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Quizzes > Science

Energy Resources Unit Review Practice Quiz

Quick, free energy resources practice quiz. Instant results.

Editorial: Review CompletedCreated By: Veronica ArtinoUpdated Aug 23, 2025
Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting The Power Up Review algebra practice quiz for high school students.

This quiz helps you review energy resources and prepare for your unit test by practicing questions on renewable and nonrenewable sources, their pros and cons, and conservation. Get quick feedback as you go, then dig deeper with our natural resource quiz, explore clean power in the solar energy quiz, or test turbines with the wind energy quiz.

Solve for x: 2x = 10.
20
5
10
2
Dividing both sides of the equation by 2 isolates x, giving x = 5. This simple division confirms the correct answer.
Which expression is equivalent to 5x + 3x?
5x²
8x
x
10x
By combining like terms, you add the coefficients 5 and 3 to get 8, which means 5x + 3x simplifies to 8x. This is a straightforward application of adding similar terms.
What is the slope of the line represented by the equation y = 2x + 3?
5
-2
2
3
In the slope-intercept form y = mx + b, the coefficient m is the slope. Here, m is 2, so the slope of the line is 2.
Solve for x: x - 5 = 3.
3
8
5
2
Adding 5 to both sides of the equation yields x = 8. This basic operation demonstrates the process of isolating the variable.
If a = 3 and b = 4, what is the value of a² + b²?
25
12
28
7
Calculating a² gives 9 and b² gives 16; adding these results in 25. This question tests the ability to correctly square numbers and add them.
Solve for x: 3x - 5 = 2x + 1.
4
6
7
5
Subtracting 2x from both sides gives x - 5 = 1, and then adding 5 to both sides results in x = 6. This demonstrates solving a simple linear equation.
Which property allows us to expand 3(x + 4) to 3x + 12?
Identity property
Distributive property
Commutative property
Associative property
The distributive property allows multiplication to be distributed over addition, so 3(x + 4) becomes 3x + 12. This is a fundamental property in algebra.
Find the value of x in the equation: 4(x + 3) = 28.
28
4
16
7
Expanding the left side gives 4x + 12, and subtracting 12 from both sides results in 4x = 16. Dividing by 4 then gives x = 4.
Which expression is equivalent to 2x + 3x - 4?
6x - 4
x - 4
5x - 4
5x + 4
Combine the like terms 2x and 3x to obtain 5x, then subtract 4 to form 5x - 4. This exercise reinforces the combining of like terms.
Evaluate the expression 2(a + 3) when a = 5.
12
16
10
18
Substitute 5 for a to get 2(5 + 3) which equals 2(8) = 16. This question tests substitution and basic arithmetic.
Which equation represents a line with a slope of 3 and a y-intercept of -2?
y = 2x + 3
y = 3x - 2
y = -3x - 2
y = -2x + 3
The slope-intercept form y = mx + b shows that the slope is the coefficient of x and the y-intercept is the constant term. Here, m is 3 and b is -2, so y = 3x - 2 is correct.
Solve for x: 15 + 2x = 35.
10
5
20
15
Subtract 15 from both sides to obtain 2x = 20, then divide by 2 to find x = 10. This straightforward operation is a key skill in solving simple equations.
Solve the inequality: 2x - 1 > 3.
x ≤ 2
x ≥ 2
x < 2
x > 2
Adding 1 to both sides gives 2x > 4, and dividing by 2 results in x > 2. The inequality sign remains unchanged because you are dividing by a positive number.
Simplify the expression: (x² - 9) / (x - 3) for x ≠ 3.
x + 9
9 - x
x + 3
x - 3
The numerator x² - 9 can be factored as (x - 3)(x + 3). Dividing by (x - 3) cancels the common factor, leaving x + 3 (with the condition x ≠ 3).
Simplify the expression: 3(x - 2) + 4.
3x + 2
3x - 10
3x - 2
3x + 10
First, distribute the 3 across (x - 2) to obtain 3x - 6, then add 4 to combine like terms, yielding 3x - 2.
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 2 and x = 3
x = 2
x = -2 and x = -3
x = 3
Factoring the quadratic gives (x - 2)(x - 3) = 0, which means the solutions are x = 2 or x = 3. Both values satisfy the original equation.
If f(x) = 2x² - 3x + 5, what is the value of f(2)?
7
10
8
9
Substitute x = 2 into the function: f(2) = 2(4) - 3(2) + 5, which simplifies to 8 - 6 + 5 = 7. This tests function evaluation.
Solve for x: (x/2) + (x/3) = 5.
5
12
6
10
Multiply the entire equation by 6 to eliminate the denominators, simplifying it to 5x = 30. Dividing by 5 gives x = 6.
Factor completely: x² - 16.
(x - 8)(x + 2)
x(x - 16)
x² - 4
(x - 4)(x + 4)
x² - 16 is a difference of squares and factors as (x - 4)(x + 4). This is a common factoring technique used in algebra.
An energy consumption model is given by E = 5t² + 3t. What is the expression for E when t is replaced by (x + 1)?
5x² + 10x + 5
3x² + 10x + 5
5x² + 13x + 8
5x² + 8x + 3
Substitute t with (x + 1) into the model to get E = 5(x + 1)² + 3(x + 1). Expanding and combining like terms yields 5x² + 13x + 8.
0
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Study Outcomes

  1. Analyze algebraic expressions and equations to determine variable relationships.
  2. Apply problem-solving strategies to simplify and solve core algebra problems.
  3. Identify areas of misconception in algebraic reasoning and energy resource concepts.
  4. Evaluate real-world energy resource scenarios using algebraic models.
  5. Synthesize mathematical principles to boost exam confidence and readiness.

Energy Resources Unit Review Cheat Sheet

  1. Solving Linear Equations - Become a balance wizard by isolating the variable on one side of the equation. For example, in 2x + 3 = 7, subtract 3 from both sides and then divide by 2 to find x = 2. Practice this step-by-step approach on different examples to build confidence and speed. Solving Linear Equations
  2. Factoring Quadratics - Crack the code of quadratics by splitting expressions into two binomials. Remember that x² - 5x + 6 factors neatly into (x - 2)(x - 3), revealing the roots x = 2 and x = 3. Mastering this helps with graphing, solving and simplifying complex algebraic problems. Factoring Quadratics
  3. Graphing Linear Equations - Turn equations into visual stories by identifying slope and y‑intercept. For y = 2x + 1, slope = 2 gives the rise/run and the intercept (0,1) drops you right onto the y‑axis. Plot a few points and connect them to see your line come alive. Graphing Linear Equations
  4. Solving Systems of Linear Equations - Handle two equations like a super-sleuth by using substitution or elimination. For instance, solve y = 2x and x + y = 6 together to pinpoint the secret values. This skill is vital for real-world problems where multiple conditions intersect. Solving Systems of Linear Equations
  5. Laws of Exponents - Become an exponent expert by mastering rules like a❿ * aᵝ = a❿❺ᵝ and (aᵝ)❿ = aᵝ❿. These shortcuts turn massive multiplications into quick power-plays. Play around with different bases and powers for instant "aha!" moments. Laws of Exponents
  6. Domain, Range, and Codomain - Map out where a function lives and what values it can take. For f(x) = x², the domain is all real numbers but the range is y ≥ 0 since squares can't go negative. Understanding these sets is crucial for deeper calculus adventures. Domain, Range, and Codomain
  7. Simplifying Rational Expressions - Shrink fractions with variables by factoring and canceling common terms. For example, (x² - 9)/(x - 3) simplifies to x + 3 once you spot the difference of squares. This neat trick clears the way for more complex algebra. Simplifying Rational Expressions
  8. Solving Inequalities - Learn to handle the "greater than" and "less than" signs, flipping them when you multiply or divide by a negative. For instance, solving 2x - 3 > 5 leads you straight to x > 4. Then sketch your solution on a number line for instant clarity. Solving Inequalities
  9. Properties of Real Numbers - Explore commutative, associative, and distributive rules that make algebra flow smoothly. Knowing that a + b = b + a or a(b + c) = ab + ac turns messy expressions into organized solutions. These properties are your toolkit for any math challenge. Properties of Real Numbers
  10. Understanding Polynomials - Dive into expressions with multiple terms and track their degree to predict behavior. For 3x² - 2x + 5, the highest exponent is 2, so it's a second-degree polynomial. Polynomials power everything from simple curves to complex models in science and engineering. Understanding Polynomials
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