Their Graphs

4.1 Slope as a rate of change
4.2 Slope-intercept form
4.3 Point-slope form
4.4 Standard form and intercepts
4.5 Parallel and perpendicular lines
4.6 Writing linear equations from context
4.7 Interpreting linear models

U5 Unit 5: Systems of Equations and Inequalities

5.1 Systems and solving by graphing
5.2 Solving by substitution
5.3 Solving by elimination
5.4 Choosing a method and special cases
5.5 Systems in context
5.6 Linear inequalities in two variables
5.7 Systems of inequalities

U6 Unit 6: Sequences and Exponential Functions

6.1 Arithmetic sequences
6.2 Geometric sequences
6.3 The exponent rules
6.4 Zero, negative and rational exponents
6.5 Exponential growth and decay
6.6 Linear against exponential
6.7 Building exponential models

U7 Unit 7: Polynomials and Factoring

7.1 Polynomials: vocabulary and adding
7.2 Multiplying polynomials
7.3 Special products
7.4 Factoring out the greatest common factor
7.5 Factoring trinomials, leading coefficient one
7.6 Factoring with a leading coefficient
7.7 Difference of squares and factoring completely

U8 Unit 8: Quadratic Functions

8.1 The parent parabola and transformations
8.2 Vertex form
8.3 Standard form
8.4 Factored form and the zeros
8.5 Converting between the three forms
8.6 Comparing linear, exponential and quadratic
8.7 Building quadratic models

U9 Unit 9: Solving Quadratic Equations

9.1 Solving by graphing and by factoring
9.2 The square root method
9.3 Completing the square
9.4 The quadratic formula
9.5 The discriminant
9.6 Choosing a method
9.7 Quadratic applications

U10 Unit 10: Radicals and Rational Expressions

10.1 Square roots and simplifying radicals
10.2 Operations with radicals
10.3 Solving radical equations
10.4 Simplifying rational expressions
10.5 Operations with rational expressions
10.6 Solving rational equations

U11 Unit 11: Descriptive Statistics and Bivariate Data

11.1 Measures of center and spread
11.2 Outliers, skew and honest summaries
11.3 Comparing distributions with plots
11.4 Two-way frequency tables
11.5 Scatter plots and lines of best fit
11.6 Correlation, residuals and causation

Keep going in the full Algebra 1 course

All of U1 (Unit 1: Expressions, Quantities and the Properties Behind Algebra) 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