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PES SS 2 Further Maths 2nd Term Exam 2025-2026 (Obj)
  • 1. If y=x3-5x2+4x, find dy/dx.
A) 3x2+4x-10
B) 4x2+3x
C) 3x2-10x+4
D) 3x2-10
  • 2. Find the derivative of f(x)=3x2+2x-5.
A) 6x+2
B) 9x+2
C) 9x2+2
D) 6x2+2
  • 3. Differentiate y=cos3.
A) -sin x
B) 3cosx2
C) -Cotx2
D) -(3(cosx)2)(sinx)
  • 4. Find the derivative of y=3x4-5x2+7.
A) 4x3-5x
B) 12x3-10x+7
C) 7x3-10x
D) 12x3-10x
  • 5. Differentiate f(x) =1/x2 with respect to x.
A) -2x2
B) 2/x3
C) -2/x3
D) -1/x
  • 6. 4. If y = (2x + 3)5, find dy/dx.
A) 10(2x + 3)5
B) 5(2x + 3)4
C) 2(2x + 3)4
D) 10(2x + 3)4
  • 7. Find the derivative of y = x2.
A) 2x2
B) 0.5x0.5
C) 1/2x2
D) 1/x2
  • 8. Differentiate y = x sin x with respect to x.
A) sin x - x cos x
B) x cos x
C) sin x + x cos x
D) cos x
  • 9. The derivative of a constant k is always:
A) 1
B) k
C) x
D) 0
  • 10. Find dy/dx if y = (x+1) / (x-1).
A) 2 / (x-1)2
B) 1
C) -2 / (x-1)2
D) 2x / (x-1)2
  • 11. If f(x) = 4x3, find f'(2)
A) 24
B) 48
C) 16
D) 12
  • 12. Find the derivative of y = 5x3.
A) 15x2
B) 5x2
C) 8x2
D) 15x
  • 13. Find the derivative of y = cos(5x).
A) 5 * sin(5x)
B) 5 * cos(5x)
C) -sin(5x)
D) -5 * sin(5x)
  • 14. If y = (x2 + 1)3, find dy/dx.
A) 6x2
B) 2x(x2 + 1)2
C) 3(x2 + 1)2
D) 6x(x2 + 1)2
  • 15. Find dy/dx for y = 3 * sin(x) - 4 * cos(x).
A) 3 * cos(x) - 4 * sin(x)
B) -3 * cos(x) + 4 * sin(x)
C) 3 * sin(x) + 4 * cos(x)
D) 3 * cos(x) + 4 * sin(x)
  • 16. Differentiate y = (2x + 3)2.
A) 4x + 6
B) 8x + 6
C) 4(2x + 3)
D) 2(2x + 3)
  • 17. Find dy/dx for y = x1/3.
A) 1/x3
B) x2/3
C) (1/3) * x-2/3
D) 3x2
  • 18. Find the derivative of y = 2 * sin(3x).
A) 6 * sin(3x)
B) 6 * cos(3x)
C) 2 * cos(3x)
D) -6 * cos(3x)
  • 19. Differentiate y = 4 / x3.
A) -12 / x2
B) -12 / x4
C) 4 / x4
D) 12 / x2
  • 20. Differentiate y = 3x-2.
A) 6x-1
B) -3x-3
C) -6x-3
D) -6x-1
  • 21. Differentiate y = x4 - 2x2 + 5.
A) 4x4 - 4x
B) x3 - 4x
C) 4x3 - 2x
D) 4x3 - 4x
  • 22. If y = x * sin(x), find dy/dx.
A) x * cos(x)
B) cos(x)
C) sin(x) + x * cos(x)
D) sin(x) - x * cos(x)
  • 23. Find the derivative of y = 10x0.5.
A) 5x0.5
B) 10x-0.5
C) x-0.5
D) 5x-0.5
  • 24. Find dy/dx for y = x2 / (x + 1).
A) 2x / (x+1)2
B) (2x) / 1
C) x / (x+1)
D) (x2 + 2x) / (x + 1)2
  • 25. Differentiate y = sin(x2).
A) x2 * cos(x)
B) cos(x2)
C) 2x * cos(x2)
D) 2 * sin(x)
  • 26. Differentiate y = 5x2 - 3x + 2.
A) 10x - 3
B) 10x + 2
C) 10x2 - 3
D) 5x - 3
  • 27. If y = (3x - 1)4, find dy/dx.
  • 28. Find the derivative of y = (x + 1)(x + 2).
A) 2x
B) 2x + 3
C) x + 3
D) 2x + 2
  • 29. Differentiate y = 1 / (2x + 1).
A) 2 / (2x + 1)2
B) -2 / (2x + 1)2
C) -1 / (2x + 1)2
D) 1 / 2
  • 30. Find dy/dx if y = 1 / x5.
A) -5x-4
B) 5x-4
C) -5x-6
D) 1 / (5x4)
  • 31. The rule used for differentiating a "function of a function" is:
A) Quotient rule
B) Product rule
C) Power rule
D) Chain rule
  • 32. Find the derivative of y = sin(x) / x.
A) (sin(x) - x * cos(x)) / x2
B) cos(x) / 1
C) (x * cos(x) - sin(x)) / x2
D) cos(x) / x2
  • 33. Differentiate y = x3 - x-3.
A) 3x2 - 3x-4
B) x2 + x-4
C) 3x2 + 3x-2
D) 3x2 + 3x-4
  • 34. Differentiate y = sin(3x + 2).
A) -3 * cos(3x + 2)
B) 3 * sin(3x + 2)
C) cos(3x + 2)
D) 3 * cos(3x + 2)
  • 35. Find dy/dx for y = x2 * cos(x).
A) 2x * cos(x) - x2 * sin(x)
B) -2x * sin(x)
C) 2x * cos(x) + x2 * sin(x)
D) 2x * sin(x)
  • 36. If y = tan(x2), find dy/dx.
A) 2 * sec2(x)
B) sec2(x2)
C) 2x * sec2(x2)
D) 2x * tan(x)
  • 37. Find the derivative of y = (4x - 1)0.5.
A) 2(4x - 1)
B) 4 / (4x - 1)0.5
C) 2 / (4x - 1)0.5
D) 1 / (4x - 1)0.5
  • 38. If y = (x2 - 1) / x, find dy/dx.
A) 2x
B) (x2 + 1) / x2
C) 1 + 1/x2
D) 1 - 1/x2
  • 39. Find the derivative of y = 2x5 - 5x2 + 3.
A) 10x4 - 10x
B) 10x4 - 5x
C) 10x5 - 10x
D) 10x4 - 10
  • 40. If y = cos(x) / sin(x), then dy/dx is:
A) sec2(x)
B) -sin2(x)
C) 1
D) -cosec2(x)
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