Algebra 1: a self-study course
A guided path through the core of Algebra 1, ordered the way it is taught: polynomials, then quadratic equations, then radicals and rational exponents, then exponential functions. Each unit teaches the idea; the worksheets right after it give you graded practice with a computed answer key. Work top to bottom and tick off each step as you go.
For Algebra 1 students (commonly Grades 8 to 10) and anyone reviewing the essentials
4 teaching units and 12 practice worksheets. Free, no login. Your progress is saved in this browser.
By the end you can
- Add, subtract and multiply polynomials fluently
- Solve quadratic equations four ways: square roots, completing the square, the formula and by reading the discriminant
- Simplify radicals and rewrite them with rational exponents
- Recognise, build and apply linear versus exponential models of growth and decay
1. Polynomials: the algebra toolkit
Everything later leans on comfortable polynomial arithmetic. Learn the moves, then drill them until they are automatic.
- Step 1Learn · teaching unitAbout three to four lessons of 45 to 60 minutesAdding, subtracting and multiplying polynomials
Start here. Learn how adding, subtracting and multiplying polynomials works, and why like terms combine.
- Step 2Practise · worksheetAlgebra 1 worksheetAdding and Subtracting Polynomials
Practise combining like terms.
2. Quadratic equations
Four methods, from the quickest special case to the formula that always works. Meet them in order so each one motivates the next.
- Step 4Practise · worksheetAlgebra 1 worksheetSolving Quadratics by Taking Square Roots
The simplest quadratics, solved by taking square roots.
- Step 5Practise · worksheetAlgebra 1 worksheetCompleting the Square (Transforming the Equation)
Rewrite in completed-square form, the setup for solving.
- Step 6Learn · teaching unitAbout four to five lessons of 45 to 60 minutesSolving quadratics: completing the square and the quadratic formula
Learn completing the square and the quadratic formula, and how they connect.
- Step 7Practise · worksheetAlgebra 1 worksheetSolving Quadratics by Completing the Square
Solve by completing the square.
- Step 9Practise · worksheetAlgebra 1 worksheetThe Discriminant
Read the discriminant to count solutions before solving.
3. Radicals and rational exponents
Quadratic answers arrive as radicals, so tidy them up and connect roots to fractional exponents.
- Step 10Learn · teaching unitAbout three lessons of 45 to 60 minutesRadicals and rational exponents
Learn to simplify radicals and switch between root and exponent notation.
- Step 12Practise · worksheetAlgebra 1 worksheetProperties of Rational Exponents
Apply the exponent laws to rational powers.
4. Exponential functions
The last big idea of Algebra 1: change that multiplies. Contrast it with linear change, then model growth and decay.
- Step 13Learn · teaching unitAbout four lessons of 45 to 60 minutesExponential functions: growth, decay and geometric sequences
Learn how exponential functions and geometric sequences model growth and decay.
- Step 14Practise · worksheetAlgebra 1 worksheetLinear vs. Exponential Tables
Tell linear and exponential tables apart.
- Step 15Practise · worksheetAlgebra 1 worksheetConstructing Linear & Exponential Functions
Build a function from a description.
- Step 16Practise · worksheetAlgebra 1 worksheetExponential Growth & Decay
Apply growth and decay to real contexts.