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Algebra 1 Help | Free Algebra 1 Lessons & Practice Problems

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. Algebra 1 help is available to everyone, but you need to create an account in order to access the practice questions and track your progress.

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: 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: 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?

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.
A094_2
What does A represent?

Lesson: Patterns and Linear Functions

Example: Is the following graph linear?
A095_1

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?
A096B_3

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.
1A

Lesson: Writing a Function Rule

Example: Write the function rule for the table of values.
A098_1

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?
A10_1
Example: What is the slope of the line that passes through the points (2, 7) and (5, 12)?

Lesson: Equation of a Line

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?

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

Lesson: Standard Form of the Equations of a Line

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

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

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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?

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Lesson: Graphing Absolute Value Functions

VI. Systems of Equations and Inequalities

Lesson: Solving a System of Equations Graphically

Lesson: Solving a System of Equations Graphically

Lesson: Solving a System of Equations Using Substitution

Lesson: Solving a System of Equations Using Substitution

Lesson: Solving a System of Equations Using Elimination

Lesson: Solving a System of Equations Using Elimination

Lesson: Applications of Linear Systems

    Example: The difference between two numbers is 4. Their sum is 18. What are the two numbers?

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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?

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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?

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Lesson: Graphing Linear Inequalities

Lesson: Graphing Linear Inequalities

Lesson: Solving a System of Linear Inequalities

VII. Exponents and Exponential Functions

Lesson: Positive Exponents

Lesson: Negative Exponents

Lesson: Multiplying & Dividing Terms that have Exponents

Lesson: Multiplying & Dividing Terms that have Exponents

Lesson: Graphs of Exponential Functions

Lesson: Exponential Growth

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

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Lesson: Exponential Decay

IX. Quadratic Functions and Equations

Lesson: Evaluating Quadratic Functions

Lesson: Properties of Quadratic Functions

Lesson: Solving Quadratic Equations by Taking Square Roots

Lesson: Solving Equations by Factoring

Lesson: Completing the Square

Lesson: Solve Equations by Completing the Square

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

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

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

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?

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Lesson: Simplifying Radical Expressions

Lesson: Adding and Subtracting Radical Expressions

Lesson: Multiplying Radical Expressions

Lesson: Dividing Radical Expressions

Lesson: Solving Equations That Have Radical Terms

Lesson: Solving Equations That Have Radical Terms

Lesson: Graphing Square Root Functions

Lesson: SOHCAHTOA (sine, cosine, tangent)

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?

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XII. Data Analysis and Probability

Lesson: Matrices

Lesson: Frequency, Cumulative Frequency, & Histograms

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?

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Lesson: Box & Whisker Plot

    Example: What is the interquartile range for the following set of data: 2,5,3,7,5,6,2,2,9,4

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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?

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Lesson: Permutations and Combinations

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?

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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?

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