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Quizzes > High School Quizzes > Science

Energy Resources Unit Review: Practice Quiz

Ace the unit review with engaging practice tests

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting The Power Up Review algebra practice quiz for high school students.

Easy
Solve for x: 2x = 10.
5
2
10
20
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?
8x
10x
5x²
x
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?
2
3
5
-2
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.
8
2
3
5
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?
7
12
25
28
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.
Medium
Solve for x: 3x - 5 = 2x + 1.
4
5
6
7
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?
Distributive property
Associative property
Commutative property
Identity 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.
4
7
16
28
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?
5x - 4
5x + 4
6x - 4
x - 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.
10
12
16
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 = 3x - 2
y = -2x + 3
y = 2x + 3
y = -3x - 2
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.
5
10
15
20
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 + 3
x - 3
x + 9
9 - x
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 + 2
3x - 10
3x + 10
First, distribute the 3 across (x - 2) to obtain 3x - 6, then add 4 to combine like terms, yielding 3x - 2.
Hard
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 2 and x = 3
x = -2 and x = -3
x = 2
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
8
9
10
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.
6
5
10
12
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 - 4)(x + 4)
x(x - 16)
(x - 8)(x + 2)
x² - 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 + 13x + 8
5x² + 8x + 3
5x² + 10x + 5
3x² + 10x + 5
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. 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. 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. 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. 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. 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. 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. 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. 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. 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
    11. Understanding Polynomials
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