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Quizzes > High School Quizzes > Mathematics

Ace Your Algebra Test Practice Quiz

Conquer Chapters, Units, and Exam Practice Today

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting an Algebra 1 Chapters 3-4 Challenge quiz for high school students.

Solve for x: x + 5 = 10.
15
10
20
5
Subtracting 5 from both sides of the equation gives x = 5. This is the only option that correctly satisfies the equation.
Solve for x: 2x = 8.
8
6
2
4
Dividing both sides of the equation 2x = 8 by 2 yields x = 4. The other options do not satisfy this equation.
Evaluate the expression: 3(2) + 4.
10
14
8
12
Following the order of operations, multiply 3 by 2 to get 6 and then add 4 to obtain 10. Only option 10 is correct.
What is the slope of the line y = 3x + 2?
1
3
2
5
The equation is written in slope-intercept form y = mx + b, where m is the slope. Therefore, the slope is 3.
Determine the y-intercept of the line y = -2x + 7.
7
2
0
-2
In the equation y = mx + b, the constant term b represents the y-intercept. Here, b is 7, which is the correct answer.
Solve for x: 2(x - 3) = 10.
8
5
7
6
Expanding the expression gives 2x - 6 = 10. Adding 6 to both sides and then dividing by 2 results in x = 8.
Solve for x: 3x + 5 - 2x = 12.
7
12
6
5
Combining like terms results in the equation x + 5 = 12. Subtracting 5 from both sides yields x = 7, which is the correct answer.
Simplify the expression: 4(2x + 3) - 5x.
3x + 12
8x - 12
x + 12
3x - 12
Distribute 4 to get 8x + 12 and then subtract 5x to simplify the expression to 3x + 12. The other options do not correctly combine like terms.
Which point lies on the line y = -2x + 5?
(2, 0)
(1, 3)
(0, -2)
(-1, 5)
By substituting x = 1 into the equation, we get y = -2(1) + 5 = 3. This confirms that the point (1, 3) lies on the line.
Solve for x: 5 - (x/2) = 3.
6
4
2
8
Subtracting 3 from 5 results in 2 = x/2. Multiplying both sides by 2 gives x = 4, which is the correct answer.
Solve the system of equations: x + y = 10 and x - y = 2.
x = 4, y = 6
x = 4, y = 2
x = 6, y = 4
x = 6, y = 2
Adding the two equations eliminates y, giving 2x = 12 and hence x = 6. Substituting x back into either equation shows that y = 4.
Solve for x: 3(x - 2) < 12.
x ≥ 6
x > 6
x ≤ 6
x < 6
Distribute to obtain 3x - 6 < 12, then add 6 to get 3x < 18. Dividing by 3 gives x < 6, which is the correct solution.
Rearrange the formula A = lw to solve for w.
w = l/A
w = A*l
w = l - A
w = A/l
Dividing both sides of the equation by l isolates w, resulting in w = A/l. This is the correct rearrangement of the formula.
Find the slope of the line passing through the points (2, 3) and (6, 11).
2
4
8
1
Using the slope formula m = (y2 - y1) / (x2 - x1), we compute (11 - 3) / (6 - 2) = 8/4 = 2. Therefore, the slope is 2.
Write the equation of a line with slope 3 that passes through the point (2, -1).
y = 3x - 1
y = 3x + 7
y = 3x + 1
y = 3x - 7
Using the point-slope form y - y₝ = m(x - x₝) with m = 3 and (x₝, y₝) = (2, -1) gives y + 1 = 3(x - 2). Simplifying leads to y = 3x - 7, which is the correct equation.
Alex bought notebooks at $3 each and pens at $2 each, spending a total of $26. Which pair best represents the numbers of notebooks and pens purchased?
(5, 5)
(7, 3)
(6, 4)
(4, 6)
The total cost is modeled by the equation 3x + 2y = 26. Only the pair (6, 4) satisfies this equation since 3(6) + 2(4) = 18 + 8 = 26.
Solve the system of equations using elimination: 2x + 3y = 12 and 4x - 3y = 6.
x = 2, y = -3
x = 2, y = 3
x = 3, y = -2
x = 3, y = 2
Adding the two equations eliminates y, resulting in 6x = 18 and thus x = 3. Substituting x = 3 into one of the equations yields y = 2, which is the correct solution.
Solve for x: (2x - 5)/3 = (x + 1)/2.
13
-13
10
7
Cross-multiply to obtain 2(2x - 5) = 3(x + 1), which simplifies to 4x - 10 = 3x + 3. Solving for x gives x = 13, the correct answer.
Solve the compound inequality: 2 < 3x - 1 ≤ 11.
x > 4
1 ≤ x ≤ 4
1 < x ≤ 4
1 ≤ x < 4
First, add 1 to all parts of the inequality to get 3 < 3x ≤ 12. Then, dividing every part by 3 results in 1 < x ≤ 4. This accurately expresses the solution set.
Determine the x-intercept of the line given by 4x + 5y = 20.
4
5
20
0
To find the x-intercept, set y = 0 in the equation, which gives 4x = 20. Dividing by 4 results in x = 5, making it the correct x-intercept.
0
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Study Outcomes

  1. Simplify and manipulate algebraic expressions accurately.
  2. Solve linear equations and inequalities using appropriate methods.
  3. Analyze relationships between variables by interpreting functions and graphs.
  4. Apply problem-solving strategies to algebraic challenges and real-world scenarios.
  5. Evaluate and justify the results of systems of equations derived from given conditions.

Algebra Test & Exam Review Cheat Sheet

  1. Slope-Intercept Form - The slope-intercept form of a line, y = mx + b, is your go-to for quick graphing and instant insight. Here, m reveals how steep your line climbs or falls, and b tells you exactly where it hits the y-axis. Mastering this makes sketching linear equations a breeze! OpenStax Intermediate Algebra Key Concepts
    2. OpenStax Intermediate Algebra Key Concepts
  2. Calculating Slope Between Two Points - Use m = (y₂ - y₝) ÷ (x₂ - x₝) to find how fast y changes for each step in x. This calculation is the backbone of understanding rates of change in algebra and real-life data. It's like measuring the steepness of a hill before you climb it! OpenStax Intermediate Algebra Key Concepts
    3. OpenStax Intermediate Algebra Key Concepts
  3. Graphing Linear Equations - Plotting points using your slope and y-intercept turns abstract equations into visual stories. Start at b, then use rise/run to land your next point, and draw the line that connects them. Practicing this builds confidence and helps you see patterns at a glance! OpenStax Intermediate Algebra Key Concepts
    4. OpenStax Intermediate Algebra Key Concepts
  4. Parallel vs. Perpendicular Lines - Parallel lines share the same slope but never meet, while perpendicular lines intersect at right angles because their slopes are negative reciprocals. Recognizing these patterns is critical for solving geometry puzzles and algebraic challenges. It's like knowing the secret handshake of lines! OpenStax Intermediate Algebra Key Concepts
    5. OpenStax Intermediate Algebra Key Concepts
  5. Understanding Functions and Notation - A function f(x) links each input x to exactly one output f(x), like a vending machine that gives one snack per code. Learning this notation is fundamental - it's how math talks about relationships and transformations. Get comfortable with f(x) and you're on your way to mastering more advanced topics! OpenStax Intermediate Algebra Key Concepts
    6. OpenStax Intermediate Algebra Key Concepts
  6. Vertical Line Test - Draw vertical lines across your graph: if any line hits the curve more than once, it's not a function. This quick visual check saves you from breaking the "one input, one output" rule. Think of it as your graph's VIP security guard! OpenStax Intermediate Algebra Key Concepts
    7. OpenStax Intermediate Algebra Key Concepts
  7. Solving Systems of Equations - Whether by graphing, substitution, or elimination, finding where two lines meet unlocks many real-world scenarios. Graphing gives a visual intersection, substitution swaps variables, and elimination cancels them out - pick your favorite strategy! Master all three to tackle any pair of linear equations. OpenStax Intermediate Algebra 2e: Systems Key Concepts
    8. OpenStax Intermediate Algebra 2e: Systems Key Concepts
  8. Graphing Linear Inequalities - Shade the solution region and decide if your boundary line is dashed (<) or solid (≤). This visual tool shows you all possible solutions at once. Practice makes perfect - soon you'll shade like a pro! OpenStax Intermediate Algebra Key Concepts
    9. OpenStax Intermediate Algebra Key Concepts
  9. Advanced Line Relationships - Dive deeper into geometric applications by exploring how slopes govern angles and distances. Understanding these properties enhances your toolkit for proofs, constructions, and real-world modeling. It's geometry and algebra teaming up in style! OpenStax Intermediate Algebra Key Concepts
    10. OpenStax Intermediate Algebra Key Concepts
  10. Real-World Systems Problems - Tackle mixture questions, cost-revenue analysis, and more by setting up systems of equations. These practical challenges show algebra's power beyond the classroom. The more you practice, the more you'll see how math solves everyday puzzles! OpenStax Intermediate Algebra Key Concepts
    11. OpenStax Intermediate Algebra Key Concepts
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