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Quizzes > High School Quizzes > Technology

RHS Practice Quiz: Boost Your Exam Skills

Tackle diverse questions to master key topics

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting RHS Rapid Review, a fast-paced high school algebra quiz.

What is the value of x in the equation 2x = 10?
x = 10
x = 5
x = 4
x = 2
Dividing both sides of the equation by 2 gives x = 10/2, which equals 5. This demonstrates the basic process of solving a simple linear equation.
Simplify the expression: 2(x + 3).
2x + 3
2x + 5
2x + 6
x + 5
Using the distributive property, multiply 2 by each term inside the parentheses: 2*x = 2x and 2*3 = 6. Thus, the simplified form is 2x + 6.
Solve for x: x + 4 = 9.
x = 13
x = 5
x = 9
x = -5
Subtracting 4 from both sides of the equation results in x = 9 - 4, which simplifies to x = 5. This is a straightforward linear equation.
What is the value of the expression 3 + 2 * 4?
14
11
24
20
According to the order of operations, multiplication is done before addition. Multiplying 2 by 4 gives 8, and adding 3 results in 11.
What operation is demonstrated by applying the formula a(b + c) = ab + ac?
Addition over multiplication
Division over addition
Subtraction over addition
Multiplication over addition
This identity shows the distributive property, where multiplication is distributed over addition. It is a fundamental property used to simplify algebraic expressions.
Simplify the expression: 3x + 4x - 2.
3x - 2
7x + 2
12x - 2
7x - 2
Combine the like terms 3x and 4x to obtain 7x. Then subtract 2 to get the simplified expression, 7x - 2.
Solve for x: 5x + 3 = 3x + 11.
x = -4
x = 8
x = 4
x = 2
Subtract 3x from both sides to obtain 2x + 3 = 11, then subtract 3 to get 2x = 8. Dividing by 2 gives x = 4.
Factor the expression: x² + 5x + 6.
(x + 1)(x + 6)
(x + 2)(x + 4)
(x + 3)(x + 4)
(x + 2)(x + 3)
To factor the quadratic, find two numbers that multiply to 6 and add to 5. Since 2 and 3 meet these conditions, the expression factors as (x + 2)(x + 3).
If y = 2x - 3, what is the value of y when x = 5?
7
8
10
12
Substitute x = 5 into the equation: y = 2(5) - 3. This calculation yields y = 10 - 3, which equals 7.
Solve the inequality: 3x - 4 > 5.
x < 3
x > 3
x < 2
x > 2
Add 4 to both sides to obtain 3x > 9, then divide by 3 to get x > 3. This is the solution to the inequality.
What is the result of subtracting the polynomial (2x² + 3x - 4) from (5x² - 2x + 1)?
3x² - 5x + 5
7x² + x - 3
3x² + x - 3
7x² - 5x - 3
Subtract the corresponding terms: (5x² - 2x + 1) - (2x² + 3x - 4) becomes 3x² - 5x + 5. This requires careful handling of subtraction across all terms.
Solve for x: 4(2x - 1) = 3x + 5.
x = 9
x = 3
x = 9/5
x = 2
Expand the left side to get 8x - 4, then set up the equation 8x - 4 = 3x + 5. Solving for x by subtracting 3x and adding 4 yields 5x = 9, so x = 9/5.
What is the next term in the sequence: 3, 7, 11, 15, ... ?
20
19
17
18
The sequence increases by 4 each time (7-3, 11-7, 15-11 are all 4). Adding 4 to the last term, 15, yields 19.
Solve for x in: 2(x - 3) = x + 1.
x = -7
x = 9
x = 5
x = 7
Distribute the 2 to get 2x - 6 = x + 1. Subtracting x from both sides and then adding 6 yields x = 7, which is the correct solution.
Which property of numbers justifies that a(b + c) = ab + ac?
Commutative Property
Associative Property
Identity Property
Distributive Property
The equality a(b + c) = ab + ac is a direct application of the distributive property. This property connects multiplication with addition by distributing the multiplication over each term inside the parentheses.
Solve for x: (x/2) + (x/3) = 5.
x = 7
x = 6
x = 10
x = 5
Find a common denominator to combine the fractions: (3x + 2x)/6 = 5 becomes 5x/6 = 5. Multiplying both sides by 6 and then dividing by 5 yields x = 6.
Factor the quadratic expression: 6x² + 11x - 10.
(3x + 5)(2x - 2)
(6x - 5)(x + 2)
(2x - 5)(3x + 2)
(2x + 5)(3x - 2)
Using the AC method, multiply 6 and -10 to get -60. The numbers 15 and -4 multiply to -60 and add to 11. Grouping the terms leads to the factors (2x + 5) and (3x - 2).
Solve for x: (3x - 4)/2 = (x + 2)/3.
x = 16/7
x = 8
x = 7/16
x = 2
Clear the fractions by cross-multiplying: 3(3x - 4) = 2(x + 2). Simplifying gives 9x - 12 = 2x + 4, and solving for x yields x = 16/7.
If f(x) = 2x² - 3x + 1, what is f(3)?
8
12
9
10
Substitute x = 3 into the function: f(3) = 2(3)² - 3(3) + 1 = 18 - 9 + 1, which simplifies to 10. This step verifies the evaluation of a quadratic function.
Solve the system of equations: x + y = 7 and x - y = 3.
x = 4, y = 3
x = 5, y = 3
x = 3, y = 4
x = 5, y = 2
Adding the two equations gives 2x = 10, hence x = 5. Substituting x = 5 into x + y = 7 results in y = 2, which is the unique solution.
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Study Outcomes

  1. Analyze key algebra concepts to quickly identify problem areas.
  2. Apply algebraic techniques to solve equations and inequalities.
  3. Evaluate solutions to determine areas for improvement.
  4. Understand the structure of algebraic expressions and relationships.

RHS Practice Questions Cheat Sheet

  1. Understand algebraic expression structure - Break down any expression by spotting terms, coefficients, and factors, so nothing seems mysterious. This foundational skill makes simplifying and solving feel like piecing together a puzzle instead of wrestling with magic symbols. OpenStax: College Algebra Key Concepts
  2. Master exponent rules - Get comfy with product, quotient, and power rules so exponents bow to your will. Once you know these tricks, simplifying exponential expressions feels like second nature and you'll blast through equations in record time. OpenStax: College Algebra Key Concepts
  3. Manipulate polynomials like a pro - Learn to add, subtract, and multiply polynomials (hello, FOIL!). Recognizing patterns here turns messy algebra into a set of easy-to-follow steps that save you from headaches on exams. OpenStax: College Algebra Key Concepts
  4. Factor with finesse - Pull out the greatest common factor and spot special products (difference of squares, anyone?) to make equations shrink before your eyes. Factoring is your secret weapon for cracking polynomial problems open. OpenStax: College Algebra Key Concepts
  5. Solve linear equations & inequalities - Balance equations like a tightrope walker and see how each operation shifts inequality solutions. Mastery here builds a sturdy bridge to tackling tougher multi-step and absolute-value problems. OpenStax: Elementary Algebra Key Concepts
  6. Tackle systems of equations - Use substitution and elimination to find where two (or more) lines meet - no graphing required. These strategies are like algebraic GPS, guiding you straight to the solution. Math Is Fun: High School Algebra Curriculum
  7. Grasp functions, domains, and ranges - Think of a function as a machine: you feed it an input, it spits out an output. Getting comfortable with notation, domain, and range lets you decode any function's secret recipe. The Core Standards: Algebra (HSA)
  8. Conquer quadratics - From factoring and completing the square to unleashing the quadratic formula, these methods unlock all parabolas. Quadratics pop up everywhere, so having multiple tools keeps you ready for any challenge. OpenStax: College Algebra Key Concepts
  9. Work with rational expressions - Simplify, multiply/divide, and add/subtract ratios of polynomials like a fraction ninja. This mastery ensures you handle any rational equation or application with ease. OpenStax: College Algebra Key Concepts
  10. Explore exponentials & logarithms - Dive into growth-and-decay models, and learn how logarithms invert exponentials to reveal hidden exponents. This dynamic duo power-tools your ability to model everything from populations to sound intensity. OpenStax: College Algebra Key Concepts
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