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Quizzes > High School Quizzes > Mathematics

Algebra Game Practice Quiz

Practice your algebra with engaging quiz answers

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting the Algebra Game Challenge, a high school level interactive quiz.

What is the sum of 2x and 3x?
5x
6x
2x²
3x²
Combining like terms 2x and 3x results in 5x, because you add the coefficients. This is a basic example of simplifying algebraic expressions.
Solve for x: x + 5 = 10.
5
10
15
0
Subtracting 5 from both sides gives x = 5. This simple equation demonstrates the use of inverse operations.
Simplify: 4(x + 2).
4x + 8
4x + 2
4x + 6
2x + 4
Using the distributive property, multiply 4 by each term inside the parentheses: 4 * x gives 4x and 4 * 2 gives 8, resulting in 4x + 8.
Identify the coefficient in the term 7y.
7
y
1
14
The coefficient of a term is the numerical factor that multiplies the variable. Here, 7 in the term 7y is the coefficient.
What does the term 'like terms' refer to in algebra?
Terms that have the same variable parts raised to the same power
Terms with different variables
Any two constants
Terms involving exponents only
Like terms are terms that contain the same variables raised to the same power, which allows their coefficients to be added or subtracted. This is fundamental for simplifying expressions.
Solve for x: 3x - 4 = 11.
5
3
7
15
Add 4 to both sides of the equation to get 3x = 15, then divide by 3 to find x = 5. This problem uses simple inverse operations.
Simplify the expression: 2(3x - 4) + 4x.
10x - 8
8x - 8
10x + 8
12x - 8
First, distribute 2 over (3x - 4) to get 6x - 8, then add 4x to receive 10x - 8. This shows the application of the distributive property and combining like terms.
If 2x + 3 = 7, what is the value of x?
2
1
3
4
Subtract 3 from both sides to obtain 2x = 4, then divide by 2 to find x = 2. This straightforward linear equation reinforces solving for a variable.
Solve for y: 4y + 2 = 18.
4
5
3
6
Subtracting 2 from both sides gives 4y = 16, and dividing by 4 yields y = 4. This problem demonstrates simple operations needed to isolate the variable.
Which equation demonstrates the distributive property for a(b + c)?
ab + ac
a + b + c
ab + c
a(b) + c
The distributive property states that multiplying a sum by a number is the same as doing each multiplication separately, which gives ab + ac. This property is essential in expanding expressions.
Solve for x: x/3 = 5.
15
5
3
8
Multiplying both sides of the equation by 3 isolates x, resulting in x = 15. This reinforces the concept of eliminating a fraction from an equation.
Which expression represents 'three more than twice a number x'?
2x + 3
3x + 2
x + 2
2(x + 3)
The phrase 'twice a number' indicates 2x, and 'three more than' means you add 3, resulting in 2x + 3. This emphasizes translation of word problems into algebraic expressions.
Simplify: x - 2 + 3x + 4.
4x + 2
4x - 6
3x + 2
4x + 1
Combine like terms by adding the x terms (x + 3x = 4x) and the constant terms (-2 + 4 = 2), which simplifies to 4x + 2. This question tests the ability to combine like terms.
Solve the equation: 5(x - 2) = 15.
5
2
3
8
Divide both sides by 5 to get x - 2 = 3, then add 2 to both sides resulting in x = 5. This illustrates solving an equation with a distributive factor.
If 7x = 21, then what is x?
3
7
21
14
Dividing both sides of the equation by 7 yields x = 3. This is a straightforward division problem reinforcing the concept of solving linear equations.
Solve for x: 2(x - 3) = x + 1.
7
5
6
8
Distribute to obtain 2x - 6 = x + 1. Subtracting x from both sides leads to x - 6 = 1, and adding 6 results in x = 7. This question tests the ability to isolate the variable in linear equations.
Solve for y: 3(2y - 4) = 4y + 2.
7
6
8
5
Expanding the left side gives 6y - 12, so the equation becomes 6y - 12 = 4y + 2. Subtracting 4y from both sides yields 2y - 12 = 2 and then adding 12 gives 2y = 14, leading to y = 7.
Factor the quadratic expression: x² + 5x + 6.
(x + 2)(x + 3)
(x + 1)(x + 6)
(x - 2)(x - 3)
(x + 5)(x + 1)
The numbers 2 and 3 multiply to 6 and add up to 5, which allows the quadratic to be factored into (x + 2)(x + 3). Factoring is a key skill in simplifying and solving quadratic equations.
Solve for x: 5(2x - 1) - 3(x + 2) = 2x + 4.
3
2
4
5
Expanding gives 10x - 5 - 3x - 6, which simplifies to 7x - 11. Setting 7x - 11 equal to 2x + 4 and then isolating x yields 5x = 15, so x = 3. This problem emphasizes the combination of distribution and isolating variables.
Solve for x: (x/2) + (x/3) = 5.
6
5
7
10
Find a common denominator (which is 6) to combine the fractions: (3x + 2x)/6 = 5, so 5x/6 = 5. Multiplying both sides by 6 gives 5x = 30, and dividing by 5 results in x = 6.
0
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Study Outcomes

  1. Analyze algebraic expressions and equations to identify their key components.
  2. Simplify complex algebraic expressions using standard operations.
  3. Solve linear equations and inequalities accurately.
  4. Apply problem-solving strategies to tackle a variety of algebra challenges.
  5. Evaluate and correct common errors to improve algebraic reasoning.

Algebra Game Worksheet Answers Cheat Sheet

  1. Order of Operations (PEMDAS) - Always tackle Parentheses first, then Exponents, Multiplication/Division, and finally Addition/Subtraction to keep your work organized and error‑free. Mastering PEMDAS feels like unlocking a secret code that makes even the most daunting expressions approachable and fun. Open Algebra
  2. Properties of Exponents - Learn to simplify expressions using product, quotient, and power rules so you can breeze through exponential problems. These rules are your toolbox for shrinking or expanding terms quickly and confidently. OpenStax College Algebra
  3. Polynomial Operations - Practice adding, subtracting, and multiplying polynomials by combining like terms and using the distributive property to avoid mistakes. Think of polynomials like Lego bricks - once you know how to snap them together, you can build anything! OpenStax Elementary Algebra
  4. Factoring Techniques - Factor out the greatest common factor, spot special products like difference of squares, and break down complex polynomials into simpler factors. Factoring is like reverse‑engineering an expression, giving you a powerful shortcut for solving equations. OpenStax College Algebra
  5. Linear Equations & Inequalities - Isolate the variable, perform inverse operations, and always check your solutions to ensure they're valid. Solving these step by step is like following a treasure map - each move brings you closer to the hidden answer! Math is Fun
  6. Graphing Lines - Find the slope and y‑intercept, plot your points, and draw the line to visualize relationships between variables. Graphing transforms abstract equations into pictures that tell a story at a glance. Open Algebra
  7. Systems of Equations - Use substitution or elimination to solve for multiple variables at once, and verify your answers by plugging them back into both equations. It's like solving a two‑piece jigsaw puzzle where each piece unlocks the other. Math is Fun
  8. Quadratic Equations - Master factoring, completing the square, and the quadratic formula so you can handle any quadratic challenge. These techniques turn complex parabolas into solutions you can calculate with confidence. OpenStax College Algebra
  9. Rational Expressions - Simplify, multiply, divide, add, and subtract fractions with polynomials by factoring and finding common denominators. Think of them as regular fractions wearing algebraic outfits - they obey the same rules! OpenStax Elementary Algebra
  10. Functions & Notation - Get comfortable with function notation (f(x)), evaluate at specific inputs, and interpret outputs in context. Functions are like machines: you feed in a value, and out comes the solution - so learn to love the assembly line! Open Algebra
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