# Algebra 1 | Free Practice Problems & Explanations

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#### 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: **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: **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 (One-Step)

*Example:* Solve for .

**Lesson: **Solving Multi-Step Equations

*Example:* Solve for .

**Lesson: **Multi-Step 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 .

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#### 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 Non-Linear 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

- Practice 01
- Practice 02
- Practice 03
- Practice 04

*Example:*What is the equation of a line with a slope of 4 and a y-intercept of 1?

**Lesson: ** Point Slope Form

- Practice 01
- Practice 02

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

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

- Practice 01
- Practice 02
- Practice 03
- Practice 04

*Example:*What is the slope intercept form of a line passing through the point (-3,0) with a slope of 1?

**Lesson: ** Standard Form of the Equations of a Line

- Practice 01
- Practice 02

*Example:*What is the standard form equation of the line ?

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

- Practice 01
- Practice 02

*Example:*What is the equation of the line that passes through (4,-2) and (0,3)?

**Lesson: **Equations of Parallel and Perpendicular Lines

- Practice 01
- Practice 02

*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

**Lesson: ** Scatterplots and Trendlines

- Practice 01
- Practice 02

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

**Lesson: **Graphing Absolute Value Functions

- Practice 01
- Practice 02

*Example:*Graph the equation

#### VI. Systems of Equations and Inequalities

**Lesson: **Solving a System of Equations Graphically

- Practice 01
- Practice 02

*Example:*Solve the following system of equations graphically: and

**Lesson: **Solving a System of Equations Graphically

- Practice 01
- Practice 02

*Example:*Solve the following system of equations graphically: and

**Lesson: **Solving a System of Equations Using Substitution

- Practice 01
- Practice 02

*Example:*Solve the following system of equations by using substitution: and

**Lesson: **Solving a System of Equations Using Substitution

- Practice 01
- Practice 02

*Example:*Solve the following system of equations by using substitution: and

**Lesson: **Solving a System of Equations Using Elimination

- Practice 01
- Practice 02

*Example:*Solve the following system of equations by using elimination: and

**Lesson: **Solving a System of Equations Using Elimination

- Practice 01
- Practice 02

*Example:*Solve the following system of equations by using elimination: and

**Lesson: ** Applications of Linear Systems

- Practice 01
- Practice 02

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

**Lesson: **Word Problems – System of Equations

- Practice 01
- Practice 02

*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?

**Lesson: **Word Problems – System of Equations

- Practice 01
- Practice 02

*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?

**Lesson: **Graphing Linear Inequalities

- Practice 01
- Practice 02

*Example:*Sketch the solution to the system of inequalities: and

**Lesson: **Graphing Linear Inequalities

- Practice 01
- Practice 02

*Example:*What system of inequalities is shown below?

**Lesson: ** Solving a System of Linear Inequalities

- Practice 01
- Practice 02

*Example:*What is the solution to the following system of inequalities: and

#### VII. Exponents and Exponential Functions

**Lesson: **Positive Exponents

- Practice 01
- Practice 02

*Example:*Evaluate

**Lesson: **Negative Exponents

- Practice 01
- Practice 02

*Example:*Evaluate

**Lesson: **Multiplying & Dividing Terms that have Exponents

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Multiplying & Dividing Terms that have Exponents

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Graphs of Exponential Functions

- Practice 01
- Practice 02

*Example:*Graph the function

**Lesson: **Exponential Growth

- Practice 01
- Practice 02

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

**Lesson: **Exponential Decay

- Practice 01
- Practice 02

*Example:*Is the function exponential decay?

#### VIII. Polynomials and Factoring

**Lesson: **Adding & Subtracting Polynomials

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Adding & Subtracting Polynomials

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Multiplying a Polynomial by a Monomial

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Dividing a Polynomial by a Monomial

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Factor Out the Greatest Common Factor

- Practice 01
- Practice 02

*Example:*Factor out the GCF from

**Lesson: **Factor Out the Greatest Common Factor

- Practice 01
- Practice 02

*Example:*Factor out the GCF from

**Lesson: **Multiplying Binomials

- Practice 01
- Practice 02

*Example:*Multiply

**Lesson: **Multiplying a Binomial by a Trinomial

- Practice 01
- Practice 02

*Example:*Multiply

**Lesson: **Multiplying a Trinomial by a Binomial

- Practice 01
- Practice 02

*Example:*Multiply

**Lesson: ** Multiplying Binomials (Special Cases)

- Practice 01
- Practice 02

*Example:*Multiply

**Lesson: ** Factoring Quadratics

- Practice 01
- Practice 02

*Example:*Factor

**Lesson: ** Factoring Quadratics

- Practice 01
- Practice 02

*Example:*Factor

**Lesson: **Difference of Perfect Squares

- Practice 01
- Practice 02

*Example:*Factor

**Lesson: **Factoring by Grouping

- Practice 01
- Practice 02

*Example:*Factor

#### IX. Quadratic Functions and Equations

**Lesson: **Evaluating Quadratic Functions

- Practice 01
- Practice 02

*Example:*Evaluate at

**Lesson: **Properties of Quadratic Functions

- Practice 01
- Practice 02

*Example:*Is the point (3,7) a solution to the function ?

**Lesson: ** Solving Quadratic Equations by Taking Square Roots

- Practice 01
- Practice 02

*Example:*What are the solutions to ?

**Lesson: ** Solving Equations by Factoring

- Practice 01
- Practice 02

*Example:*What are the solutions to ?

**Lesson: **Completing the Square

- Practice 01
- Practice 02

*Example:*What should be the value for when completing the square for ?

**Lesson: **Solve Equations by Completing the Square

- Practice 01
- Practice 02

*Example:*Find the solutions to by completing the square

**Lesson: **Vertex From of a Quadratic Function by Completing the Square

- Practice 01
- Practice 02

*Example:*Complete the square to find the vertex of

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

- Practice 01
- Practice 02

*Example:*Solve the following system of equations graphically: and

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

- Practice 01
- Practice 02

*Example:*Solve the following system of equations by using substitution: and

#### X. Radical Expressions and Functions

**Lesson: **Pythagorean Theorem

- Practice 01
- Practice 02

*Example:*If the legs of a right triangle measure 5 and 12, what is the length of the hypotenuse?

**Lesson: **Simplifying Radical Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Adding and Subtracting Radical Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: ** Multiplying Radical Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Dividing Radical Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Solving Equations That Have Radical Terms

- Practice 01
- Practice 02

*Example:*Solve for x:

**Lesson: **Solving Equations That Have Radical Terms

- Practice 01
- Practice 02

*Example:*Solve for x:

**Lesson: **Graphing Square Root Functions

- Practice 01
- Practice 02

*Example:*Graph the function

**Lesson: **SOHCAHTOA (sine, cosine, tangent)

- Practice 01
- Practice 02

*Example:*In , is a right angle, , and . What is the measure of ?

**Lesson: **Inverse Trigonometric Functions

- Practice 01
- Practice 02

*Example:*Given that is a right triangle with as the right angle, and . What is the measure of ?

#### XI. Rational Expressions and Functions

**Lesson: **Simplifying Rational Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Multiplying and Dividing Rational Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Dividing Polynomials

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Adding and Subtracting Rational Expressions

- Practice 01
- Practice 02

*Example:*Simplify

**Lesson: **Fractional Equations

- Practice 01
- Practice 02

*Example:*Solve for x:

**Lesson: **Solving Rational Equations

- Practice 01
- Practice 02

*Example:*Solve for x:

**Lesson: **Inverse Variation

- Practice 01
- Practice 02

*Example:*If varies inversely with , and when , find when is

**Lesson: **Graphing Rational Functions

- Practice 01
- Practice 02

*Example:*Graph

#### XII. Data Analysis and Probability

**Lesson: **Matrices

- Practice 01
- Practice 02

*Example:*What are the dimensions of this matrix?

**Lesson: **Frequency, Cumulative Frequency, & Histograms

- Practice 01
- Practice 02

*Example:*What is the frequency of the letter A in the following: AADBABACCADDCAD

**Lesson: **Measures of Central Tendency & Dispersion

- Practice 01
- Practice 02

*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?

**Lesson: **Box & Whisker Plot

- Practice 01
- Practice 02

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

**Lesson: **Samples and Surveys

- Practice 01
- Practice 02

*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?

**Lesson: **Permutations and Combinations

- Practice 01
- Practice 02

*Example:*Evaluate

**Lesson: **Theoretical vs. Experimental Porbability

- Practice 01
- Practice 02

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

**Lesson: **Probability of Compound Events

- Practice 01
- Practice 02

*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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