40 Algebra Quiz Questions With Answers and Explanations

These 40 algebra quiz questions cover expressions, equations, inequalities, linear functions, word problems, and a final factoring challenge. Each question includes an answer and a short explanation. Students can practice one round at a time, while teachers can select questions to match a lesson or build a shorter quiz.

Use these 40 algebra quiz questions with answers and explanations to practice expressions, equations, inequalities, linear graphs, word problems, and factoring. The questions are organized into six rounds so students and teachers can choose a focused review or combine several skills.

Solving algebra equations on a classroom chalkboard filled with mathematical formulas.

Algebra quiz questions: Round 1 — Expressions and substitution

  1. What is the value of 3x − 2 when x = 4?
    Answer: 10. Explanation: Substitute 4 for x: 3(4) − 2 = 10.
  2. Evaluate 2a + 5 when a = −3.
    Answer: −1. Explanation: 2(−3) + 5 = −6 + 5 = −1.
  3. Simplify 7x + 3x − 4.
    Answer: 10x − 4. Explanation: Combine the like terms 7x and 3x.
  4. Simplify 4(2x − 3) + 2x.
    Answer: 10x − 12. Explanation: Distribute 4 to get 8x − 12, then add 2x.
  5. Evaluate 5 − 2(b + 1) when b = 3.
    Answer: −3. Explanation: Replace b with 3: 5 − 2(4) = −3.
  6. Simplify 3y − 2( y − 4).
    Answer: y + 8. Explanation: Distribute −2 to get 3y − 2y + 8, then combine like terms.
  7. Evaluate x² − y when x = −2 and y = 3.
    Answer: 1. Explanation: (−2)² − 3 = 4 − 3 = 1.
  8. Simplify 6a − 3 + 2 − 4a.
    Answer: 2a − 1. Explanation: Combine 6a − 4a and −3 + 2.

Round 2 — One-step and multi-step equations

  1. Solve x + 7 = 19.
    Answer: x = 12. Explanation: Subtract 7 from both sides.
  2. Solve 5x = −20.
    Answer: x = −4. Explanation: Divide both sides by 5.
  3. Solve 3x + 5 = 14.
    Answer: x = 3. Explanation: Subtract 5 to get 3x = 9, then divide by 3.
  4. Solve x/4 − 2 = 3.
    Answer: x = 20. Explanation: Add 2 to get x/4 = 5, then multiply by 4.
  5. Solve 2(x − 4) = x + 3.
    Answer: x = 11. Explanation: Expand to get 2x − 8 = x + 3; subtract x and add 8.
  6. Solve 4x + 1 = 2x + 9.
    Answer: x = 4. Explanation: Subtract 2x and 1 to get 2x = 8.
  7. Solve 3(2x + 1) = 15.
    Answer: x = 2. Explanation: Divide by 3, then solve 2x + 1 = 5.
  8. Solve 7 − 2x = 15.
    Answer: x = −4. Explanation: Subtract 7 to get −2x = 8, then divide by −2.

Round 3 — Inequalities and solution sets

  1. Solve x + 4 < 10.
    Answer: x < 6. Explanation: Subtract 4 from both sides; the inequality direction stays the same.
  2. Solve 3x ≥ 12.
    Answer: x ≥ 4. Explanation: Divide both sides by the positive number 3.
  3. Solve −2x > 6.
    Answer: x < −3. Explanation: Dividing both sides by −2 reverses the inequality sign.
  4. Does x = 4 satisfy 2x + 1 ≤ 9?
    Answer: Yes. Explanation: Substitution gives 9 ≤ 9, which is true because equality is included.
  5. Solve 5 − x ≤ 2.
    Answer: x ≥ 3. Explanation: Subtract 5 to get −x ≤ −3, then divide by −1 and reverse the sign.
  6. Which integers satisfy both x > −2 and x ≤ 2?
    Answer: −1, 0, 1 and 2. Explanation: List the integers greater than −2 and no greater than 2.

Round 4 — Linear graphs and function values

  1. What is the slope of the line through (1, 2) and (4, 11)?
    Answer: 3. Explanation: The slope is (11 − 2)/(4 − 1) = 9/3 = 3.
  2. What is the y-intercept of the line y = −2x + 5?
    Answer: (0, 5). Explanation: Set x = 0 to find where the line crosses the y-axis.
  3. If f(x) = 2x − 3, what is f(5)?
    Answer: 7. Explanation: Substitute 5 for x: 2(5) − 3 = 7.
  4. What is the x-intercept of y = 3x − 12?
    Answer: (4, 0). Explanation: Set y = 0 and solve 3x − 12 = 0.
  5. What is the slope of the line y = 4?
    Answer: 0. Explanation: The line is horizontal, so its y-value does not change as x changes.
  6. Write an equation for the line with slope 2 and y-intercept (0, −1).
    Answer: y = 2x − 1. Explanation: Substitute the slope and intercept into y = mx + b.

Round 5 — Algebra word problems

  1. A notebook costs $3 and a pen costs $2. If three notebooks and x pens cost $15, how many pens were bought?
    Answer: 3 pens. Explanation: Let x be the number of pens. Then 9 + 2x = 15, so x = 3.
  2. A rectangle has width x and length x + 3. If its perimeter is 26 units, what is its width?
    Answer: 5 units. Explanation: Use 2x + 2(x + 3) = 26. Then 4x = 20, so x = 5.
  3. A taxi charges a $4 starting fee plus $2 per mile. If the fare is $18, how many miles were traveled?
    Answer: 7 miles. Explanation: Let m be the miles traveled. Solve 4 + 2m = 18 to get m = 7.
  4. Maya has three more stickers than twice the number Leo has. Maya has 17 stickers. How many does Leo have?
    Answer: 7 stickers. Explanation: Let l be Leo’s number. Then 2l + 3 = 17, so l = 7.
  5. A cyclist travels 36 miles at a constant speed of 12 miles per hour. How long does the trip take?
    Answer: 3 hours. Explanation: Let t be the time in hours. Since 12t = 36, t = 3.
  6. A $25 gift card is used to buy tickets costing $4 each. After the purchase, $5 remains. How many tickets were bought?
    Answer: 5 tickets. Explanation: Let n be the number of tickets. Solve 25 − 4n = 5 to get n = 5.

Round 6 — Factoring and quadratic equations

Use this optional round when you are ready to practice factoring and quadratic equations.

  1. Factor x² + 5x + 6.
    Answer: (x + 2)(x + 3). Explanation: The numbers 2 and 3 multiply to 6 and add to 5.
  2. Factor x² − 9.
    Answer: (x − 3)(x + 3). Explanation: This is a difference of squares: x² − 3².
  3. Factor 3x² + 6x completely.
    Answer: 3x(x + 2). Explanation: The greatest common factor of both terms is 3x.
  4. Solve x² − 5x + 6 = 0.
    Answer: x = 2 or x = 3. Explanation: Factor as (x − 2)(x − 3) = 0, then set each factor equal to zero.
  5. Solve x² = 16.
    Answer: x = −4 or x = 4. Explanation: Both numbers have a square of 16.
  6. Solve x² + 4x = 0.
    Answer: x = 0 or x = −4. Explanation: Factor as x(x + 4) = 0, then set each factor equal to zero.

How to write and use better algebra quiz questions

Algebra quiz questions illustrated with handwritten equations, graphs, and mathematical diagrams.

Choose questions by skill and available time

For a short review, select 10 questions from the skills covered in class; for a broader practice session, choose 20 across several rounds. Leave factoring for learners who have studied it, and allow extra time for word problems.

Make each prompt and expected answer clear

State whether students should simplify, factor or solve, and include units or other needed conditions. For self-practice, cover each answer until you have worked through the question.

Use mistakes to guide review

Sort incorrect answers by skill, such as distributing a negative sign or reversing an inequality. Rework those questions and explain each step rather than treating a score as a standardized measure of ability.

Write plausible answer choices when needed

For multiple choice, include one correct answer and distinct alternatives based on realistic errors. Check that only one option is correct under the conditions stated.

For a mixed-topic checkpoint beyond algebra, try the math quiz with answers for students and teachers and choose questions that match your class.

Explore more algebra quiz formats

Students building their foundations can start with Algebra 1 quiz. For more advanced functions, rational equations, and logarithms, move on to Algebra 2 practice questions with solutions.

Ready to create an algebra quiz?

Select questions that fit the lesson, verify each solution, and agree on how to score reasoning as well as answers. Create an online activity with NineQuiz and explore Quick Quiz for your class.