Algebra 1 Course Outline
Every unit and lesson in Algebra 1, from real numbers and linear equations to factoring and quadratics. Each lesson comes with worked examples, practice questions and a full answer key.
Try the student practice samples in the first expanded unit below. The detailed notes will be discussed during the course, with worked examples, guided practice, and time for questions. Enroll to work through the remaining lessons with your tutor.
Explore the study guide1Unit 1: Foundations of AlgebraNumber sets, order of operations, properties and writing algebraic expressions.6 lessons + review
- 1.1MCQ Sample
Real Numbers and the Number Line
Classify numbers as natural, whole, integer, rational or irrational.
- 1.2FRQ Sample
Order of Operations and Evaluating Expressions
Apply PEMDAS and evaluate expressions for given values.
- 1.3Enroll Now
Properties of Real Numbers
Use commutative, associative, identity and inverse properties.
- 1.4Enroll Now
Combining Like Terms and the Distributive Property
Simplify expressions by distributing and combining like terms.
- 1.5Enroll Now
Operations with Fractions and Rational Numbers
Add, subtract, multiply and divide fractions and signed numbers.
- 1.6Enroll Now
Translating Words into Expressions
Turn verbal phrases into algebraic expressions and equations.
- 1REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 1.
2Unit 2: Linear EquationsSolving linear equations from one step to multi-step, with formulas, proportions and word problems.6 lessons + review
- 2.1Enroll Now
One- and Two-Step Equations
Solve equations with inverse operations and check solutions.
- 2.2Enroll Now
Multi-Step Equations
Combine like terms and distribute before isolating the variable.
- 2.3Enroll Now
Variables on Both Sides
Collect variables on one side; spot no-solution and identity cases.
- 2.4Enroll Now
Literal Equations and Formulas
Solve formulas for a chosen variable.
- 2.5Enroll Now
Ratios, Proportions and Percent
Set up proportions and solve percent, markup and discount problems.
- 2.6Enroll Now
Word Problems with Linear Equations
Define a variable, write an equation and interpret the answer.
- 2REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 2.
3Unit 3: Linear InequalitiesSolving and graphing inequalities, compound inequalities and absolute value.4 lessons + review
- 3.1Enroll Now
Solving and Graphing Inequalities
Solve one-variable inequalities and graph them on a number line.
- 3.2Enroll Now
Multi-Step Inequalities
Solve inequalities that need several steps, including flipping the sign.
- 3.3Enroll Now
Compound Inequalities
Solve and graph AND and OR inequalities.
- 3.4Enroll Now
Absolute Value Equations and Inequalities
Solve |x| equations and inequalities as two cases.
- 3REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 3.
4Unit 4: Coordinate Geometry and Linear FunctionsFunctions, slope and the three forms of a line, plus graphing inequalities and fitting data.8 lessons + review
- 4.1Enroll Now
The Coordinate Plane and Relations
Plot points, read relations and identify domain and range.
- 4.2Enroll Now
Functions and Function Notation
Use the vertical line test and evaluate f(x).
- 4.3Enroll Now
Slope and Rate of Change
Find slope from points, graphs and tables as a rate of change.
- 4.4Enroll Now
Slope-Intercept Form
Graph and write lines in y = mx + b form.
- 4.5Enroll Now
Point-Slope and Standard Form
Write lines from a point and slope; convert to Ax + By = C.
- 4.6Enroll Now
Parallel and Perpendicular Lines
Use slopes to identify and write parallel and perpendicular lines.
- 4.7Enroll Now
Graphing Linear Inequalities
Graph two-variable inequalities with boundary lines and shading.
- 4.8Enroll Now
Scatter Plots and Lines of Fit
Describe correlation and write a line of best fit.
- 4REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 4.
5Unit 5: Systems of Equations and InequalitiesThree ways to solve a system, applications and systems of inequalities.5 lessons + review
- 5.1Enroll Now
Solving Systems by Graphing
Find the intersection of two lines on a graph.
- 5.2Enroll Now
Solving Systems by Substitution
Solve a system by isolating and substituting a variable.
- 5.3Enroll Now
Solving Systems by Elimination
Add or subtract equations to eliminate a variable.
- 5.4Enroll Now
Applications of Systems
Model mixture, cost and rate problems with two equations.
- 5.5Enroll Now
Systems of Linear Inequalities
Graph overlapping solution regions for two inequalities.
- 5REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 5.
6Unit 6: Exponents and RadicalsExponent rules, scientific notation, square roots and simplifying radicals.5 lessons + review
- 6.1Enroll Now
Properties of Exponents
Apply product, quotient and power rules for exponents.
- 6.2Enroll Now
Zero and Negative Exponents
Rewrite expressions with zero and negative exponents.
- 6.3Enroll Now
Scientific Notation
Write and compute with very large and very small numbers.
- 6.4Enroll Now
Square Roots and Irrational Numbers
Estimate square roots and identify irrational numbers.
- 6.5Enroll Now
Simplifying Radical Expressions
Simplify radicals and add, subtract and multiply them.
- 6REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 6.
7Unit 7: Polynomials and FactoringPolynomial operations and every factoring pattern, ending with factoring completely.8 lessons + review
- 7.1Enroll Now
Adding and Subtracting Polynomials
Classify polynomials and combine like terms.
- 7.2Enroll Now
Multiplying Polynomials
Multiply monomials, binomials and polynomials.
- 7.3Enroll Now
Special Products
Use (a + b)², (a − b)² and (a + b)(a − b) patterns.
- 7.4Enroll Now
Factoring the Greatest Common Factor
Factor out the GCF, including grouping.
- 7.5Enroll Now
Factoring Trinomials (a = 1)
Factor x² + bx + c using sum and product.
- 7.6Enroll Now
Factoring Trinomials (a ≠ 1)
Factor ax² + bx + c by grouping (the ac method).
- 7.7Enroll Now
Difference of Squares and Perfect-Square Trinomials
Recognize and factor special patterns.
- 7.8Enroll Now
Factoring Completely
Choose and chain factoring methods until fully factored.
- 7REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 7.
8Unit 8: Quadratic Functions and EquationsGraphing parabolas and solving quadratics by graphing, factoring, square roots, completing the square and the formula.7 lessons + review
- 8.1Enroll Now
Graphing Quadratic Functions
Graph parabolas and find the vertex, axis and zeros.
- 8.2Enroll Now
Solving Quadratics by Graphing
Read solutions as x-intercepts of a parabola.
- 8.3Enroll Now
Solving Quadratics by Factoring
Use the zero product property after factoring.
- 8.4Enroll Now
Solving with Square Roots
Isolate the square and take square roots of both sides.
- 8.5Enroll Now
Completing the Square
Rewrite a quadratic to solve it and find the vertex.
- 8.6Enroll Now
The Quadratic Formula and the Discriminant
Solve any quadratic and use the discriminant to count solutions.
- 8.7Enroll Now
Quadratic Word Problems
Model area, projectile and revenue problems with quadratics.
- 8REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 8.
Independently developed by Code Scholars Tutoring. Lesson order and pacing can be adapted to the student’s school syllabus.