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Quizzes > Mathematics

Algebra 1 Final Exam Practice Test

Quick quiz with instant results to prep for your Algebra 1 final practice test.

Editorial: Review CompletedCreated By: Christopher TranUpdated Aug 25, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style algebra exam with equations functions and variable symbols on golden yellow background

This Algebra 1 final exam practice test helps you check what you know and what to review across equations, functions, inequalities, and word problems. Work at your own pace with instant results and simple explanations after each question. For extra review, build skills with our algebra practice test, and when you want a next step, try the algebra 2 practice test.

Simplify the expression 3x + 5x.
2x
15x
3+5x
8x
Combining like terms involves adding coefficients of the same variable. Here, 3x + 5x equals (3+5)x which is 8x. Like terms must have identical variable parts to be combined or added. For more on combining like terms, see .
Solve for x: x + 7 = 12.
5
-19
19
-5
To isolate x, subtract 7 from both sides of the equation: x = 12 - 7, giving x = 5. This one-step equation demonstrates the inverse operation of addition. Checking the solution in the original equation verifies correctness. For more practice, see .
Evaluate f(2) if f(x) = 3x + 4.
12
6
8
10
To evaluate f(2), substitute x = 2 into the expression: f(2) = 3(2) + 4 = 6 + 4 = 10. Function evaluation means replacing the input variable with the given value. Always perform multiplication before addition to maintain order of operations. See more at .
Simplify 2^3 × 2^4.
128
16
32
64
When multiplying powers with the same base, you add the exponents: 2^3 × 2^4 = 2^(3+4) = 2^7 = 128. This is a core exponent rule for simplifying expressions. Always ensure the bases are identical before adding exponents. For more, see .
What is the slope of the line passing through (1, 2) and (3, 6)?
-2
1/2
4
2
Slope is rise over run: (6 - 2) / (3 - 1) = 4/2 = 2. It measures the steepness of a line between two points. Always subtract y-values first, then x-values to get the correct ratio. For details, see .
Solve 2x - 5 = 9 for x.
-2
7
-7
14
Add 5 to both sides to get 2x = 14, then divide by 2 to find x = 7. This two-step linear equation uses inverse operations to isolate x. Always perform addition or subtraction before division when following order of operations in solving. More examples at .
What is the y-intercept of the line y = 4x - 3?
3
4
0
-3
In slope-intercept form y = mx + b, the constant term b is the y-intercept. Here, the line crosses the y-axis at (0, -3). This value shows where x is zero. Learn more at .
Combine like terms: 6a - 2a + 3a.
6a
7a
11a
a
Like terms share the same variable: 6a - 2a = 4a, then 4a + 3a = 7a. Combining like terms simplifies polynomial expressions. Ensure you only add or subtract terms with identical variables and exponents. See for more.
Use the distributive property to expand 3(x + 5).
3x + 5
15x + 3
x + 15
3x + 15
The distributive property multiplies each term inside the parentheses by the factor outside: 3×x + 3×5 = 3x + 15. This method removes parentheses and simplifies expressions. Check each multiplication carefully. More at .
Solve x/5 = 7.
35
2.8
-35
12
Multiply both sides by 5 to isolate x: x = 7 × 5 = 35. This operation undoes division by 5. Always apply the inverse operation to solve for the variable. For more examples, see .
Simplify the expression -(-x + 4).
x - 4
-x - 4
-x + 4
x + 4
Distribute the negative sign: -1×(-x) = x, and -1×4 = -4, giving x - 4. Removing parentheses with the correct sign is key. Verify by plugging in a value for x. See for more on distribution with negatives.
Solve the system: 2x + y = 8 and x - y = 2.
(10/3, 4/3)
(3, 2/3)
(2, 4)
(4, 2)
From x - y = 2, x = y + 2. Substitute into 2(y + 2) + y = 8 to get 3y + 4 = 8, so y = 4/3 and x = 10/3. Checking both equations confirms the solution. For substitution tutorials, see .
Multiply (x + 3)(x - 5).
x^2 - 15x + 15
x^2 + 15x - 15
x^2 + 2x - 15
x^2 - 2x - 15
Use FOIL: x·x + x·(-5) + 3·x + 3·(-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15. Always multiply in the order First, Outer, Inner, Last. To practice, see .
Factor the trinomial x^2 - 6x + 9.
(x + 3)^2
(x - 3)^2
(x - 9)(x + 1)
(x - 3)(x + 3)
x^2 - 6x + 9 is a perfect square trinomial because (-3)^2 = 9 and 2·(-3) = -6. It factors to (x - 3)(x - 3), or (x - 3)^2. Recognizing patterns speeds factoring. More at .
Simplify the rational expression (3x^2)/(9x).
3x
x/3
x^2/9
1/3
Divide numerator and denominator by 3x: (3x^2)/(9x) = x/3. Cancel common factors to simplify rational expressions. Restrict x ? 0 to avoid division by zero. For more, see .
Solve the inequality 3x - 4 < 8.
x < 4
x ? 4
x ? 4
x > 4
Add 4 to both sides: 3x < 12, then divide by 3: x < 4. Inequality direction stays the same when dividing by a positive number. Graphing this shows all values less than 4. Learn more at .
Solve |x - 2| = 5.
x = 7 or x = -3
x = 3 or x = -1
x = 2 or x = -2
x = 5 or x = -5
Absolute value equations split into two cases: x - 2 = 5 ? x = 7, or x - 2 = -5 ? x = -3. Check both in the original equation. This method handles distance from zero definitions. See .
Find g(f(1)) if f(x) = 2x + 1 and g(x) = x^2.
4
9
5
7
First evaluate f(1): 2(1) + 1 = 3. Then g(3) = 3^2 = 9. Function composition means input the result of one function into the next. For more, see .
What is the domain of f(x) = ?(x - 2)?
x ? 2
All real x
x ? 2
x > 2
The expression under the square root must be nonnegative: x - 2 ? 0 ? x ? 2. Domain restrictions come from even roots. Values below 2 would make the radicand negative. See .
Simplify the expression x^0 + 5.
x + 5
5
1
6
By definition, any nonzero base to the zero power is 1: x^0 = 1 (as long as x ? 0). Therefore, x^0 + 5 = 1 + 5 = 6. Understanding exponent properties helps simplify expressions. More at .
Solve 4(x - 1) = 2x + 6.
-5
5
1
4
Expand left side: 4x - 4 = 2x + 6. Subtract 2x: 2x - 4 = 6; add 4: 2x = 10; divide by 2: x = 5. Always apply operations in inverse order to isolate the variable. See .
Convert y - 2 = 3(x + 1) to slope-intercept form and identify slope and y-intercept.
Slope = -3, y-intercept = 5
Slope = 5, y-intercept = 3
Slope = 3, y-intercept = -5
Slope = 3, y-intercept = 5
Distribute: y - 2 = 3x + 3 ? y = 3x + 5, so slope m = 3 and y-intercept b = 5. Rewrite into y = mx + b to read slope and intercept. Always perform distribution before isolating y. For more, see .
Solve x^2 + 6x + 5 = 0 by completing the square.
x = -1 or x = -5
x = 2 or x = 3
x = -2 or x = -4
x = 1 or x = 5
x^2 + 6x + 5 = 0 ? x^2 + 6x + 9 = 4 ? (x + 3)^2 = 4 ? x + 3 = ±2 ? x = -1 or -5. Completing the square involves adding (b/2)^2 to both sides. Check both solutions in the original equation. For steps, see .
Use the quadratic formula to solve 2x^2 - 8x + 6 = 0.
x = 1 or x = 3
x = -1 or x = -3
x = 1 or x = 2
x = 2 or x = 3
For ax^2+bx+c=0, x = [8 ± ?(64 - 48)]/(4) = (8 ± 4)/4 ? x = 3 or 1. Quadratic formula handles any quadratic equation. Always simplify under the radical before proceeding. More at .
Simplify (x^2 - 9)/(x - 3).
x - 3
x^2 + 3
x + 3
1
Factor numerator: (x - 3)(x + 3)/(x - 3) = x + 3, x ? 3. Cancelling common factors simplifies the expression. Watch for excluded values where the original denominator is zero. See .
Simplify 2x^3 × 3x^2.
6x^5
6x^6
5x^6
5x^5
Multiply coefficients: 2×3 = 6, and add exponents: 3 + 2 = 5 ? 6x^5. This is the product rule for exponents. Always handle numeric and variable parts separately. For more, see .
Factor the sum of cubes x^3 + 8.
(x + 2)(x^2 - 2x + 4)
(x - 2)(x^2 + 2x + 4)
(x + 2)^3
(x + 2)(x^2 + 2x + 4)
Sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here a = x, b = 2, so (x + 2)(x^2 - 2x + 4). Recognizing special products aids factoring. More at .
Simplify (4x^-2)/(2x^-5).
8x^2
x^3/2
2x^3
2/x^3
Divide coefficients: 4/2 = 2, and subtract exponents: -2 - (-5) = 3 ? 2x^3. The quotient rule for exponents is used. Keep track of negative signs carefully. See .
Solve ?(x + 4) = 3.
9
-9
5
-5
Square both sides: x + 4 = 9 ? x = 5. Check that x + 4 ? 0; 5 + 4 = 9 is valid. Radical equations require checking for extraneous roots. More at .
Multiply (x/(x+2)) × ((x+2)/(x-1)).
x/(x-1)
(x+2)/(x-1)
x^2/(x^2+1)
(x-1)/x
Cancel the common factor (x + 2) and multiply numerators/denominators: x/(x-1). Excluded values: x ? -2, 1. Simplifying before multiplying prevents extra work. For more, see .
Factor 9x^2 - 16.
(3x - 4)(3x + 4)
(9x + 16)
9x^2 + 16
(3x - 4)^2
This is a difference of squares: (3x)^2 - 4^2 = (3x - 4)(3x + 4). Recognizing a^2 - b^2 = (a - b)(a + b) is key. Be careful with signs. See .
Simplify (x^(1/2))^4.
x^2
x^4
2x
x
Raise a power to a power by multiplying exponents: (x^(1/2))^4 = x^(1/2 × 4) = x^2. This is a basic exponent rule. Ensure to multiply fractions correctly. More at .
Solve the inequality x^2 - 4x + 3 ? 0.
x < 1 or x > 3
1 ? x ? 3
x ? 1
x ? 3
Factor: (x - 1)(x - 3) ? 0. The parabola opens up, so values between the roots inclusive satisfy the inequality: 1 ? x ? 3. Test points to confirm. For more, see .
Solve the absolute value inequality |2x - 3| > 5.
x ? -1 or x ? 4
x < -1 or x > 4
x > -1 and x < 4
-1 < x < 4
Split into two cases: 2x - 3 > 5 ? x > 4, and 2x - 3 < -5 ? x < -1. The solution set is x < -1 or x > 4. Always reverse the inequality when multiplying/dividing by negative in absolute value cases. See .
Solve for x: (x + 1)/(x - 2) = 3.
5/2
5/3
7/2
-7/2
Multiply both sides by (x - 2): x + 1 = 3x - 6 ? -2x = -7 ? x = 7/2. Exclude x = 2 from the domain because it makes the denominator zero. Always check for domain restrictions in rational equations. See .
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Study Outcomes

  1. Solve Linear Equations -

    Apply step-by-step techniques to solve one-variable and multi-step equations, ensuring accuracy on Algebra 1 final exam questions.

  2. Simplify Algebraic Expressions -

    Use properties of operations to combine like terms, distribute, and simplify expressions for efficient problem solving.

  3. Factor Polynomials -

    Identify and apply factoring methods, including greatest common factors and special products, to rewrite polynomials in factored form.

  4. Graph and Interpret Functions -

    Plot linear and nonlinear functions on a coordinate plane and interpret key features such as slope, intercepts, and curvature.

  5. Analyze Systems of Equations -

    Solve systems using substitution and elimination methods to find intersection points and verify solutions.

  6. Apply Quadratic Concepts -

    Use factoring, completing the square, and the quadratic formula to solve quadratic equations and understand their graphs.

Cheat Sheet

  1. Slope-Intercept Form Mastery -

    Review the slope-intercept formula y = mx + b, where m represents the rate of change and b is the starting value. For example, y = 2x + 3 describes a line rising two units every step right and crossing the y-axis at 3. This foundational concept is emphasized by the Common Core State Standards for Understanding Linear Functions.

  2. Solving Systems of Equations -

    Practice substitution and elimination methods to solve pairs of linear equations, like solving 2x + y = 5 and x - y = 1 simultaneously. Substitution isolates one variable first, while elimination adds equations to cancel a variable - choose whichever feels more intuitive. These techniques are widely taught in university algebra courses such as those at MIT OpenCourseWare.

  3. Factoring and the Quadratic Formula -

    Master factoring trinomials (ax² + bx + c) into (dx + e)(fx + g) and apply the zero-product property to find roots. When factoring is tricky, use the quadratic formula x = [ - b ± √(b² - 4ac)]/(2a) for a foolproof solution. This approach is validated by research in educational journals like the Journal of Mathematical Behavior for boosting problem-solving fluency.

  4. Exponents and Scientific Notation -

    Memorize exponent rules - such as a^m × a^n = a^(m+n) and (a^m)^n = a^(mn) - and apply them to simplify expressions quickly. Practice converting large or small numbers into scientific notation (e.g., 6.02×10^23) to handle data more efficiently, a skill endorsed by the National Institute of Standards and Technology. Use the mnemonic "Multiply bases? Add exponents!" to recall the laws under pressure.

  5. Functions, Domain, and Range -

    Understand that a function f(x) uniquely assigns each input x to one output y, and sketching its graph requires checking the vertical line test. Identify the domain (allowable x-values) and range (resulting y-values) by analyzing where the function is defined, for example f(x)=√(x - 2) has domain x ≥ 2. The National Council of Teachers of Mathematics highlights these concepts as essential for fluency in Algebra 1 final exam problems.

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