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 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 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
Lesson: Real Numbers (Including Rational vs. Irrational Numbers)
Lesson: Order of Operations with Substitution
Example: If , what is the value of ?
Lesson: Adding and Subtracting Real Numbers
Example: Evaluate
Lesson: Multiplying and Dividing Real Numbers
Example: Evaluate
Lesson: Properties of Real Numbers
Example: Which property justifies the following equation:
Lesson: Distributive Property
Example: Simplify
Lesson: Finding the Solution to an Equation
Example: Is 7 a solution to the equation ?
II. Solving Equations
Lesson: Solving Algebraic Equations (OneStep)
Example: Solve for .
Lesson: Solving MultiStep Equations
Example: Solve for .
Lesson: MultiStep Equations (Variable on Both Sides)
Example: Solve for .
Lesson: Linear Equations
Example: Solve for .
Lesson: Solving Proportions
Example: Solve for .
Lesson: Solving Complex Proportions
Example: Solve for .
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
Lesson: Solving Inequalities Using Addition or Subtraction
Example: Solve for .
Lesson: Solving Inequalities Using Multiplication or Division
Example: Solve for .
Lesson: Solving Inequalities
Example: Solve for .
Lesson: Solving Compound Inequalities
Example: Solve for .
<
Lesson: Solving and Graphing Compound Inequalities
Example: Solve for and graph.
<
Lesson: Absolute Value Equations
Example: Solve for .
Lesson: Absolute Value Inequalities
Example: Solve for .
>
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.
What does A represent?
Lesson: Patterns and Linear Functions
Example: Is the following graph linear?
Example: For each set of ordered pairs, write the rule that represents the function.
Lesson: Patterns and NonLinear Functions
Example: Is the following a linear or nonlinear function?
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.
Lesson: Writing a Function Rule
Example: Write the function rule for the table of values.
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?
Example: What is the slope of the line that passes through the points (2, 7) and (5, 12)?
 Practice 01 – Slope from a graph & from 2 points
 Practice 02 – Slope from a graph & from 2 points
 Practice 03 – Slope from 2 Points
 Practice 04 – Slope from 2 Points
Lesson: Equation of a Line
Example:
 What is the equation of a line with a slope of 4 and a yintercept of 1?
 Practice 01
 Practice 02
 Practice 03
 Practice 04
Lesson: Point Slope Form
Example:
 What is the pointslope 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:
 What is the slope intercept form of a line passing through the point (3,0) with a slope of 1?
 Practice 01
 Practice 02
 Practice 03
 Practice 04
Lesson: Standard Form of the Equations of a Line
Example:
 What is the standard form equation of the line ?
 Practice 01
 Practice 02
Lesson: Finding the Equation of a Line, Given Two Points
Example:
 What is the equation of the line that passes through (4,2) and (0,3)?
 Practice 01
 Practice 02
Lesson: Equations of Parallel and Perpendicular Lines
Example:

 What is the equation of the line that passes through (2,4) and is parallel to
Example:
 What is the equation of the line that passes through (2,4) and is perpendicular to
 Practice 01
 Practice 02
Lesson: Scatterplots and Trendlines
Example:

 If the trend continues, what is the expected yvalue when x is 8, based on the scatterplot shown below?
Lesson: Graphing Absolute Value Functions
Example:
 Graph the equation
 Practice 01
 Practice 02
VI. Systems of Equations and Inequalities
Lesson: Solving a System of Equations Graphically
Example:
 Solve the following system of equations graphically: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Graphically
Example:
 Solve the following system of equations graphically: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Using Substitution
Example:
 Solve the following system of equations by using substitution: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Using Substitution
Example:
 Solve the following system of equations by using substitution: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Using Elimination
Example:
 Solve the following system of equations by using elimination: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Using Elimination
Example:
 Solve the following system of equations by using elimination: and
 Practice 01
 Practice 02
Lesson: Applications of Linear Systems
Example:
 The difference between two numbers is 4. Their sum is 18. What are the two numbers?
 Practice 01
 Practice 02
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:
 Sketch the solution to the system of inequalities: and
 Practice 01
 Practice 02
Lesson: Graphing Linear Inequalities
Example:

 What system of inequalities is shown below?
Lesson: Solving a System of Linear Inequalities
Example:
 What is the solution to the following system of inequalities: and
 Practice 01
 Practice 02
VII. Exponents and Exponential Functions
Lesson: Positive Exponents
Example:
 Evaluate
 Practice 01
 Practice 02
Lesson: Negative Exponents
Example:
 Evaluate
 Practice 01
 Practice 02
Lesson: Multiplying & Dividing Terms that have Exponents
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Multiplying & Dividing Terms that have Exponents
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Graphs of Exponential Functions
Example:
 Graph the function
 Practice 01
 Practice 02
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:
 Is the function exponential decay?
 Practice 01
 Practice 02
VIII. Polynomials and Factoring
Lesson: Adding & Subtracting Polynomials
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Adding & Subtracting Polynomials
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Multiplying a Polynomial by a Monomial
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Dividing a Polynomial by a Monomial
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Factor Out the Greatest Common Factor
Example:
 Factor out the GCF from
 Practice 01
 Practice 02
Lesson: Factor Out the Greatest Common Factor
Example:
 Factor out the GCF from
 Practice 01
 Practice 02
Lesson: Multiplying Binomials
Example:
 Multiply
 Practice 01
 Practice 02
Lesson: Multiplying a Binomial by a Trinomial
Example:
 Multiply
 Practice 01
 Practice 02
Lesson: Multiplying a Trinomial by a Binomial
Example:
 Multiply
 Practice 01
 Practice 02
Lesson: Multiplying Binomials (Special Cases)
Example:
 Multiply
 Practice 01
 Practice 02
Lesson: Factoring Quadratics
Example:
 Factor
 Practice 01
 Practice 02
Lesson: Factoring Quadratics
Example:
 Factor
 Practice 01
 Practice 02
Lesson: Difference of Perfect Squares
Example:
 Factor
 Practice 01
 Practice 02
Lesson: Factoring by Grouping
Example:
 Factor
 Practice 01
 Practice 02
IX. Quadratic Functions and Equations
Lesson: Evaluating Quadratic Functions
Example:
 Evaluate at
 Practice 01
 Practice 02
Lesson: Properties of Quadratic Functions
Example:
 Is the point (3,7) a solution to the function ?
 Practice 01
 Practice 02
Lesson: Solving Quadratic Equations by Taking Square Roots
Example:
 What are the solutions to ?
 Practice 01
 Practice 02
Lesson: Solving Equations by Factoring
Example:
 What are the solutions to ?
 Practice 01
 Practice 02
Lesson: Completing the Square
Example:
 What should be the value for when completing the square for ?
 Practice 01
 Practice 02
Lesson: Solve Equations by Completing the Square
Example:
 Find the solutions to by completing the square
 Practice 01
 Practice 02
Lesson: Vertex Form of a Quadratic Function by Completing the Square
Example:
 Complete the square to find the vertex of
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Graphically (Linear & Quadratic)
Example:
 Solve the following system of equations graphically: and
 Practice 01
 Practice 02
Lesson: Solving a System of Equations Using Substitution (Linear & Quadratic)
Example:
 Solve the following system of equations by using substitution: and
 Practice 01
 Practice 02
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:
 Simplify
 Practice 01
 Practice 02
Lesson: Adding and Subtracting Radical Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Multiplying Radical Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Dividing Radical Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Solving Equations That Have Radical Terms
Example:
 Solve for x:
 Practice 01
 Practice 02
Lesson: Solving Equations That Have Radical Terms
Example:
 Solve for x:
 Practice 01
 Practice 02
Lesson: Graphing Square Root Functions
Example:
 Graph the function
 Practice 01
 Practice 02
Lesson: SOHCAHTOA (sine, cosine, tangent)
Example:
 In , is a right angle, , and . What is the measure of ?
 Practice 01
 Practice 02
Lesson: Inverse Trigonometric Functions
Example:
 Given that is a right triangle with as the right angle, and . What is the measure of ?
 Practice 01
 Practice 02
XI. Rational Expressions and Functions
Lesson: Simplifying Rational Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Multiplying and Dividing Rational Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Dividing Polynomials
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Adding and Subtracting Rational Expressions
Example:
 Simplify
 Practice 01
 Practice 02
Lesson: Fractional Equations
Example:
 Solve for x:
 Practice 01
 Practice 02
Lesson: Solving Rational Equations
Example:
 Solve for x:
 Practice 01
 Practice 02
Lesson: Inverse Variation
Example:
 If varies inversely with , and when , find when is
 Practice 01
 Practice 02
Lesson: Graphing Rational Functions
Example:
 Graph
 Practice 01
 Practice 02
XII. Data Analysis and Probability
Lesson: Matrices
Example:

 What are the dimensions of this matrix?
Lesson: Frequency, Cumulative Frequency, & Histograms
Example:
 What is the frequency of the letter A in the following: AADBABACCADDCAD
 Practice 01
 Practice 02
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:
 What is the interquartile range for the following set of data: 2,5,3,7,5,6,2,2,9,4
 Practice 01
 Practice 02
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:
 Evaluate
 Practice 01
 Practice 02
Lesson: Theoretical vs. Experimental Probability
Example:
 Joanna rolled a sixsided 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 sixsided die twice. What is the probability that she rolls a 2 and then an odd number?
 Practice 01
 Practice 02
Sign up for a free membership on our algebra 1 lessons & start learning today. Learn about the importance of learning algebra here.
Caddell Prep offers online test prep, webbased math assignments, and inperson tutoring and test prep.