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Quizzes > High School Quizzes > Electives

Ace Topic Quiz A-2 Practice Test

Sharpen your exam skills with engaging questions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting the A-2 Ace Challenge, a high school algebra quiz.

Solve for x: 2x + 3 = 7.
2
3
1
4
Subtracting 3 from both sides gives 2x = 4, and dividing by 2 results in x = 2. This basic linear equation reinforces fundamental solving techniques.
Simplify the expression: 3x + 4x.
7x
12x
x
1x
By combining like terms, 3x and 4x add up to 7x. This simple operation is essential for understanding algebraic expressions.
Solve for y: y/3 = 5.
15
5
3
8
Multiplying both sides by 3 gives y = 15. This direct approach demonstrates the inverse operation needed to isolate the variable.
Evaluate the expression: 2(4 + 3).
14
18
7
21
First, add the numbers inside the parentheses (4 + 3 = 7), and then multiply by 2 to get 14. This problem reinforces the order of operations.
Find the value of x if x - 5 = 10.
15
5
10
20
Adding 5 to both sides of the equation results in x = 15. This basic operation shows how to isolate the variable in a simple equation.
Solve for x: 3(x - 2) = 12.
6
4
8
10
Expanding the left side gives 3x - 6 = 12. Adding 6 and then dividing by 3 results in x = 6.
Simplify the expression: 5(2x + 3) - 4x.
6x + 15
10x + 15
5x + 3
x + 15
Distribute 5 to get 10x + 15, then subtract 4x to combine like terms, resulting in 6x + 15. This tests basic distribution and combination skills.
Solve for x: (4x)/2 = 8.
4
2
8
16
Dividing 4x by 2 simplifies to 2x, and setting 2x equal to 8 gives x = 4 after dividing both sides by 2.
Factor the expression: x² - 9.
(x - 3)(x + 3)
x(x - 9)
(x + 3)²
x²(1 - 9)
Recognize that x² - 9 is a difference of squares, which factors into (x - 3)(x + 3). This pattern recognition is key in algebraic factorization.
Solve the equation: x/2 + 3 = 7.
8
4
7
10
Subtract 3 from both sides to isolate x/2, resulting in x/2 = 4, and then multiply by 2 to find x = 8. This is a straightforward application of inverse operations.
Solve for x: 2x - 3 = 5.
4
3
5
8
Adding 3 to both sides gives 2x = 8, and dividing by 2 results in x = 4. This reinforces simple techniques for solving linear equations.
Solve for x: 3x + 4 = 19.
5
4
6
7
Subtracting 4 from both sides produces 3x = 15, and dividing by 3 leads to x = 5. This problem emphasizes fundamental equation solving.
Solve for x: x/3 + 2 = 5.
9
6
3
5
Subtract 2 from both sides to isolate x/3, which gives x/3 = 3, and then multiply by 3 to obtain x = 9. This tests understanding of basic fraction manipulation.
Solve for x: 2(x + 3) = 16.
5
6
7
8
Expanding the equation gives 2x + 6 = 16. After subtracting 6 and dividing by 2, we find x = 5, showing a common method for solving linear equations.
If 2x + 4 = 12, what is the value of x?
4
6
5
8
Subtract 4 from both sides to obtain 2x = 8 and then divide by 2 to get x = 4. This classic problem reinforces linear equation solving skills.
Solve for x: (x - 3)/4 = (2x + 1)/6.
-11
-7
7
11
Cross-multiplying results in 6(x - 3) = 4(2x + 1). Simplifying this equation leads to x = -11, demonstrating the process for solving equations with fractions.
Solve for y: 2(3y - 4) = y + 8.
16/5
8/5
5
4
First, distribute the 2 to obtain 6y - 8 = y + 8. Then, subtract y from both sides and add 8 to isolate y, resulting in y = 16/5.
Solve for x: 0.5x + 2 = 3x - 4.
12/5
2
3
4
Multiply the entire equation by 2 to eliminate the decimal, yielding x + 4 = 6x - 8. Solving this equation results in x = 12/5.
Simplify the expression: 2x - 3(x - 4) + 5.
-x + 17
5x - 7
2x + 3
x - 17
Distribute -3 across (x - 4) to get -3x + 12, then combine with 2x and add 5 to simplify the expression to -x + 17. This tests both distribution and combining like terms.
Solve for x: (3x + 5)/2 - (x - 1)/3 = 4.
1
2
3
4
Multiplying the entire equation by 6 clears the denominators, resulting in 3(3x + 5) - 2(x - 1) = 24. Simplifying and solving the equation leads to x = 1.
0
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Study Outcomes

  1. Analyze and solve linear equations and inequalities.
  2. Apply algebraic techniques to simplify expressions and factor polynomials.
  3. Interpret exam-style questions to determine appropriate problem-solving strategies.
  4. Evaluate the accuracy of solutions by identifying common errors in algebraic work.
  5. Synthesize feedback to pinpoint strengths and address areas for improvement.

A-2 Topic Quiz - Practice Test Cheat Sheet

  1. Standard Form (ax² + bx + c) - This classic setup shows the parabola's direction (a > 0 opens up, a < 0 opens down) and instantly gives you the y‑intercept (c). Perfect for sketching graphs and plugging into formulas without extra fuss. Quadratic Formulas Cheat Sheet
    2. Fiveable Quadratic Functions & Formulas
  2. Vertex Form (a(x - h)² + k) - Spotting the vertex at (h, k) is a breeze in this form, making shifts and stretches crystal clear. Use it to glide through graph transformations like a math ninja. Vertex Form Deep Dive
    3. Fiveable Quadratic Functions & Formulas
  3. Factored Form (a(x - r₝)(x - r₂)) - Roots jump right off the page in this layout, showing you exactly where the parabola crosses the x‑axis. It's your go‑to for solving equations by inspection. Factored Form Guide
    4. Fiveable Quadratic Functions & Formulas
  4. Quadratic Formula - When factoring flops, x = ( - b ± √(b² - 4ac))❄(2a) saves the day by handing you solutions for any quadratic. Memorize it once, and you've got a universal problem‑solver in your back pocket. Quadratic Formula Essentials
    5. OpenStax Intermediate Algebra 2e
  5. Equation‑Solving Methods - Flex your skills by factoring, completing the square, and wielding the quadratic formula. Mastering all three tricks means you'll always pick the fastest path to the answer. Solving Strategies
    6. OpenStax Intermediate Algebra 2e
  6. Discriminant (b² - 4ac) - Peek under the radical to see if your solutions are two real roots, one perfect touchpoint, or a pair of complex buddies. It's like a fortune‑telling tool for your quadratic's story. Discriminant Decoder
    7. OpenStax Intermediate Algebra 2e
  7. Parabola Properties - Learn the axis of symmetry (x = - b❄(2a)) and plug it back in to find your vertex coordinates. These gems turn curve‑drawing from guesswork into precision art. Parabola Playbook
    8. OpenStax Intermediate Algebra 2e
  8. Pythagorean Theorem - a² + b² = c² isn't just for triangles - it's a secret weapon for distance, coordinate geometry, and even quadratic proofs. Keep it handy for quick right‑triangle checkups. Pythagorean Quick Guide
    9. OpenStax Intermediate Algebra 2e
  9. Arithmetic Sequences - Add a constant difference each time and watch terms take off in a straight line. Use aₙ = a₝ + (n - 1)d to teleport to any term without the slow counting. Arithmetic Sequence Tips
    10. OpenStax Intermediate Algebra 2e
  10. Geometric Sequences - Multiply by a constant ratio to grow (or shrink) your sequence exponentially. Jump straight to aₙ = a₝·r^(n - 1) for instant term tracking like a pro. Geometric Sequence Tricks
    11. OpenStax Intermediate Algebra 2e
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