Solve the following questions. The questions are designed to test your conceptual understanding of algebra at a Class 9 level. This sheet includes evaluation, factorization, simplification, and solving equations.
📘 Section A: Evaluate the Expression
Q1. Evaluate: 2^3 + 3^2
Q2. Evaluate: \dfrac{3^3}{3} + 5
Q3. Evaluate: (5^2 - 3^2)
Q4. Evaluate: 2^{-1} + 4^0
Q5. Evaluate: \dfrac{1}{2} + \dfrac{3}{4}
Q6. Evaluate: (\dfrac{2}{3})^2 + \dfrac{1}{9}
Q7. Evaluate: 2^4 - 2^2
Q8. Evaluate: 5^{-1} + 10^{-1}
Q9. Evaluate: \dfrac{3^3 - 2^2}{5}
Q10. Evaluate: \dfrac{4^2}{2^3} + 1
Q11. Evaluate: 10 - (3^2 + 2)
Q12. Evaluate: (1/2)^2 + (3/4)^2
Q13. Evaluate: 9^0 + 2^{-2}
Q14. Evaluate: (\dfrac{5}{6})^2
Q15. Evaluate: (3 + 2)^2 - 3^2
Q16. Evaluate: \dfrac{2}{5} + \dfrac{3}{10}
Q17. Evaluate: (2^3)^2
Q18. Evaluate: \dfrac{2^3 + 4^2}{2}
Q19. Evaluate: (\dfrac{3}{4})^{-1} + 1
Q20. Evaluate: \dfrac{1}{2^{-3}}
📗 Section B: Factorize the Expression
Q21. Factorize: x^2 + 5x + 6
Q22. Factorize: x^2 - 9
Q23. Factorize: 2x^2 + 7x + 3
Q24. Factorize: x^2 - 4x
Q25. Factorize: 3x^2 - 27
Q26. Factorize: x^2 - 2x - 8
Q27. Factorize: x^2 + 6x + 9
Q28. Factorize: 4x^2 - 25y^2
Q29. Factorize: x^2 + 3x - 10
Q30. Factorize: 2x^2 + 4x
📙 Section C: Simplify the Expression
Q31. Simplify: (x+2)^2 - (x-2)^2
Q32. Simplify: x^2 + 2x + 1 - x^2 + x - 1
Q33. Simplify: 3x(2x + 4) - x(5x + 1)
Q34. Simplify: (2x + 3)^2
Q35. Simplify: 2(x - 3) + 3(x + 4)
Q36. Simplify: x^2 + 4x + 4 - (x^2 - 4x + 4)
Q37. Simplify: x(x + 2) + x(2x + 1)
Q38. Simplify: 5x^2 - (2x^2 - 3x)
Q39. Simplify: (3x + 2)(x - 1)
Q40. Simplify: (x^2 + 2x + 1)^2
📒 Section D: Solve the Equation
Q41. Solve: 2x + 3 = 7
Q42. Solve: 4x - 5 = 3x + 2
Q43. Solve: 5x - (2x + 3) = 4
Q44. Solve: \dfrac{x - 1}{3} = 2
Q45. Solve: 6x + 4 = 2x + 20
Q46. Solve: 3(x - 2) = 2(x + 1)
Q47. Solve: \dfrac{2x}{5} + 3 = 7
Q48. Solve: x - \dfrac{1}{2} = \dfrac{1}{3}
Q49. Solve: 4x - 7 = x + 5
Q50. Solve: 2(x + 3) = x + 8
✅ Answer Key
Q1. 17
Q2. 14
Q3. 16
Q4. 1.5
Q5. 5/4
Q6. 5/9
Q7. 12
Q8. 3/10
Q9. 5
Q10. 3
Q11. 1
Q12. 13/16
Q13. 1.25
Q14. 25/36
Q15. 16
Q16. 7/10
Q17. 64
Q18. 12
Q19. 7/3
Q20. 1/8
Q21. (x+2)(x+3)
Q22. (x+3)(x-3)
Q23. (2x+1)(x+3)
Q24. x(x-4)
Q25. 3(x+3)(x-3)
Q26. (x-4)(x+2)
Q27. (x+3)^2
Q28. (2x+5y)(2x-5y)
Q29. (x+5)(x-2)
Q30. 2x(x+2)
Q31. 8x
Q32. 3x
Q33. x(1x + 11)
Q34. 4x^2 + 12x + 9
Q35. 5x + 6
Q36. 8x
Q37. 3x^2 + 3x
Q38. 3x^2 + 3x
Q39. 3x^2 - x - 2
Q40. x^4 + 4x^3 + 6x^2 + 4x + 1
Q41. x = 2
Q42. x = 7
Q43. x = \frac{7}{3}
Q44. x = 7
Q45. x = 4
Q46. x = 8
Q47. x = 10
Q48. x = \frac{5}{6}
Q49. x = 4
Q50. x = 2