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Quizzes > Mathematics

Algebra Test: 20 Practice Questions with Answers

Quick algebra practice test with instant results and explanations.

Editorial: Review CompletedCreated By: Profesora PoloUpdated Aug 25, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Ace Your Algebra trivia quiz for high school students.

This algebra test helps you check Grade 8 skills across expressions, equations, and functions. Answer 20 questions, get instant results, and review brief explanations to fix mistakes. For more practice, try 10 algebra questions and answers, build line skills with a slope quiz, or prep for bigger checks with an algebra 1 practice test.

Solve for x: 2x + 3 = 11.
x = 4
x = 3
x = 5
x = -4
Subtracting 3 from both sides gives 2x = 8 and then dividing by 2 yields x = 4. This is a straightforward application of solving simple linear equations.
Simplify the expression: 3x + 5x.
15x
2x
x^2
8x
By combining like terms, add the coefficients of x (3 + 5) to get 8x. This reinforces the concept of simplifying algebraic expressions.
Evaluate the expression: 4(x - 2) when x = 5.
9
7
20
12
Substitute x = 5 into the expression to get 4(5 - 2) = 4(3) = 12. This demonstrates basic substitution followed by multiplication.
Which property states that a(b + c) = ab + ac?
Associative property
Commutative property
Distributive property
Identity property
The distributive property allows one to multiply a number by a sum by distributing the multiplication over each addend. This property is fundamental for simplifying algebraic expressions.
Solve for x: x/3 = 6.
2
9
3
18
Multiplying both sides of the equation by 3 yields x = 18. This simple equation is solved by isolating the variable using inverse operations.
Solve for x: 3x - 5 = 10.
15
5
10
20
Adding 5 to both sides gives 3x = 15, and dividing by 3 results in x = 5. This reinforces the systematic approach to solving linear equations.
Which expression represents the expanded form of 2(x + 4)?
2x + 8
x + 4
x + 8
2x + 4
By applying the distributive property, multiply 2 by both x and 4 to get 2x + 8. This is a fundamental skill in expanding expressions.
Simplify the expression: 2x + 3 - 4x + 5.
2x + 8
-2x + 8
-2x - 8
6x + 8
Combine like terms by subtracting 4x from 2x to obtain -2x and adding 3 and 5 to get 8. The simplified expression is -2x + 8.
Solve for y: 2y/3 = 8.
16
10
6
12
Multiplying both sides by 3 yields 2y = 24 and then dividing by 2 results in y = 12. This problem emphasizes clearing fractions to solve the equation.
Evaluate the expression: 3^2 + 4^2.
23
24
18
25
Calculating the squares separately yields 9 and 16, whose sum is 25. This reinforces the use of exponents and addition in computations.
Solve for x: 5(x - 1) = 20.
5
4
10
6
Distribute to get 5x - 5 = 20, then add 5 resulting in 5x = 25, so x = 5. This demonstrates the step-by-step approach to solving equations using the distributive property.
Factor the expression: x^2 - 9.
x(x - 9)
(x + 3)^2
(x - 3)(x + 3)
(x - 9)(x + 1)
Recognize that x^2 - 9 is a difference of squares and factors into (x - 3)(x + 3). This is a key factoring technique in algebra.
If f(x) = 2x + 1, what is f(3)?
6
7
9
8
Substitute x = 3 into the function to get f(3) = 2(3) + 1 = 7. This question reinforces evaluating functions at a specific point.
Solve the equation: x/2 + 3 = 7.
4
6
8
10
Subtract 3 from both sides to obtain x/2 = 4, and then multiply by 2 to solve for x = 8. This problem highlights working with fractions in equations.
Find the value of x in the equation: 2(x + 5) = x + 15.
15
0
5
10
Expanding the left side gives 2x + 10, and setting it equal to x + 15 leads to isolating x and finding x = 5. This utilizes distribution and basic algebraic manipulation.
Solve for x: 2x + 3 = 3x - 4.
x = 7
x = -7
x = -4
x = 4
Subtracting 2x from both sides leads to 3 = x - 4, and adding 4 gives x = 7. This process shows how to collect like terms and isolate the variable.
Solve for y in terms of x: 3y + 2x = 12.
y = 12 - 2x
y = (2x - 12) / 3
y = (12 + 2x) / 3
y = (12 - 2x) / 3
Subtract 2x from both sides to obtain 3y = 12 - 2x and then divide by 3 to solve for y. This separates y in terms of x effectively.
Determine the slope of the line represented by the equation 4x - 2y = 8.
1/2
-2
2
-4
Rearrange the equation to slope-intercept form: -2y = -4x + 8 leads to y = 2x - 4. The coefficient of x in this form is the slope, which is 2.
If the product of two consecutive integers is 72, what are the integers?
8 and 9
9 and 10
7 and 8
6 and 7
Let the integers be n and n+1, so n(n+1) = 72, which leads to the quadratic equation n² + n - 72 = 0. Solving this gives n = 8, hence the integers are 8 and 9.
Solve the inequality: 2x - 5 > 3.
x ≥ 4
x ≤ 4
x > 4
x < 4
Add 5 to both sides to get 2x > 8, and then divide by 2 resulting in x > 4. This demonstrates the proper method for solving linear inequalities.
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Study Outcomes

  1. Understand how to simplify algebraic expressions and combine like terms.
  2. Solve linear equations and inequalities using appropriate methods.
  3. Apply the properties of operations to manipulate and transform expressions.
  4. Analyze word problems to formulate and solve algebraic equations.
  5. Evaluate algebraic functions and interpret their components in context.

Algebra Quiz: Practice & Review Cheat Sheet

  1. Real Number Properties - Tap into the magic of commutative, associative, distributive, identity, and inverse properties to simplify expressions and solve equations with ease. Mastering these rules is like having a secret decoder ring for algebraic puzzles!
  2. Order of Operations (PEMDAS) - Harness the power of parentheses, exponents, multiplication/division, and addition/subtraction to conquer even the trickiest expressions. Think of it as following a recipe for perfect math results every time!
  3. Exponent Rules - Learn the product, quotient, power, zero, and negative exponent rules to tame expressions with powers like a seasoned algebra wizard. These shortcuts will save you time and brainpower on tests!
  4. Polynomial Operations - Practice adding, subtracting, multiplying, and dividing polynomials, and spot special products like the difference of squares or perfect square trinomials. Polynomials are like LEGO blocks - once you know how to snap them together, you can build anything!
  5. Factoring Techniques - Sharpen your skills in factoring out the greatest common factor, breaking down trinomials, and recognizing patterns like sum/difference of cubes. Factoring is your secret weapon for dismantling complex expressions!
  6. Solving Linear Equations & Inequalities - Apply properties of equality and inequality to crack linear equations and graph your solutions like a pro. Visualizing the answer on a number line or coordinate plane makes everything click!
  7. Systems of Linear Equations - Master graphing, substitution, and elimination methods to find where two lines meet (or don't!). Think of it as solving a mystery by collecting clues from each equation.
  8. Functions, Domain & Range - Decode what functions do, identify their domain and range, and practice plotting different types to reveal their behavior. Functions are like machines: feed them inputs, get outputs, and draw the picture!
  9. Quadratic Equations - Tackle quadratics with factoring, completing the square, and the quadratic formula, and learn how the discriminant reveals the nature of your solutions. Quadratics are parabolas dancing on your graph - join the dance!
  10. Exponential & Logarithmic Functions - Dive into growth and decay with exponentials, then flip them into logarithms to solve equations. These inverse buddies help you model everything from bacterial growth to pH levels!
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