Ready to master your algebra fundamentals? Our free Algebra 1 Quiz is designed to challenge your skills in simplifying expressions, test your solving equations practice, and push your factoring polynomials test to the limit. Whether you're gearing up for a big exam or just want a confidence boost, this algebra fundamentals quiz adapts to your level and gives instant feedback on every question. Students, teachers, and lifelong learners alike will find tips and tricks to sharpen their algebra test performance. Dive in now to discover your strengths, build confidence, and take your math game to the next level - start the quiz today!
Combine like terms: 2x + 3x
2x3x
6x
5x
x + 6
When two terms have the same variable and exponent, you can add their coefficients. 2x + 3x adds 2 + 3 to get 5, resulting in 5x. Combining like terms simplifies expressions. Learn more.
Simplify the expression: 4y + 2y - y
6y
5y
y
4y
All terms share the same variable y, so you add or subtract their coefficients: 4 + 2 - 1 = 5. That yields 5y. Simplifying like this makes expressions easier to work with. Learn more.
Distribute and simplify: 3(a + 4)
a + 12
3a + 12
7a
3a + 4
Use the distributive property: multiply 3 by each term inside the parentheses. 3 × a = 3a and 3 × 4 = 12. So the simplified result is 3a + 12. Learn more.
Evaluate the expression when n = 2: 5n - 3
5
7
2
-1
Substitute n = 2 into the expression: 5(2) - 3 = 10 - 3 = 7. Evaluating an expression means replacing the variable with its value. Learn more.
Solve for x: x - 5 = 8
5
13
3
-13
Add 5 to both sides of the equation: x - 5 + 5 = 8 + 5, so x = 13. Isolating the variable by undoing operations finds the solution. Learn more.
Solve for x: 3x = 12
3
4
9
12
Divide both sides by 3 to isolate x: 3x ÷ 3 = 12 ÷ 3, giving x = 4. One-step equations require a single inverse operation. Learn more.
Simplify the expression: 9m - 9m + 5
0
5
-m
9m
Combine like terms: 9m - 9m = 0, leaving 0 + 5 = 5. Subtracting identical terms cancels them out. Learn more.
Evaluate: 2(4) + 7
15
11
8
-15
First multiply: 2 × 4 = 8. Then add 7 to get 15. Follow the order of operations: multiplication before addition. Learn more.
Solve for x: 2x + 5 = 13
-4
3
9
4
Subtract 5 from both sides: 2x = 8, then divide by 2: x = 4. Two-step equations use inverse operations in sequence. Learn more.
Distribute and simplify: 3(x - 2) + 4
3x - 2
3x + 4
3x - 8
x + 2
Apply distribution: 3x - 6, then add 4 to get 3x - 2. Always perform multiplication inside parentheses before combining like terms. Learn more.
Factor out the greatest common factor: 6x^2 - 9x
9x(2x - 1)
6x(x - 3)
3x(2x - 3)
x(6x - 9)
Both terms share a factor of 3x. Dividing gives 6x^2 ÷ 3x = 2x and -9x ÷ 3x = -3. So the factored form is 3x(2x - 3). Learn more.
Solve for x: (x/4) + 2 = 5
3
12
8
-12
Subtract 2: x/4 = 3, then multiply both sides by 4: x = 12. Handling fractions involves undoing division with multiplication. Learn more.
Combine like terms: 2x + 3 - 4x + 5
6x + 8
2x - 2
-2x + 8
-6x + 5
Combine x-terms: 2x - 4x = -2x and constants: 3 + 5 = 8, giving -2x + 8. Group like terms first for clarity. Learn more.
Solve for x: 5x - 7 = 3x + 5
5
1
-6
6
Subtract 3x: 2x - 7 = 5, add 7: 2x = 12, divide by 2: x = 6. Align variables on one side and constants on the other. Learn more.
Use exponent rules: (x^2)(x^3) = ?
x
x^5
x^6
x^8
When multiplying like bases, add their exponents: 2 + 3 = 5, so x^5. This is a basic exponent rule. Learn more.
Simplify the rational expression: (4x^3) / (2x)
2x^2
4x^2
x^2
2x^3
Divide coefficients: 4 ÷ 2 = 2, and subtract exponents on x: 3 - 1 = 2, giving 2x^2. Simplifying fractions with exponents uses the quotient rule. Learn more.
Factor the quadratic: x^2 - 5x + 6
(x - 1)(x - 6)
(x + 1)(x + 6)
(x + 2)(x - 3)
(x - 2)(x - 3)
Find two numbers that multiply to +6 and add to -5: -2 and -3. So the factorization is (x - 2)(x - 3). Learn more.
Factor the difference of squares: 4x^2 - 9
(4x + 3)(x - 3)
(2x - 9)(2x + 1)
(4x - 3)(x + 3)
(2x - 3)(2x + 3)
Recognize 4x^2 and 9 as squares: (2x)^2 - 3^2. The difference of squares factors as (2x - 3)(2x + 3). Learn more.
Solve by factoring: x^2 + x - 6 = 0
x = 1 or -6
x = 2 or -3
x = 6 or -1
x = 3 or -2
Factor as (x + 3)(x - 2) = 0. Set each factor to zero: x + 3 = 0 gives x = -3, x - 2 = 0 gives x = 2. Learn more.
Solve the absolute value equation: |2x - 4| = 6
x = 2 or -3
x = -5 or 1
x = 5 or -1
x = 10 or -2
Set 2x - 4 = 6 ? 2x = 10 ? x = 5, and 2x - 4 = -6 ? 2x = -2 ? x = -1. Absolute value equations yield two cases. Learn more.
Solve the system: x + y = 5 and x - y = 1
(4, 1)
(3, 2)
(2, 3)
(1, 4)
Add equations to eliminate y: 2x = 6 ? x = 3. Substitute x into x + y = 5 gives y = 2. Systems can be solved by addition or substitution. Learn more.
Simplify using exponent rules: x^3 · x^-1
x^4
1
x^-2
x^2
When multiplying like bases, add exponents: 3 + (-1) = 2. So x^3 · x^-1 = x^2. This uses the product rule for exponents. Learn more.
Multiply the monomials: (2x^2 y^3)(3x y^-1)
6x^3 y^2
6x^3 y^4
6x^2 y^4
5x^3 y^3
Multiply coefficients: 2·3 = 6. Add exponents of x: 2 + 1 = 3. Add exponents of y: 3 + ( - 1) = 2. The result is 6x^3 y^2. Learn more.
Solve the quadratic equation using the quadratic formula: x^2 - 4x + 1 = 0
1 ± ?2
2 ± ?2
2 ± ?3
-2 ± ?3
Use x = [4 ± ?(16 - 4)]/2 = [4 ± ?12]/2 = [4 ± 2?3]/2 = 2 ± ?3. The quadratic formula applies when ax^2+bx+c=0. Learn more.
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Study Outcomes
Simplify Algebraic Expressions -
Apply order of operations and combine like terms to streamline complex expressions in the simplifying expressions quiz.
Solve Linear Equations -
Demonstrate proficiency in one- and two-step equations by finding variable values accurately through solving equations practice.
Factor Polynomial Expressions -
Break down polynomials into their simplest components using common factor and grouping techniques in the factoring polynomials test.
Analyze Algebra Skills -
Evaluate your performance on each algebra fundamentals quiz section to understand your strengths and areas needing reinforcement.
Identify Improvement Areas -
Pinpoint specific topics - simplifying, solving, or factoring - that require additional focus to enhance your overall Algebra 1 mastery.
Build Algebra Confidence -
Leverage instant feedback and progress tracking to reinforce core concepts and boost your confidence in Algebra 1.
Cheat Sheet
Master the Distributive Property & Combining Like Terms -
Use a(b + c) = ab + ac to expand expressions - e.g., 3(x + 4) = 3x + 12 - and group like terms by matching variable parts to simplify polynomials. A handy mnemonic for order of operations is PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). These steps align with best practices from Khan Academy and university algebra curricula.
Develop Reliable Equation-Solving Strategies -
Isolate variables step-by-step using inverse operations; for 2x + 5 = 13, subtract 5 then divide by 2 to keep equations balanced. Always perform the same operation on both sides, a method endorsed by National Council of Teachers of Mathematics (NCTM). For fractional coefficients, multiply both sides by the least common denominator to clear denominators before solving.
Factor Out the Greatest Common Factor (GCF) -
Always look for the GCF before other factoring methods; for 6x² + 9x, factor out 3x to get 3x(2x + 3). This step often simplifies later factoring and aligns with recommendations from Purplemath's algebra guides. Remember the GCF is the highest term that divides all coefficients and variable powers.
Practice Factoring Quadratic Expressions Efficiently -
For x² + 5x + 6, find two numbers that multiply to 6 and add to 5 (2 and 3) and write (x + 2)(x + 3). Use the product-sum method or trial-and-error so you can quickly factor most quadratics with integer roots. These techniques mirror exercises found in collegiate algebra textbooks.
Leverage the Zero Product Property & Verify Solutions -
After factoring, set each factor equal to zero to find roots: if (x - 4)(x + 2) = 0, then x = 4 or x = - 2. Always substitute solutions back into the original equation to check for extraneous roots and confirm accuracy. This habit builds confidence and follows best practices in algebra problem-solving guides.
