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Algebra 1 Help | Free Algebra 1 Lessons & Practice Problems

Free Algebra 1 Help
Go through the lessons and practice problems below to help you learn Algebra 1 and excel in school. We’ll track your progress and help you identify your strengths and weaknesses. Our Algebra 1 lessons are available for free to everyone. If you’re a teacher and need worksheets for your students, we have free printable Algebra 1 worksheets.

I. Introduction to Algebra

Lesson: Verbal to Algebraic Expressions & Equations

Example: How do you write 5 greater than x algebraically?  

Lesson: Declaring Variables

Example: Mike is 3 inches taller than Semande. If Semande is s inches tall, express Mike’s height in terms of s.

Lesson: Order of Operations

Example: Evaluate 3 - (5-8)^2  

Lesson: Real Numbers (Including Rational vs. Irrational Numbers)

Lesson: Order of Operations with Substitution

Example: If x=2, what is the value of 2x^2-3x?  

Lesson: Adding and Subtracting Real Numbers

Example: Evaluate 5 - (-2)  

Lesson: Multiplying and Dividing Real Numbers

Example: Evaluate -3 \times 4  

Lesson: Properties of Real Numbers

Example: Which property justifies the following equation: 5(x+2y)+5=5x+10y+5

Lesson: Distributive Property

Example: Simplify 3(4x-5)

Lesson: Finding the Solution to an Equation

Example: Is 7 a solution to the equation 12 = 3x - 9?

II. Solving Equations

Lesson: Solving Algebraic Equations (One-Step)

Example: Solve for x. x+7=12

Lesson: Solving Multi-Step Equations

Example: Solve for x. 2x + 4 = 18

Lesson: Multi-Step Equations (Variable on Both Sides)

Example: Solve for x. 2x - 4 = -3x + 11

Lesson: Linear Equations

Example: Solve for y. 3y + 2x = 12  

Lesson: Solving Proportions

Example: Solve for x. \dfrac{x}{6} = \dfrac{20}{15}

Lesson: Solving Complex Proportions

Example: Solve for x. \dfrac{x+5}{4} = \dfrac{3}{8}

Lesson: Percents

Example: What is 48% of 30?

Lesson: Percent Change

Example: What is the percent change from 50 to 72?

III. Solving Inequalities

Lesson: Graphing Inequalities

Example: Graph k < 1 Algebra 1 Lessons

Lesson: Solving Inequalities Using Addition or Subtraction

Example: Solve for x. x - 12 > 8

Lesson: Solving Inequalities Using Multiplication or Division

Example: Solve for x. -4x \geq 12

Lesson: Solving Inequalities

Example: Solve for x. -7x + 19 \leq -2

Lesson: Solving Compound Inequalities

Example: Solve for x. -3 \leq 2x -5 < 21

Lesson: Solving and Graphing Compound Inequalities

Example: Solve for x and graph. 0 \leq r + 5 < 9 Algebra 1 Lessons

Lesson: Absolute Value Equations

Example: Solve for p. 9 + |5p + 1| = 18

Lesson: Absolute Value Inequalities

Example: Solve for x. 3|5x + 1| > 12

IV. Functions

Lesson: Using Graphs to Relate Two Quantities

Example: A bird flies above ground in search of worms. This is represented in the table below. Algebra 1 Lessons What does A represent?

Lesson: Patterns and Linear Functions

Example: Is the following graph linear? Algebra 1 Lessons Example: For each set of ordered pairs, write the rule that represents the function. (0, 3), (1, 8), (2, 13), (3, 18), (4, 23)

Lesson: Patterns and Non-Linear Functions

Example: Is the following a linear or nonlinear function? Algebra 1 Lessons Example: For the set of ordered pairs, write the rule that represents the function. (0,1),(1,3),(2,9),(3,27),(4,81)

Lesson: Graphing a Function Rule

Example: Match the function with its graph. Algebra 1 Lessons

Lesson: Writing a Function Rule

Example: Write the function rule for the table of values. Algebra 1 Lessons

Lesson: Formalizing Relations and Functions

Example: Is the following relation shown a function? (-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)

V. Linear Functions

Lesson: Slope

Example: What is the slope of the line below? Algebra 1 Lessons Example: What is the slope of the line that passes through the points (2, 7) and (5, 12)?

Lesson: Equation of a Line

Example:

Lesson: Point Slope Form

Example:
    What is the point-slope form of a line passing through the point (1,2) with a slope of -2?
  • Practice 01
  • Practice 02

Lesson: Finding the Equation of a Line, Given the Slope and a Point

Example:

Lesson: Standard Form of the Equations of a Line

Example:
    • What is the standard form equation of the line 30-3y=15x?
    • Practice 01
 

Lesson: Finding the Equation of a Line, Given Two Points

Example:

Lesson: Equations of Parallel and Perpendicular Lines

Example:
    • What is the equation of the line that passes through (2,4) and is parallel to y=3x-1
Example:
    What is the equation of the line that passes through (2,4) and is perpendicular to y=3x-1
  • Practice 01

Lesson: Scatterplots and Trendlines

Example:
    • If the trend continues, what is the expected y-value when x is 8, based on the scatterplot shown below?
Algebra 1 Lessons

Lesson: Graphing Absolute Value Functions

Example:

VI. Systems of Equations and Inequalities

Lesson: Solving a System of Equations Graphically

Example:
    • Solve the following system of equations graphically: y=2x+3 and y=-3x+3
    • Practice 01

Lesson: Solving a System of Equations Graphically

Example:

Lesson: Solving a System of Equations Using Substitution

Example:

Lesson: Solving a System of Equations Using Substitution

Example:
    Solve the following system of equations by using substitution: y=x and y=-7x+3
  • Practice 01

Lesson: Solving a System of Equations Using Elimination

Example:

Lesson: Solving a System of Equations Using Elimination

Example:

Lesson: Applications of Linear Systems

Example:

Lesson: Word Problems – System of Equations

Example:
    Smith and Jones are selling cookies. Smith sold 4 chocolate chip and 6 sugar cookies for a total of $60. Jones sold 5 chocolate chip and 3 sugar cookies for a total of $30. How much does a chocolate chip cookie cost?
  • Practice 01
  • Practice 02

Lesson: Word Problems – System of Equations

Example:
    Rose is selling tickets to the school play to the first and second graders. The first graders bought 12 tickets for Friday night and 15 tickets to Saturday night for a total of $400. The second graders bought 14 tickets to Friday night and 10 tickets to Saturday night for a total of $420. How much does a Friday night ticket cost?
  • Practice 01
  • Practice 02

Lesson: Graphing Linear Inequalities

Example:

Lesson: Graphing Linear Inequalities

Example:
    • What system of inequalities is shown below?
Algebra 1 Lessons

Lesson: Solving a System of Linear Inequalities

Example:

VII. Exponents and Exponential Functions

Lesson: Positive Exponents

Example:

Lesson: Negative Exponents

Example:

Lesson: Multiplying & Dividing Terms that have Exponents

Example:

Lesson: Multiplying & Dividing Terms that have Exponents

Example:

Lesson: Graphs of Exponential Functions

Example:

Lesson: Exponential Growth

Example:
    The population of an ant colony increases by 100 each year. Is this linear or exponential growth?
  • Practice 01
  • Practice 02

Lesson: Exponential Decay

Example:

VIII. Polynomials and Factoring

Lesson: Adding & Subtracting Polynomials

Example:

Lesson: Adding & Subtracting Polynomials

Example:

Lesson: Multiplying a Polynomial by a Monomial

Example:

Lesson: Dividing a Polynomial by a Monomial

Example:

Lesson: Factor Out the Greatest Common Factor

Example:

Lesson: Factor Out the Greatest Common Factor

Example:

Lesson: Multiplying Binomials

Example:

Lesson: Multiplying a Binomial by a Trinomial

Example:

Lesson: Multiplying a Trinomial by a Binomial

Example:

Lesson: Multiplying Binomials (Special Cases)

Example:

Lesson: Factoring Quadratics

Example:

Lesson: Factoring Quadratics

Example:

Lesson: Difference of Perfect Squares

Example:

Lesson: Factoring by Grouping

Example:

IX. Quadratic Functions and Equations

Lesson: Evaluating Quadratic Functions

Example:

Lesson: Properties of Quadratic Functions

Example:

Lesson: Solving Quadratic Equations by Taking Square Roots

Example:

Lesson: Solving Equations by Factoring

Example:

Lesson: Completing the Square

Example:
    What should be the value for c when completing the square for a^2 -8a +c?
  • Practice 01

Lesson: Solve Equations by Completing the Square

Example:

Lesson: Vertex Form of a Quadratic Function by Completing the Square

Example:

Lesson: Solving a System of Equations Graphically (Linear & Quadratic)

Example:

Lesson: Solving a System of Equations Using Substitution (Linear & Quadratic)

Example:

X. Radical Expressions and Functions

Lesson: Pythagorean Theorem

Example:
    If the legs of a right triangle measure 5 and 12, what is the length of the hypotenuse?
  • Practice 01
  • Practice 02

Lesson: Simplifying Radical Expressions

Example:

Lesson: Adding and Subtracting Radical Expressions

Example:

Lesson: Multiplying Radical Expressions

Example:

Lesson: Dividing Radical Expressions

Example:

Lesson: Solving Equations That Have Radical Terms

Example:

Lesson: Solving Equations That Have Radical Terms

Example:

Lesson: Graphing Square Root Functions

Example:

Lesson: SOHCAHTOA (sine, cosine, tangent)

Example:

Lesson: Inverse Trigonometric Functions

Example:
    Given that \triangle ABC is a right triangle with \angle C as the right angle, \overline{AB} = 12 and \overline{BC} = 7. What is the measure of \angle A?
  • Practice 01
  • Practice 02

XI. Rational Expressions and Functions

Lesson: Simplifying Rational Expressions

Example:

Lesson: Multiplying and Dividing Rational Expressions

Example:

Lesson: Dividing Polynomials

Example:

Lesson: Adding and Subtracting Rational Expressions

Example:

Lesson: Fractional Equations

Example:

Lesson: Solving Rational Equations

Example:

Lesson: Inverse Variation

Example:

Lesson: Graphing Rational Functions

Example:

XII. Data Analysis and Probability

Lesson: Matrices

Example:
    • What are the dimensions of this matrix?
Algebra 1 Lessons

Lesson: Frequency, Cumulative Frequency, & Histograms

Example:

Lesson: Measures of Central Tendency & Dispersion

Example:
    James scored a 91 and a 94 on his first two tests. What score must he receive on his third test to maintain a 90 average?
  • Practice 01
  • Practice 02

Lesson: Box & Whisker Plot

Example:

Lesson: Samples and Surveys

Example:
    John is trying to find out how many students in his school prefer math class over english class. He surveys every 5th ninth grader who walks into school. Is this sample biased?
  • Practice 01
  • Practice 02

Lesson: Permutations and Combinations

Example:

Lesson: Theoretical vs. Experimental Probability

Example:
    Joanna rolled a six-sided die. What is the theoretical probability that it will land on an even number?
  • Practice 01
  • Practice 02

Lesson: Probability of Compound Events

Example:
    Patricia rolled a six-sided die twice. What is the probability that she rolls a 2 and then an odd number?
  • Practice 01
  • Practice 02