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Quizzes > Mathematics

Algebra Quiz: Test Your Skills with Instant Answers

Quick, self-checking algebra quiz with answers. See mistakes and learn fast.

Editorial: Review CompletedCreated By: Nazli DasdemirUpdated Aug 27, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration promoting a free algebra quiz on a golden yellow background

Use this algebra quiz to practice core skills, solve equations, and get instant answers. For more targeted practice, try a grade 8 algebra test, work through an intermediate algebra practice test, or sharpen polynomials with a factoring polynomials quiz.

Solve for x: 2x + 5 = 17
x = -6
x = 12
x = 11
x = 6
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Simplify: 3(x - 2) + 2(x + 4)
5x - 14
5x - 2
5x + 14
5x + 2
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Evaluate x^2 - 3x when x = -2
10
2
-2
-10
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Factor completely: x^2 - 5x + 6
(x + 1)(x + 6)
(x + 2)(x + 3)
(x - 1)(x - 6)
(x - 2)(x - 3)
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Find the x-intercept of y = 2x + 5
x = -5
x = 5
x = 2.5
x = -2.5
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Expand: (x + 2)(x - 3)
x^2 - 6
x^2 - 5x + 6
x^2 - x - 6
x^2 + 5x - 6
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What is the y-intercept of y = -3x + 4?
-4
-3
4
3
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Find the slope of the line through (1, 2) and (3, 6)
1/2
2
4
-2
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Solve the inequality: 5 - 2x > 9
x < -2
x > -2
x > 2
x < 2
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Solve the system: x + y = 7 and x - y = 1
(4, 3)
(3, 4)
(7, 1)
(1, 7)
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Simplify: (2a^3b^2)(-3ab)
-6a^3b^2
-5a^4b^3
-6a^4b^3
6a^4b^3
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Rationalize the denominator: 5 / sqrt(2)
(sqrt(2))/5
5sqrt(2)
(10sqrt(2))/5
(5sqrt(2))/2
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Solve the quadratic: x^2 - 4x - 5 = 0
x = 5 or x = -1
x = -4 or x = 5
x = 4 or x = -5
x = 1 or x = -5
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Find the domain of f(x) = 1 / (x - 2)
All real x except x = 2
x > 2 only
x < 2 only
All real x
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Solve the inequality: 2|x + 1| <= 6
x <= -4 or x >= 2
-4 <= x <= 2
-2 <= x <= 4
x < -2 or x > 4
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Find the inverse function of f(x) = (x - 5) / 2
f^{-1}(x) = x/2 - 5
f^{-1}(x) = (x + 5)/2
f^{-1}(x) = 2x + 5
f^{-1}(x) = 2x + 5
undefined
Solve for x: x / (x - 1) = 2, x != 1
x = 1/2
x = -2
x = 2
No solution
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Complete the square: Rewrite x^2 + 6x as (x + a)^2 + b
(x + 3)^2 + 9
(x + 2)^2 - 4
(x + 3)^2 - 9
(x + 6)^2 - 36
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Divide polynomials: (x^3 - 1) / (x - 1), x != 1
x^2 - 1
x^2 - x + 1
x^2 + x + 1
x^2 + 1
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Combine the expressions: 1/(x + 1) + 1/(x - 1)
(2) / (x^2 - 1)
(x^2 + 1) / (x^2 - 1)
(x^2 - 1) / (2x)
(2x) / (x^2 - 1)
undefined
0

Study Outcomes

  1. Solve Linear Equations -

    Apply step-by-step methods to solve one-variable linear equations, reinforcing key algebraic principles and boosting confidence in equation solving.

  2. Simplify Algebraic Expressions -

    Combine like terms and use the distributive property to simplify expressions, ensuring a solid grasp of foundational algebraic manipulation.

  3. Analyze Variable Relationships -

    Interpret how variables interact within equations and develop strategies to isolate and solve for unknown values accurately.

  4. Verify Solutions Instantly -

    Use instant feedback on answers to check work, understand common mistakes, and reinforce correct problem-solving approaches in real time.

  5. Apply Algebraic Strategies -

    Transfer learned techniques to a variety of simple algebra questions, enhancing overall problem-solving skills and readiness for more advanced practice.

Cheat Sheet

  1. Understanding Variables and Constants -

    Variables represent unknown values while constants are fixed numbers, for example in x + 5 = 12 you have x as the variable and 5 and 12 as constants. According to Khan Academy, clear identification of these elements is essential when tackling simple algebra questions with answers. Remember "letters for unknowns, numbers for fixed values" as a quick reference during your algebra quiz.

  2. Order of Operations (PEMDAS) -

    The PEMDAS rule (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) guides you through complex expressions step by step. The University of Texas at Austin highlights the mnemonic "Please Excuse My Dear Aunt Sally" to lock in the sequence for solving easy algebra questions. Applying PEMDAS consistently prevents errors in both algebra practise tests and quizzes.

  3. Applying the Distributive Property -

    The distributive property a(b + c) = ab + ac simplifies expressions before solving, as detailed by MIT OpenCourseWare. For instance, 3(x + 4) becomes 3x + 12, making subsequent steps in algebra questions with answers much clearer. Mastering this property speeds you through algebra quizzes with confidence.

  4. Solving One- and Two-Step Equations -

    Begin with inverse operations to isolate variables, subtracting or dividing both sides as needed; for example, to solve 2x + 3 = 11, subtract 3 then divide by 2. The University of Cambridge emphasizes practicing a variety of these problems so you'll breeze through simple algebra questions with answers on your next test. Consistent practice in algebra quizzes builds speed and accuracy.

  5. Factoring Basics and Solution Verification -

    Factoring common terms (e.g., 6x + 9 = 3(2x + 3)) is key for simplifying and solving quadratic or linear expressions, according to the National Council of Teachers of Mathematics. After finding a solution, always substitute it back into the original equation to verify accuracy - a step often overlooked in algebra practise tests. This double-check habit ensures you ace easy algebra questions every time.

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