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Quizzes > High School Quizzes > Mathematics

Expressions and Equations Practice Quiz

Boost skills with engaging module practice questions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting a trivia quiz on expressions and equations mastery for high school students.

Simplify the expression: 2x + 3x.
x^5
5x
6x
5
By combining the like terms 2x and 3x, you add the coefficients to obtain 5x. This demonstrates the basic process of combining like terms.
Which expression is equivalent to: 4 + (2x - 3)?
2x - 1
4 + 2x
2x + 7
2x + 1
When you remove the parentheses, combine the constant terms (4 - 3) to get 1 and place the variable term first, forming 2x + 1. This is a fundamental step in simplifying expressions.
Solve for x: x + 5 = 12.
x = 7
x = 5
x = -7
x = 17
Subtracting 5 from both sides isolates the variable, yielding x = 7. This is an example of solving a simple linear equation.
Which term is the constant in the expression 3x^2 + 2x + 7?
2x
3
3x^2
7
A constant is a term that does not contain any variables; in this expression, 7 is the constant. Identifying the constant is key to understanding the structure of a polynomial.
Evaluate the expression 2(x - 3) when x = 5.
10
6
4
7
Substituting x = 5 into the expression gives 2(5 - 3) which simplifies to 2(2) = 4. This exercise reinforces substitution and basic arithmetic operations.
Simplify the expression: 3x + 4 - 2x + 7.
x - 3
x + 11
5x + 11
x + 7
Combining like terms, 3x - 2x results in x and 4 + 7 equals 11, so the simplified expression is x + 11. This demonstrates the process of merging similar terms.
Solve the equation: 2(x - 4) = 10.
x = 6
x = 9
x = 7
x = 10
Dividing both sides after distributing gives x - 4 = 5, and adding 4 to both sides results in x = 9. This problem employs the distributive property and basic equation solving.
Which property is applied when rewriting 5x + 7x as 12x?
Combining like terms
Distributive property
Commutative property
Associative property
Adding the coefficients of similar terms is known as combining like terms. This process simplifies expressions by merging terms that have the same variable factor.
Solve for x: 3x - 4 = 2x + 1.
x = 1
x = 4
x = 5
x = -5
Subtracting 2x from both sides yields x - 4 = 1, and then adding 4 to both sides results in x = 5. This demonstrates simple techniques to isolate the variable.
What is the value of the expression 2x^2 - 3x + 4 when x = 2?
8
10
12
6
By substituting x = 2 into the expression, you get 2(4) - 3(2) + 4, which simplifies to 8 - 6 + 4 = 6. This emphasizes the importance of using the correct order of operations when evaluating expressions.
Which expression is equivalent to 3(4x - 2) - 5x?
12x - 6
7x - 6
3x + 2
7x + 6
Distributing 3 results in 12x - 6, and subtracting 5x gives 7x - 6. This problem highlights the combined use of the distributive property and combining like terms.
Solve the equation: 4(x + 3) = 2x + 18.
x = -3
x = 3
x = 4.5
x = 6
Expanding the left side gives 4x + 12, and setting this equal to 2x + 18 leads to 2x = 6, so x = 3. This reinforces the method of isolating x after distribution.
Simplify the expression: 6x - 3(2x - 4).
12x
6x + 4
12
0
Distributing -3 into (2x - 4) yields -6x + 12, and adding this to 6x cancels the x-terms, leaving 12. This problem illustrates effective use of distribution and term cancellation.
If 2x + 5 = 17, what is the value of x?
11
5
6
7
Subtracting 5 from both sides gives 2x = 12, and dividing by 2 results in x = 6. This is a straightforward example of solving a linear equation.
Simplify completely: 2(3x + 4) - x.
6x + 8
5x + 8
5x - 8
6x - 8
Distributing 2 gives 6x + 8, and subtracting x results in 5x + 8. This exercise reinforces the proper use of the distributive property followed by combining like terms.
Solve for x: (x/2) + (x/3) = 5.
5
6
10
30
Finding a common denominator (6) allows you to combine the fractions: (3x + 2x)/6 = 5, leading to (5x)/6 = 5 and thus x = 6. This problem requires careful handling of fractional expressions.
Solve the equation: 4(2x - 3) - 3(3x + 2) = x.
x = 9
x = 6
x = -9
x = -6
Expanding both expressions gives 8x - 12 - 9x - 6 = x, which simplifies to -x - 18 = x; adding x to both sides leads to -18 = 2x and finally x = -9. This problem tests both distribution and combining like terms.
Factor completely: 6x^2 + 5x - 6.
(6x + 5)(x - 1)
(3x + 2)(2x - 3)
(2x + 3)(3x - 2)
(2x - 3)(3x + 2)
By splitting the middle term and grouping, the quadratic factors as (2x + 3)(3x - 2). Factoring such expressions requires identification of a pair of numbers that multiply to -36 and add to 5.
Find the solutions for x if 4x^2 - 9 = 0.
x = 3/2 and x = -3/2
x = -3/2
x = 3 and x = -3
x = 3/2
Recognizing 4x^2 - 9 as a difference of squares, factor it as (2x - 3)(2x + 3) = 0. Setting each factor equal to zero gives the solutions x = 3/2 and x = -3/2.
Solve for y in terms of x: 3y - 4x = 12.
y = (3/4)x - 4
y = (4x/3) - 4
y = (4/3)x + 4
y = (3/4)x + 4
To solve for y, add 4x to both sides to obtain 3y = 4x + 12, and then divide by 3, resulting in y = (4/3)x + 4. This expresses y as a linear function of x.
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Study Outcomes

  1. Analyze and simplify algebraic expressions using key properties.
  2. Solve linear equations by isolating variables and applying equivalent operations.
  3. Interpret and verify solutions to ensure accuracy in equation solving.
  4. Apply factoring techniques to decompose expressions and solve quadratic equations.
  5. Evaluate different strategies for manipulating expressions to enhance problem-solving skills.

Expressions & Equations Module Quiz D Cheat Sheet

  1. Master integer exponents - Get comfortable with the rules of exponents so you can simplify expressions like 3² × 3❻❵ into 3❻³, then 1/3³, and finally 1/27 without breaking a sweat. This skill is essential for tackling algebraic manipulations and spotting shortcuts. Practice makes perfect, so challenge yourself with a variety of exponent problems! thecorestandards.org
  2. Conquer roots and radicals - Learn how to use square roots (√) and cube roots (∛) to solve equations like x² = p or x³ = p, and discover why √2 can never be written as a fraction. Understanding irrational numbers opens the door to richer number concepts. Soon you'll be spotting when a radical simplifies nicely (or doesn't) in no time! thecorestandards.org
  3. Express numbers in scientific notation - When numbers get huge or tiny, scientific notation is your best friend: think of the U.S. population as roughly 3 × 10❸. This notation keeps your work neat and makes comparisons a breeze. Play around with different powers of ten to build your intuition! thecorestandards.org
  4. Operate with scientific notation - Multiply, divide, add, and subtract numbers in scientific notation and switch back to decimal form without losing accuracy. Mastering this lets you handle real-world applications in physics, chemistry, and beyond. Team up with classmates for lively practice sessions! thecorestandards.org
  5. Link proportions to linear equations - Recognize that a constant unit rate in a proportion is the same as the slope in a linear graph. This connection helps you interpret real-world situations like speed or cost per item on a straight line. Soon, graph reading will feel as natural as scrolling social media! thecorestandards.org
  6. Use similar triangles to find slope - By comparing tiny triangles on a line, you'll see why the slope m stays the same between any two points. This insight leads directly to writing equations in the form y = mx or y = mx + b like a pro. Geometry and algebra team up to make your life easier! thecorestandards.org
  7. Solve single-variable linear equations - Tackle equations in one variable and categorize them: one solution, no solution, or infinitely many. Learning these outcomes helps you predict what's coming and avoid algebraic roadblocks. You'll gain confidence and speed with each problem you crack! thecorestandards.org
  8. Tackle systems of linear equations - Find where two lines intersect by solving pairs of equations, and interpret that point as the real-world solution. Whether you use substitution, elimination, or graphing, you'll be mastering teamwork between equations. Bring on the puzzles! thecorestandards.org
  9. Apply the distributive property - Expand expressions like a(b + c) into ab + ac, then combine like terms to simplify everything neatly. This basic tool underpins more complex algebraic tasks, so make it one of your go-to strategies. You'll see how many "mysteries" in algebra vanish with this move! openstax.org
  10. Balance equations on both sides - Develop a step-by-step plan for moving variables and constants until the equation is perfectly balanced. A systematic approach prevents mistakes and builds strong algebraic habits. Soon, even multi-step problems will feel like second nature! openstax.org
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