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Quizzes > High School Quizzes > Mathematics

Algebra 1 Builder Practice Quiz Answers

Master Algebra 2 Challenges with Proven Strategies

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Algebra Builder Blitz, a high school algebra practice quiz.

Easy
Solve for x: 2x + 5 = 13.
x = 6
x = 4
x = 3
x = 5
To solve for x, subtract 5 from both sides to get 2x = 8, then divide by 2 to arrive at x = 4. This is a straightforward example of solving a basic linear equation.
Simplify the expression: 3x + 4x.
x
7x
12x
0
Combine like terms by adding the coefficients of x: 3 and 4, which gives 7x. This exercise reinforces the concept of combining similar terms in an algebraic expression.
Find the value of the expression 5x - 3 when x = 2.
7
5
8
10
Substitute x with 2 to get 5(2) - 3 = 10 - 3, which equals 7. This problem highlights the basic process of substituting a value into an algebraic expression.
What is the greatest common factor (GCF) of 12 and 18?
12
6
9
3
The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest common factor shared by both is 6.
Solve for x: x/3 = 4.
12
4
7
1/12
Multiply both sides of the equation by 3 to isolate x, resulting in x = 12. This problem emphasizes the technique of clearing fractions to solve for the variable.
Medium
Solve for x: 3(x - 2) = 12.
6
8
2
4
Distribute 3 over (x - 2) to get 3x - 6 = 12. Then, add 6 to both sides and divide by 3 to find x = 6.
Simplify the expression: 2(x + 3) - 4.
2x + 6
2x + 3
2x
2x + 2
First, distribute 2 to obtain 2x + 6, then subtract 4 to combine like terms and get 2x + 2. This strengthens understanding of distribution and combining like terms.
Solve the equation: 2x + 3 = 5x - 6.
9
-3
3
1
Subtract 2x from both sides to obtain 3 = 3x - 6, then add 6 to get 3x = 9, and finally divide by 3 to find x = 3. This problem practices moving terms across the equality.
Factor the quadratic expression: x² + 5x + 6.
(x + 3)(x + 4)
(x + 2)(x + 4)
(x + 1)(x + 6)
(x + 2)(x + 3)
Find two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3, so the quadratic factors as (x + 2)(x + 3).
Solve for x: (x/2) + 3 = 7.
10
7
4
8
Subtract 3 from both sides to isolate the fractional term, getting x/2 = 4, then multiply both sides by 2 to arrive at x = 8. This problem demonstrates solving equations with fractions.
If f(x) = 2x + 3, what is the value of f(4)?
11
8
10
9
Substitute x = 4 into the function f(x) = 2x + 3, resulting in 2(4) + 3 = 11. Evaluating functions is a fundamental algebra skill.
Simplify: 4(2x - 3) + 5x.
13x
8x - 12
13x - 12
9x
First distribute 4 to get 8x - 12, then add 5x to combine like terms, which results in 13x - 12. This question practices use of the distributive property followed by combining like terms.
Solve for x: 7 - 2(x - 3) = 3x + 1.
5/2
12/5
2
3
Expand the left side to obtain 7 - 2x + 6, which simplifies to 13 - 2x. Equate 13 - 2x to 3x + 1, then solve for x by combining like terms to get x = 12/5.
If 3x - 4 = 2, what is the value of 3x?
2
4
6
8
Add 4 to both sides of the equation to get 3x = 6. This simple manipulation reinforces the steps needed to solve for a variable in a linear equation.
Solve the system of equations: x + y = 10 and x - y = 2.
x = 2, y = 8
x = 4, y = 6
x = 6, y = 4
x = 5, y = 5
Add the two equations to eliminate y, which yields 2x = 12 and therefore x = 6. Substituting x into one of the equations gives y = 4, successfully solving the system.
Hard
Solve for x: (x² - 9) / (x + 3) = 4, given x ≠ -3.
1
4
-7
7
Factor the numerator as (x - 3)(x + 3) and cancel the common factor (x + 3). This simplifies the expression to x - 3 = 4, leading to the solution x = 7.
What is the sum of the solutions to the quadratic equation x² - 4x - 5 = 0?
-4
0
4
5
Using Vieta's formula, the sum of the solutions for ax² + bx + c = 0 is -b/a. Here, -(-4)/1 equals 4, confirming the sum is 4.
Solve for x: √(2x + 3) = 5.
16
14
10
11
Square both sides to eliminate the square root, resulting in 2x + 3 = 25. Then, subtract 3 and divide by 2 to find x = 11.
Simplify the expression: (2³)² ÷ 2❴.
2
4
8
16
Calculate (2³)² by multiplying the exponents to get 2❶, then apply the quotient rule to subtract the exponents: 2❶ ÷ 2❴ equals 2², which is 4.
Express the quadratic function f(x) = x² - 2x + 1 in its factored form.
(x + 1)²
(x - 1)²
x(x - 1)
(x - 2)²
Recognize that x² - 2x + 1 is a perfect square trinomial that factors into (x - 1)². This identification is crucial for simplifying quadratic expressions.
0
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Study Outcomes

  1. Apply algebraic techniques to solve equations and inequalities.
  2. Analyze various algebra problems to determine the appropriate methods for solving them.
  3. Utilize variable manipulation and simplification to streamline complex expressions.
  4. Evaluate and verify solutions through substitution and consistency checks.

Algebra 2 1.3 Answers Cheat Sheet

  1. Master the Quadratic Formula - Say goodbye to guesswork when factoring gets tough! This handy formula, x = ( - b ± √(b² - 4ac))❄(2a), unlocks the roots of any quadratic. Keep this tool in your back pocket and you'll breeze through those x's in no time. OpenStax: Solve Quadratic Equations Using the Quadratic Formula
    2. OpenStax: Solve Quadratic Equations Using the Quadratic Formula
  2. Understand Arithmetic Sequences - Think of a sequence as a staircase where each step rises by the same height. Use a_n = a₝ + (n - 1)d to find any term, where d is your constant "step size." Perfect for spotting patterns in number puzzles and real‑world scenarios! OpenStax: Arithmetic Sequences
    3. OpenStax: Arithmetic Sequences
  3. Grasp Geometric Sequences - Picture a sequence where each term multiplies by the same ratio r - like compounding interest or population growth. The nth term is a₝·r❿❻¹, so you can leap straight to huge terms without writing them all out. It's your secret weapon for exponential thinking! OpenStax: Geometric Sequences and Series
    4. OpenStax: Geometric Sequences and Series
  4. Learn the Binomial Theorem - Ever wondered how to expand (a + b)❿ without writing it out term by term? The Binomial Theorem and its coefficients (think Pascal's Triangle) have your back. It's the shortcut to big expansions - fast! OpenStax: Binomial Theorem
    5. OpenStax: Binomial Theorem
  5. Apply the Distance Formula - Want to measure the "straight‑line" gap between (x₝,y₝) and (x₂,y₂)? Plug into d = √((x₂ - x₝)² + (y₂ - y₝)²) and voilà - Pythagoras saves the day. Great for everything from map routes to game physics! OpenStax: The Rectangular Coordinate Systems and Graphs
    6. OpenStax: The Rectangular Coordinate Systems and Graphs
  6. Understand Linear Inequalities - These work like equations, but watch out: multiply or divide by a negative and the inequality flips! Sketch the solution on a number line or graph, and you'll nail everything from budget constraints to optimization problems. OpenStax: Solve Linear Inequalities
    7. OpenStax: Solve Linear Inequalities
  7. Master Absolute Value Equations - Absolute value loves both positive and negative outcomes. For |x| = a, split the problem into x = a and x = - a. This two‑for‑one trick is key for understanding piecewise functions and real‑world "distance from zero" contexts. OpenStax: Solve Absolute Value Inequalities
    8. OpenStax: Solve Absolute Value Inequalities
  8. Learn Factoring Techniques - Factoring is like reverse multiplication: break expressions into building blocks. Practice grouping, perfect squares, and the difference of squares to simplify or solve equations in a snap. Soon you'll spot factors faster than a speeding bullet! OpenStax: Factor Trinomials
    9. OpenStax: Factor Trinomials
  9. Understand Function Notation - Functions map inputs to outputs using f(x) like a math vending machine: drop in x, get out f(x). Mastering this lets you describe relationships clearly, whether you're plotting graphs or modeling real‑world data. OpenStax: Functions and Function Notation
    10. OpenStax: Functions and Function Notation
  10. Apply the Slope-Intercept Form - y = mx + b is your go‑to for graphing lines: m is the steepness, b is the "drop‑in" starting point. Tweak m and b to see instant changes - perfect for visual learners and anyone who loves a quick sketch. OpenStax: Linear Equations in One Variable
    11. OpenStax: Linear Equations in One Variable
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