Why Algebra Practice Matters
Algebra is the gateway to advanced mathematics. Whether you're preparing for board exams, competitive tests, or simply building a strong foundation, mastering algebra is non-negotiable. This guide covers the 50 most important algebra questions every student should practice.
Linear Equations (Questions 1–15)
Basic Linear Equations
- Solve: 2x + 5 = 15 → **x = 5**
- Solve: 3x − 7 = 14 → **x = 7**
- Solve: 5x + 3 = 28 → **x = 5**
- Solve: 4x − 9 = 11 → **x = 5**
- Solve: 7x + 2 = 23 → **x = 3**
Multi-Step Equations
- Solve: 2(x + 3) = 16 → **x = 5**
- Solve: 3(2x − 1) = 15 → **x = 3**
- Solve: 4(x + 2) − 3 = 17 → **x = 3**
- Solve: 5(x − 4) + 2x = 8 → **x = 4**
- Solve: 2x + 3(x − 1) = 12 → **x = 3**
Equations with Fractions
11. Solve: x/2 + 3 = 7 → x = 8 12. Solve: 2x/3 = 10 → x = 15 13. Solve: (x + 1)/4 = 3 → x = 11 14. Solve: x/5 − 2 = 3 → x = 25 15. Solve: (2x − 3)/5 = 1 → x = 4
Simplification (Questions 16–25)
16. Simplify: 4x + 3x − 2x → 5x 17. Simplify: 2a²b × 3ab² → 6a³b³ 18. Simplify: (x + 2)(x + 3) → x² + 5x + 6 19. Simplify: (2x − 1)² → 4x² − 4x + 1 20. Simplify: (a + b)(a − b) → a² − b² 21. Expand: 3(x² + 2x − 5) → 3x² + 6x − 15 22. Factor: x² + 7x + 12 → (x + 3)(x + 4) 23. Factor: x² − 9 → (x + 3)(x − 3) 24. Simplify: (12x³y²)/(4xy) → 3x²y 25. Simplify: √(16x⁴) → 4x²
Quadratic Equations (Questions 26–40)
26. Solve: x² − 5x + 6 = 0 → x = 2, 3 27. Solve: x² + x − 6 = 0 → x = 2, −3 28. Solve: x² − 9 = 0 → x = ±3 29. Solve: 2x² − 8 = 0 → x = ±2 30. Solve: x² − 4x + 4 = 0 → x = 2 31. Solve: x² + 6x + 9 = 0 → x = −3 32. Solve: x² − x − 12 = 0 → x = 4, −3 33. Solve: 2x² + 5x − 3 = 0 → x = 1/2, −3 34. Find discriminant: x² + 4x + 5 = 0 → D = −4 (no real roots) 35. Solve: x² = 16 → x = ±4
Word Problems
36. The product of two consecutive numbers is 72. Find them. → 8 and 9 37. A number exceeds its square root by 12. Find the number. → 16 38. Sum of a number and its reciprocal is 10/3. Find the number. → 3 or 1/3 39. Area of rectangle is 48 cm². Length exceeds width by 2. Find dimensions. → 8 × 6 40. Sum of squares of two consecutive odd numbers is 74. Find them. → 5 and 7
Algebraic Identities (Questions 41–50)
41. Expand using identity: (a + 5)² → a² + 10a + 25 42. Expand: (3x − 2y)² → 9x² − 12xy + 4y² 43. Find: 101² using identity → (100 + 1)² = 10201 44. Find: 99² using identity → (100 − 1)² = 9801 45. Find: 103 × 97 → (100 + 3)(100 − 3) = 9991 46. If x + 1/x = 5, find x² + 1/x² → 23 47. If a − b = 3, ab = 10, find a² + b² → 29 48. Factorize: 8x³ + 27 → (2x + 3)(4x² − 6x + 9) 49. Factorize: x³ − 125 → (x − 5)(x² + 5x + 25) 50. If a + b + c = 0, prove a³ + b³ + c³ = 3abc → Using identity a³+b³+c³ − 3abc = (a+b+c)(a²+b²+c²−ab−bc−ca) = 0
Practice These Questions on TugMaster AI
Ready to test yourself under timed pressure? TugMaster AI turns these algebra questions into an exciting tug-of-war competition. Choose your difficulty level, compete against friends or AI, and watch your algebra skills improve dramatically.