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Quizzes > Mathematics > Algebra

Free Beginning Algebra Quiz - Test Your Basics Now

Ready to Dive into a Basic Algebra Practice Quiz?

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art algebra expressions symbols and equations on coral background for beginning algebra quiz challenge

Ready to unlock equations with our free beginning algebra quiz? Whether you're tackling x's and y's for the first time or refreshing foundational skills, this basic algebra practice quiz brings algebra fundamentals trivia - simplifying expressions and solving equations - together in one interactive challenge. Dive into our fun algebra quiz and boost your confidence before putting your speed to the test in the simplifying expressions quiz . Perfect for students and self-learners seeking a beginner algebra test online, it's time to level up your problem-solving. Start now and show what you can do!

Simplify 4x + 7x.
11x
3x
x
28x
Like terms have the same variable part. To combine like terms, add their coefficients. Here, 4x + 7x equals 11x. This simplifies the expression to a single term. Learn more about combining like terms.
Distribute the expression 3(2x - 5).
6x + 15
5x - 6
6(x - 5)
6x - 15
The distributive property allows you to multiply each term inside the parentheses by the factor outside. Multiply 3 by 2x to get 6x, and 3 by -5 to get -15. Combining both gives 6x - 15. See the distributive law.
Solve for x: x/3 = 4.
-12
12
7
1.333
To solve x/3 = 4, multiply both sides by 3. This isolates x, giving x = 4 × 3 = 12. Always perform the inverse operation to solve one-step equations. Overview of solving linear equations.
Simplify -2y + 5y.
3y
y
-7y
7y
Combine like terms by adding their coefficients: -2 + 5 = 3. The variable part remains y, so -2y + 5y = 3y. This is a basic step in simplifying expressions. More on like terms.
Evaluate 3a² when a = 2.
10
8
6
12
First calculate a²: when a = 2, a² = 4. Then multiply by 3: 3 × 4 = 12. Evaluating expressions means substituting the given value and simplifying. Understanding exponents.
Combine like terms: 5m - 2(m - 3).
3m - 6
-m + 6
7m - 6
3m + 6
First distribute: 5m - 2m + 6. Then combine like terms: 5m - 2m = 3m, so the result is 3m + 6. Distribute before combining like terms. See distributive law.
Solve for x: -3x = 12.
4
-3
-4
3
Divide both sides by -3 to isolate x: x = 12 / -3 = -4. Always perform the inverse operation to solve one-step linear equations. More on solving linear equations.
Solve for x: 2x + 3 = 11.
-4
8
4
7
Subtract 3 from both sides to get 2x = 8, then divide by 2: x = 4. This is a standard two-step equation. Learn more about linear equations.
Simplify the expression 6x²y - 4xy + 2x²y.
8x²y - 4xy
4x²y - 4xy
12x²y - 4xy
2x²y - 4xy
Combine like terms in x²y: 6x²y + 2x²y = 8x²y, and the -4xy term stays separate. The simplified result is 8x²y - 4xy. Combining like terms.
Factor x² + 5x.
x(x - 5)
x + 5
x² + 5
x(x + 5)
Both terms share a common factor x. Factoring it out gives x(x + 5). Factoring simplifies expressions and is a key skill in algebra. Introduction to factoring.
Solve for x: 3(x - 2) = 2x + 4.
-10
-2
10
2
Distribute on the left: 3x - 6 = 2x + 4. Subtract 2x: x - 6 = 4. Then add 6: x = 10. See solving steps.
Simplify (4x³)/(2x).
4x²
2x²
2x
x²
Divide coefficients: 4/2 = 2. Subtract exponents for x: 3 - 1 = 2, giving 2x². This uses the quotient rule for exponents. Exponent rules.
Simplify 9a²b³ / (a²b).
9ab²
9a²b²
ab²
9b²
Cancel a² and subtract exponents for b: 3 - 1 = 2. The coefficient stays 9, so the result is 9b². Learn about dividing exponents.
Solve for x: 2x/5 + 4 = 6.
2.5
5
-5
10
Subtract 4: 2x/5 = 2. Multiply both sides by 5: 2x = 10, then divide by 2: x = 5. Steps combine inverse operations. More examples.
Solve x² - 5x + 6 = 0.
x = -1 or x = -6
x = 2 or x = 3
x = 1 or x = 6
x = -2 or x = -3
Factor the quadratic: (x - 2)(x - 3) = 0. Setting each factor to zero gives solutions x = 2 or x = 3. Factoring is quick when integer roots exist. Learn more about factoring quadratics.
Factor 4x² - 9.
(4x - 3)(x + 3)
(2x - 3)²
(2x + 9)(2x - 1)
(2x - 3)(2x + 3)
This is a difference of squares: a² - b² = (a - b)(a + b). Here a = 2x and b = 3, so it factors to (2x - 3)(2x + 3). See difference of squares.
Simplify ?50.
25?2
?10
10?2
5?2
Break 50 into 25 × 2. ?25 = 5, so ?50 = 5?2. Simplifying radicals pulls out perfect squares. Radical simplification.
Solve for x: (x + 1)/(x - 1) = 2.
x = 3
x = 1
x = -3
x = 2
Multiply both sides by (x - 1): x + 1 = 2x - 2. Then subtract x and add 2: 3 = x. Check x ? 1. Solving rational equations.
Simplify (2x³y²)².
2x?y³
4x?y?
8x?y?
4x³y²
Raise each factor to the power 2: 2²=4, x³×2 = x?, y²×2 = y?. The result is 4x?y?. This uses the power-of-a-power rule. Exponent rules.
Solve x² + 6x + 9 = 0.
x = 9
x = -3
x = 3
x = -9
Recognize a perfect square: (x + 3)² = 0. So x + 3 = 0 and x = -3. Perfect square trinomials factor easily. See perfect squares.
Factor completely: x³ - 3x² - x + 3.
(x + 3)(x² - 1)
(x - 1)(x² - 3)
(x - 1)(x + 1)(x - 3)
(x - 3)(x² - 1)
Group terms: x²(x - 3) -1(x - 3) = (x - 3)(x² - 1). Then factor x² - 1 as (x - 1)(x + 1). Full factorization is (x - 3)(x - 1)(x + 1). Factor by grouping.
Solve |2x - 4| = 6.
x = 1 or x = -1
x = 5 or x = 1
x = 5 or x = -1
x = 6 or x = -6
Set up two equations: 2x - 4 = 6 ? 2x = 10 ? x = 5; and 2x - 4 = -6 ? 2x = -2 ? x = -1. Absolute value splits into positive and negative cases. Absolute value definitions.
Solve the system: 2x + y = 5 and x - y = 1.
(3, -1)
(-2, 7)
(2, 1)
(1, 2)
From x - y = 1, y = x - 1. Substitute into 2x + (x - 1) = 5 ? 3x - 1 = 5 ? 3x = 6 ? x = 2, y = 1. Systems can be solved by substitution. Solving systems of equations.
Simplify: (3x² - 2x + 1) - (x² + 4x - 3).
2x² + 2x - 2
x² + 2x - 2
4x² - 2x - 2
2x² - 6x + 4
Distribute the negative: 3x² - 2x + 1 - x² - 4x + 3 = (3x² - x²) + (-2x - 4x) + (1 + 3) = 2x² - 6x + 4. Combine like terms methodically. More on combining terms.
Solve x³ - 2x² - x + 2 = 0.
x = -2, 1, or 2
x = -1, 2, or 3
x = 1, -1, or 2
x = 1 or 2
Factor by grouping: x²(x - 2) -1(x - 2) = (x - 2)(x² - 1). Then x² - 1 = (x - 1)(x + 1). Solutions are x = 2, 1, -1. Grouping and factoring cubics.
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Study Outcomes

  1. Simplify Algebraic Expressions -

    Use techniques like combining like terms and applying the distributive property to reduce expressions to their simplest form.

  2. Solve Linear Equations -

    Apply one-step and two-step methods to isolate variables and find accurate solutions to basic algebraic equations.

  3. Apply Scientific Notation -

    Convert numbers to and from scientific notation and perform calculations with very large or very small values confidently.

  4. Identify Algebraic Components -

    Recognize variables, constants, coefficients, and terms within expressions and equations for clearer problem analysis.

  5. Evaluate Algebraic Expressions -

    Substitute numerical values into expressions to compute results and verify the correctness of equation solutions.

  6. Enhance Algebraic Reasoning -

    Develop critical thinking skills through varied practice questions, building a strong foundation in algebra fundamentals.

Cheat Sheet

  1. Understanding Variables and Expressions -

    Variables are symbols like x or y that stand in for numbers in algebraic expressions; for example, in 2x + 3 = 11 you solve for x. Recognizing how constants and coefficients interact helps you interpret any beginning algebra quiz question with confidence. According to Khan Academy, mastering this foundation makes more advanced topics feel much more approachable.

  2. Order of Operations (PEMDAS) -

    Memorize the PEMDAS rule - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction - to simplify expressions correctly (MIT OpenCourseWare). Use the mnemonic "Please Excuse My Dear Aunt Sally" to recall each step in your basic algebra practice quiz. Applying these rules ensures you'll never mix up which operation comes first when simplifying.

  3. Combining Like Terms & Distributive Property -

    Group terms with the same variable (like 3x and 5x) by adding their coefficients, then simplify: 3x + 5x = 8x. Use the distributive property a(b + c) = ab + ac - e.g., 4(x + 2) = 4x + 8 - to expand or factor expressions in your simplify algebra expressions quiz. These techniques are core to algebra fundamentals trivia and streamline complex problems.

  4. Solving One-Step and Two-Step Equations -

    Isolate the variable by performing inverse operations: for 2x + 5 = 13 subtract 5 then divide by 2 to find x = 4. In a beginner algebra test online, you'll apply addition/subtraction and multiplication/division in sequence to solve two-step equations. Practicing with varied examples from university math departments builds accuracy and speed.

  5. Working with Scientific Notation -

    Express large or small numbers as m × 10❿; for instance, 6,500 becomes 6.5 × 10³ and 0.0042 is 4.2 × 10❻³. Converting back and forth in your algebra fundamentals trivia sharpens your number sense and prepares you for scientific applications. The National Institute of Standards and Technology (NIST) provides clear guidelines to strengthen this key skill.

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