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Quizzes > Mathematics

Algebra 1 Quiz: Practice Problems with Answers

Quick, scored algebra 1 practice quiz with instant feedback and answers.

Editorial: Review CompletedCreated By: Christa SaegerUpdated Aug 24, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style illustration of algebra symbols equations functions and inequalities on coral background for a quiz

This Algebra 1 quiz helps you practice equations, functions, and inequalities and see where you need review. Get instant scoring and step-by-step answers, then build skills with an algebra practice test, try a free algebra quiz, or check your speed with 10 algebra questions and answers.

Simplify the expression: 2x + 3x.
6x
5x
x
2x
To simplify 2x + 3x, you combine like terms by adding their coefficients: 2 + 3 equals 5, so the result is 5x. Understanding how to combine like terms is foundational in algebra. For more examples on simplifying expressions, see .
Solve for x: x + 5 = 12.
5
7
-7
17
To solve x + 5 = 12, subtract 5 from both sides to isolate x, giving x = 7. This is a basic one-step linear equation. For more practice on one-variable equations, visit .
Evaluate the function f(x) = 2x + 1 at x = 3.
5
6
8
7
To evaluate f(3) for f(x) = 2x + 1, substitute 3 for x: 2(3) + 1 = 6 + 1 = 7. Evaluating functions by substitution is a key skill in algebra. Learn more about function evaluation at .
What is the slope of the line passing through (0, 0) and (4, 2)?
2
-1/2
1/2
4
Slope is rise over run: change in y divided by change in x. Here, (2 - 0)/(4 - 0) = 2/4 = 1/2. Mastering slope calculations is crucial for graphing lines. For more on slope, see .
Solve for x: 2x - 3 = 7.
7
2
5
-5
Add 3 to both sides to get 2x = 10, then divide by 2 yielding x = 5. This is a straightforward two-step equation. For more practice on linear equations, see .
Solve for x: 3(x + 2) = 15.
-3
3
1
5
First distribute: 3x + 6 = 15. Subtract 6 to get 3x = 9, then divide by 3 giving x = 3. This reinforces the distributive property in equations. Review the distributive property at .
What is the y-intercept of the line y = -x + 3?
3
-1
-3
0
In slope-intercept form y = mx + b, b is the y-intercept. Here b = 3, so the line crosses the y-axis at (0,3). Understanding intercepts is key to graphing. More on graphing lines at .
Simplify the product: 4x^2y × 3xy^3.
12x^3y^4
7x^3y^3
12x^2y^3
4x^3y^3
Multiply coefficients (4 × 3 = 12) and add exponents for like bases: x^2 × x = x^(2+1) = x^3, y × y^3 = y^(1+3) = y^4. The result is 12x^3y^4. For more on multiplying polynomials, visit .
Solve the quadratic equation: 2x^2 - 8x + 6 = 0.
x = 2 and x = -1
x = -1 and x = 3
x = 1 and x = 3
x = -3 and x = 1
Use the quadratic formula or factor: 2x^2 - 8x + 6 = 0 factors to 2(x^2 - 4x + 3) = 0, giving (x - 1)(x - 3) = 0, so x = 1 or 3. Understanding both factoring and the quadratic formula is essential. See more at .
Solve the inequality: 2x + 3 ? 7.
x ? 2
x ? -2
x ? 2
x > 2
Subtract 3 from both sides to get 2x ? 4, then divide by 2: x ? 2. Remember that dividing by a positive number leaves the inequality direction unchanged. For more on linear inequalities, see .
Find the inverse of the function f(x) = (x - 2) / 3.
f?¹(x) = (3x - 2)
f?¹(x) = x/3 - 2
f?¹(x) = 3x + 2
f?¹(x) = (x + 2) / 3
To find the inverse, swap x and y: x = (y - 2)/3, then solve for y: y - 2 = 3x, y = 3x + 2. Thus f?¹(x) = 3x + 2. For detailed steps, visit .
Determine the vertex of the parabola f(x) = x^2 - 4x + 4.
(0, 4)
(2, 0)
(-2, 0)
(2, 4)
The vertex of y = ax^2 + bx + c is at ( - b/(2a), f( - b/(2a))). Here a = 1, b = -4, so h = 4/2 = 2, and k = f(2) = 4 - 8 + 4 = 0. Hence the vertex is (2,0). For more on vertices, see .
Solve the absolute value equation: |2x - 3| = 7.
x = -5 or x = 2
x = 7 or x = -3
x = 3 or x = -7
x = 5 or x = -2
Set up two cases: 2x - 3 = 7 gives x = 5; 2x - 3 = -7 gives x = -2. Solving absolute value equations requires considering both positive and negative scenarios. For strategy on absolute value, see .
Solve the compound inequality: 1 < 2x + 1 ? 5.
0 < x ? 2
-1 < x < 2
1 < x ? 3
0 ? x < 2
Subtract 1 from all parts: 0 < 2x ? 4, then divide each part by 2: 0 < x ? 2. Compound inequalities must be solved and simplified across the entire inequality chain. For examples, check .
0
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Study Outcomes

  1. Solve Linear Equations -

    Apply algebra 1 skills to simplify and solve one-step and multi-step equations with confidence.

  2. Interpret Functions -

    Analyze function notation and graphs to understand relationships between variables in an Algebra I test online format.

  3. Manipulate Inequalities -

    Use algebraic techniques to solve and graph inequalities, mastering basic algebra questions on variable ranges.

  4. Assess Quiz Performance -

    Review your score from the free algebra 1 quiz to pinpoint strengths and areas for improvement.

  5. Identify Knowledge Gaps -

    Recognize specific algebra topics where additional practice is needed to sharpen your algebra practice quiz results.

  6. Boost Math Confidence -

    Build comfort with algebra 1 skills through instant feedback, preparing you for exams and real-world problem solving.

Cheat Sheet

  1. Mastering Linear Equations -

    Linear equations are the backbone of algebra 1 skills; practice isolating variables using inverse operations - e.g., in 2x + 3 = 7, subtract 3 then divide by 2. According to Khan Academy, mastering one-step to multi-step equations boosts confidence and prepares you for harder challenges in your algebra practice quiz.

  2. Graphing Functions in Slope-Intercept Form -

    Functions like y = mx + b form a core topic in basic algebra questions; identify slope (m) and y-intercept (b) to graph quickly. Use the "rise over run" mnemonic and challenge yourself with an Algebra I test online to reinforce your graphing skills.

  3. Solving and Graphing Inequalities -

    Inequalities follow the same rules as equations, but remember to flip the inequality sign when multiplying or dividing by a negative number - e.g., in - 2x > 6, dividing by - 2 gives x < - 3. Graph solutions on a number line with open or closed circles per National Council of Teachers of Mathematics (NCTM) guidelines for clarity.

  4. Factoring Quadratics Efficiently -

    Factoring expressions like x² + 5x + 6 requires finding two numbers that multiply to c and add to b; here 2 and 3 yield (x + 2)(x + 3). Use the FOIL (First, Outer, Inner, Last) method as a memory trick - factoring is a staple of many free algebra 1 quizzes.

  5. Applying Exponent and Radical Rules -

    Exponent rules such as a^m * a^n = a^(m+n) and (a^m)^n = a^(mn) streamline problem-solving and often appear on algebra practice quizzes. Convert between radical and exponential form - √a = a^(1/2) - to simplify expressions, a tip frequently endorsed by university math departments.

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