Algebra 1 Quiz Answers: 30 Practice Questions

Algebra 1 quiz answers are easier to study when problems are grouped by skill. This 30-question practice set covers expressions, equations, inequalities, graphs, exponents, and basic quadratics. Work through the six-question rounds before checking each answer and explanation.

Expressions and properties: Questions 1–6

1. What is 3x + 2 when x = 4?
   Answer: 14. Explanation: Substitute 4 for x: 3(4) + 2 = 14.
2. Simplify 2(x + 3) + x.
   Answer: 3x + 6. Explanation: Distribute 2 to get 2x + 6, then combine 2x and x.
3. Simplify 7a − 3a + 5.
   Answer: 4a + 5. Explanation: Combine the like terms 7a and −3a; the constant 5 remains.
4. Evaluate 2m − n when m = −2 and n = 3.
   Answer: −7. Explanation: Substitute the values: 2(−2) − 3 = −4 − 3 = −7.
5. Use the distributive property to expand −3(2x − 4).
   Answer: −6x + 12. Explanation: Multiply both terms inside the parentheses by −3.
6. Which property shows that 5 + x = x + 5?
   Answer: The commutative property of addition. Explanation: Changing the order of the addends does not change their sum.

Equations and inequalities: Questions 7–12

1. Solve x + 8 = 13.
   Answer: x = 5. Explanation: Subtract 8 from both sides.
2. What is x if 2x + 3 = 11?
   Answer: x = 4. Explanation: Subtract 3 to get 2x = 8, then divide by 2.
3. Solve 3(x − 2) = 12.
   Answer: x = 6. Explanation: Divide by 3 to get x − 2 = 4, then add 2.
4. Solve 5x + 2 = 2x + 11.
   Answer: x = 3. Explanation: Subtract 2x and 2 from both sides to get 3x = 9.
5. Solve −2x > 6.
   Answer: x < −3. Explanation: Divide both sides by −2 and reverse the inequality. For example, x = −4 gives 8 > 6.
6. Solve 3x − 4 ≤ 8.
   Answer: x ≤ 4. Explanation: Add 4 to get 3x ≤ 12, then divide by positive 3; the inequality direction stays the same.

Linear relationships and systems: Questions 13–18

1. What is the slope of the line through (3, 2) and (−1, 0)?
   Answer: 1/2. Explanation: Using change in y over change in x gives (2 − 0)/(3 − (−1)) = 2/4 = 1/2.
2. What is the y-intercept of y = −2x + 5?
   Answer: 5, at the point (0, 5). Explanation: Set x = 0 to find where the line crosses the y-axis.
3. For f(x) = 3x − 1, find f(4).
   Answer: 11. Explanation: Substitute 4 for x: f(4) = 3(4) − 1 = 11.
4. Write an equation for a line with slope 2 and y-intercept −3.
   Answer: y = 2x − 3. Explanation: Substitute the slope and intercept into y = mx + b.
5. Does the point (2, 7) lie on the line y = 3x + 1?
   Answer: Yes. Explanation: Substituting x = 2 gives y = 3(2) + 1 = 7, matching the point.
6. Solve the system x + y = 5 and x − y = 1.
   Answer: (x, y) = (3, 2). Explanation: Add the equations to get 2x = 6, so x = 3 and y = 2. Both original equations hold.

Exponents, radicals, and polynomials: Questions 19–24

1. What is 2³ × 2²?
   Answer: 32. Explanation: Add the exponents for powers with the same base: 2⁵ = 32.
2. Simplify (x³)².
   Answer: x⁶. Explanation: Multiply the exponents when raising a power to another power.
3. What is the principal square root of 81?
   Answer: 9. Explanation: The principal square root is nonnegative, and 9² = 81.
4. Simplify √50.
   Answer: 5√2. Explanation: Since 50 = 25 × 2, √50 = √25 × √2.
5. Simplify (x² + 3x) − (2x² − x).
   Answer: −x² + 4x. Explanation: Distribute the minus sign to get x² + 3x − 2x² + x, then combine like terms.
6. Multiply (x + 2)(x + 3).
   Answer: x² + 5x + 6. Explanation: Multiply each term in one factor by each term in the other and combine 3x + 2x.

Quadratics and word problems: Questions 25–30

1. Factor x² + 7x + 12.
   Answer: (x + 3)(x + 4). Explanation: 3 and 4 multiply to 12 and add to 7.
2. What are the solutions to x² − 5x + 6 = 0?
   Answer: x = 2 or x = 3. Explanation: Factor as (x − 2)(x − 3) = 0 and set each factor equal to zero.
3. Solve x² = 16.
   Answer: x = 4 or x = −4. Explanation: Both 4² and (−4)² equal 16.
4. A number increased by 7 is 19. What is the number?
   Answer: 12. Explanation: Write n + 7 = 19 and subtract 7. Check: 12 + 7 = 19.
5. Three notebooks cost $12 in total. If they all cost the same amount, how much does one notebook cost?
   Answer: $4. Explanation: Let p be the price of one notebook. Then 3p = 12, so p = 4.
6. A rectangle has width x units and length x + 2 units. Its area is 15 square units. What are its dimensions?
   Answer: Width 3 units and length 5 units. Explanation: x(x + 2) = 15 gives (x + 5)(x − 3) = 0. Reject x = −5 because a width must be positive; 3 × 5 = 15.

How to write and use better Algebra 1 quiz questions

Choose questions by skill

Teachers can select a few questions from one round to check a specific skill, such as distributing or finding slope. Students can use the same grouping to focus their review.

State assumptions and give enough information

Include the full equation, coordinates or context needed to answer. For geometry problems, make clear which quantities must be positive.

Check solutions and common errors

Substitute proposed solutions into the original equation and check every step. Pay particular attention to reversing an inequality when dividing by a negative number and to finding both roots when appropriate.

Use mistakes to guide practice

Identify the first step that went wrong, then try another question on the same skill without looking at its answer. For a particular textbook or test, consult its corresponding materials; this original practice set is not its answer key.

For a broader review after Algebra 1, use the math quiz with answers to revisit arithmetic, geometry, and other foundational skills.

Explore more Algebra 1 quiz formats

To keep practicing core algebra, try these algebra quiz questions with answers and explanations. For students ready to extend their skills to functions, advanced equations, and logarithms, continue with Algebra 2 practice questions with solutions.

Ready to create an Algebra 1 quiz?

Choose the Algebra 1 questions that fit your learning goal, check the answers, and decide whether students should show their working. You can create an online quiz with NineQuiz and explore Quick Quiz to organize a practice round.