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Quizzes > High School Quizzes > Mathematics

Interactive Math Worksheets Practice Quiz

Boost Your Algebra Skills with Engaging Worksheets

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Algebra Kickstart Quiz for middle and high school students.

Evaluate the expression 3x + 5 for x = 2.
11
13
7
8
Substituting x with 2 gives 3*2 + 5 = 6 + 5, which equals 11. This demonstrates correct use of substitution and arithmetic operations.
Simplify the expression: 2x + 3x.
5x
6x
2x
3x
Combining like terms by adding their coefficients gives 2x + 3x = 5x. This is a fundamental concept in simplifying algebraic expressions.
Which property allows 5 + x to be written as x + 5?
Commutative Property
Associative Property
Distributive Property
Identity Property
The commutative property of addition allows the order of terms to be changed without affecting the sum. This property is a key element in algebraic manipulation.
Solve for x: x + 4 = 9.
5
1
9
13
Subtracting 4 from both sides of the equation gives x = 9 - 4, which simplifies to x = 5. This teaches the basic principle of isolating the variable in simple equations.
What is the value of 2(3) using the order of operations?
6
7
5
8
According to the order of operations, multiplication is performed, so 2 multiplied by 3 equals 6. This basic question reinforces arithmetic operations.
Solve for x: 2x - 3 = 7.
5
2
7
10
Adding 3 to both sides yields 2x = 10, then dividing by 2 gives x = 5. This question emphasizes the use of inverse operations to solve linear equations.
Solve for x: 3(x - 4) = 12.
8
4
6
12
Dividing both sides by 3 gives x - 4 = 4, and adding 4 to both sides results in x = 8. This problem integrates the distributive property with inverse operations.
Simplify the expression: 4x + 2 - x + 5.
3x + 7
5x + 7
4x + 7
3x + 2
By combining like terms, 4x - x gives 3x and 2 + 5 gives 7, resulting in 3x + 7. This question tests the fundamental skill of combining like terms in algebra.
Solve for x: 2(x + 3) = 2x + 8.
No solution
x = 1
x = 2
x = 5
Expanding the left side gives 2x + 6, so the equation becomes 2x + 6 = 2x + 8. Subtracting 2x from both sides leads to 6 = 8, a contradiction. Thus, there is no solution.
Solve for x: (3x + 6)/3 = 7.
5
7
15
21
Multiplying both sides by 3 gives 3x + 6 = 21; subtracting 6 results in 3x = 15, and dividing by 3 yields x = 5. This problem reinforces solving equations with fractions.
If y = 2x - 3 and x = 4, what is the value of y?
5
8
7
6
Substitute x = 4 into the equation to obtain y = 2(4) - 3, which simplifies to y = 8 - 3 = 5. This question tests straightforward substitution in a linear equation.
Simplify the expression: 5(2x - 4) - 3(2x - 1).
4x - 17
4x - 23
8x - 17
8x - 23
First distribute to get 10x - 20 and -6x + 3, then combine like terms to obtain 4x - 17. This tests both the distributive property and the combining of like terms.
Solve for x: 4x - 5 = 3x + 2.
7
2
3
5
Subtracting 3x from both sides gives x - 5 = 2, and then adding 5 to both sides yields x = 7. This is a classic example of solving a simple linear equation.
Evaluate the expression 2x² when x = 3.
18
9
15
12
Substituting x = 3 into the expression gives 2*(3²) = 2*9 = 18. This question reinforces substitution and exponentiation.
Solve for y: 3y/4 = 9.
12
9
15
36
Multiplying both sides by 4 eliminates the fraction, resulting in 3y = 36; dividing by 3 then gives y = 12. This emphasizes solving linear equations that include fractions.
Solve for x: 2(3 - x) + 4(x + 1) = 5x + 7.
1
3
0
7
Expanding gives 6 - 2x + 4x + 4 = 5x + 7, which simplifies to 10 + 2x = 5x + 7. Isolating x leads to x = 1. This problem requires careful distribution and combining like terms.
Factor and simplify the expression: 6x² + 9x.
3x(2x + 3)
6x(x + 1.5)
9x((2/3)x + 1)
3(2x² + 3x)
Both terms share a greatest common factor of 3x, so factoring it out yields 3x(2x + 3). This is a basic example of factoring common terms in polynomial expressions.
Solve the equation: (x/2) + (x/3) = 5.
6
5
10
15
Finding a common denominator (which is 6) allows you to combine the fractions into (5x/6)=5. Multiplying both sides by 6 and then dividing by 5 gives x = 6.
If 5(x - 2) = 2(x + 3) + 3x, what is the value of x?
No solution
x = -4
x = 0
x = 4
Expanding the equation gives 5x - 10 = 2x + 6 + 3x, which simplifies to 5x - 10 = 5x + 6. Subtracting 5x from both sides results in -10 = 6, a contradiction that indicates there is no solution.
What is the correct first step to solve the equation 3x - (2 - x) = 10?
Distribute the negative sign to get 3x - 2 + x = 10
Subtract 2 from both sides to get 3x - (2 - x) = 8
Combine like terms inside the parentheses
Divide both sides by 3
The correct initial step is to distribute the negative sign across the parentheses, converting -(2 - x) into -2 + x. This step is crucial for accurately simplifying and solving the equation.
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Study Outcomes

  1. Analyze algebraic expressions and equations to identify key components and relationships.
  2. Apply problem-solving strategies to solve linear equations and inequalities.
  3. Evaluate solutions through substitution and verification techniques.
  4. Create and manipulate algebraic models to represent real-world scenarios.
  5. Synthesize multiple algebraic concepts to tackle complex challenges.

Algebra Worksheet Quiz: Practice & Review Cheat Sheet

  1. Master the Order of Operations (PEMDAS) - Sorting through a jumble of symbols is a breeze when you follow PEMDAS: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction (left to right). This golden rule guarantees you simplify every expression accurately. Dive into algebra concepts
  2. Understand Linear Equations - Linear equations graph as straight lines, usually in the form y = mx + b, where m is slope and b is the y‑intercept. Grasping how slope and intercept shift your line helps you predict outcomes and solve real‑world problems. Scholastic's 8th Grade Math Guide
  3. Grasp the Concept of Functions - A function assigns each input exactly one output, often written as f(x). Recognizing functions helps you see how one quantity depends on another and keeps your math toolbox sharp. GreatSchools Function Fundamentals
  4. Learn the Pythagorean Theorem - In a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c². This powerful relation unlocks distance problems and geometric proofs in a snap. Scholastic's Geometry Essentials
  5. Solve Systems of Linear Equations - Systems ask where two lines meet, and you can crack them with substitution or elimination. Mastering these methods paints a clear picture of intersection points in coordinate planes. Internet4Classrooms Systems Solver
  6. Work with Rational Expressions - Rational expressions are fractions with polynomials, and you simplify them by factoring and canceling common terms. Getting comfortable with this process strengthens your algebraic fluency. OpenStax Quick Reference
  7. Explore Quadratic Functions - Quadratics look like y = ax² + bx + c and graph as parabolas that open up or down. Understanding how a, b, and c affect the vertex and width helps you tackle optimization puzzles. Albert.io Quadratic Topics
  8. Understand Exponential Functions - Exponential functions follow y = a·b^x and model lightning‑fast growth or gradual decay. Spotting these patterns unlocks insights into populations, investments, and natural processes. USF's College Algebra Guide
  9. Learn about Radical Expressions - Radicals involve roots like √x, and you simplify them by rewriting exponents or rationalizing denominators. Master these steps to tame even the wildest square‑root adventures. GreatSchools Radical Review
  10. Practice Graphing and Interpreting Functions - Plotting functions on a coordinate plane brings equations to life and reveals trends at a glance. Regular practice sharpens your ability to read slopes, intercepts, and behavior. USF Graphing Toolkit
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