Build algebra skills with practice questions covering equations, inequalities, functions, polynomials, and graphing. Each problem includes step-by-step solutions showing algebraic methods and common pitfalls. Perfect for Algebra 1, Algebra 2, SAT/ACT math prep, or college placement tests. Our practice set covers everything from linear equations to quadratic functions, helping you master foundational algebra concepts.
12 sample questions. Expand to see answers and explanations.
1. Solve for x: 5x - 8 = 27
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Answer
x = 7
Explanation
Add 8 to both sides: 5x = 35. Divide by 5: x = 7. Check: 5(7) - 8 = 35 - 8 = 27 ✓
Type: multiple choice
2. Factor: x² + 7x + 12
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Answer
(x + 3)(x + 4)
Explanation
Find two numbers that multiply to 12 and add to 7: 3 and 4. So x² + 7x + 12 = (x + 3)(x + 4). Verify by FOIL: x² + 4x + 3x + 12 = x² + 7x + 12.
Type: multiple choice
3. What is the slope of y = -2x + 5?
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Answer
-2
Explanation
In slope-intercept form y = mx + b, m is slope and b is y-intercept. Slope = -2, y-intercept = 5. Negative slope means line goes down left-to-right.
Type: multiple choice
4. Solve the system: x + y = 7 and x - y = 3
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Answer
x = 5, y = 2
Explanation
Add equations: 2x = 10, so x = 5. Substitute: 5 + y = 7, so y = 2. Check both: 5 + 2 = 7 ✓ and 5 - 2 = 3 ✓
Type: multiple choice
5. Simplify: (3x²)(4x³)
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Answer
12x⁵
Explanation
Multiply coefficients: 3 × 4 = 12. Add exponents: x² · x³ = x⁵. Result: 12x⁵. Remember: when multiplying powers with same base, add exponents.
Type: multiple choice
6. True or False: The equation y = x² represents a linear function.
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Answer
False
Explanation
False. y = x² is a quadratic function (parabola), not linear. Linear functions have form y = mx + b (straight lines). Quadratics have x² terms.
Type: true false
7. If f(x) = 2x - 3, find f(5).
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Answer
7
Explanation
Substitute x = 5 into f(x): f(5) = 2(5) - 3 = 10 - 3 = 7. Function notation means 'plug in the value and evaluate'.
Type: multiple choice
8. Solve the inequality: 3x - 5 > 10
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Answer
x > 5
Explanation
Add 5: 3x > 15. Divide by 3: x > 5. Solution set is all numbers greater than 5 (not equal to 5).
Type: multiple choice
9. Which is greater: 3⁴ or 4³?
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Answer
3⁴ = 81, 4³ = 64, so 3⁴ is greater
Explanation
3⁴ = 3×3×3×3 = 81. 4³ = 4×4×4 = 64. Therefore 3⁴ > 4³.
Type: multiple choice
10. Factor completely: 2x² + 8x
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Answer
2x(x + 4)
Explanation
Factor out GCF first: 2x is common factor. 2x² + 8x = 2x(x + 4). Cannot factor further.
Type: multiple choice
11. What is the vertex of y = (x - 3)² + 2?
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Answer
(3, 2)
Explanation
Vertex form is y = (x - h)² + k where vertex is (h, k). Here h = 3, k = 2, so vertex is (3, 2).
Type: multiple choice
12. Solve: x/4 + 2 = 7
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Answer
x = 20
Explanation
Subtract 2: x/4 = 5. Multiply by 4: x = 20. Check: 20/4 + 2 = 5 + 2 = 7 ✓
Type: multiple choice
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Generate Now — FreePractice questions cover linear equations, quadratic equations, functions, graphing, polynomials, factoring, exponents, inequalities, and systems of equations for Algebra 1 and Algebra 2 curriculum.
Yes. Every problem includes detailed solution steps, identifies common mistakes to avoid, and explains the reasoning behind each method so you understand not just how but why.
Yes. Many SAT math problems are algebra-based, covering topics like linear equations, systems, functions, and quadratics. Generate SAT-style questions by uploading practice material or official SAT math content.
Master Algebra 1 fundamentals first: solving linear equations, graphing lines, basic factoring, and systems. If you can consistently solve these practice questions, you're ready for Algebra 2 topics like rational expressions and logarithms.