JAMB Mathematics questions: Differentiation

24 questions with answers and explanations. Tap an option to check yourself.

1. Question 1· Differentiation· JAMB

   Find the gradient of the curve y = x² − 4x + 1 at the point where x = 3.

   • A6
   • B−2
   • C2
   • D4

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2. Question 2· Differentiation· JAMB

   Find the minimum point of the curve y = 2x² − 8x + 3.

   • A(2, 3)
   • B(2, −5)
   • C(−2, 27)
   • D(4, 3)

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3. Question 3· Differentiation· JAMB

   Find the gradient of the curve y = x³ at the point (2, 8).

   • A6
   • B8
   • C12
   • D4

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4. Question 4· Differentiation· JAMB

   Find dy/dx if y = 1/x².

   • A−2/x³
   • B2/x³
   • C−1/x
   • D2x

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5. Question 5· Differentiation· JAMB

   The displacement of a particle is s = 2t³ − 4t metres. Find its velocity when t = 2 s.

   • A24 m/s
   • B8 m/s
   • C20 m/s
   • D12 m/s

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6. Question 6· Differentiation· JAMB

   Differentiate y = 3x⁴ − 2x² + 7x.

   • A3x³ − 2x + 7
   • B12x³ − 4x
   • C12x³ − 4x + 7
   • D12x⁴ − 4x² + 7

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7. Question 7· Differentiation· JAMB

   Differentiate y = 1/x with respect to x.

   • A1/x²
   • B−1/x²
   • C−1/x
   • Dx²

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8. Question 8· Differentiation· JAMB

   Find the gradient of the curve y = x³ − 2x at x = 2.

   • A12
   • B4
   • C10
   • D6

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9. Question 9· Differentiation· JAMB

   The area of a circle is A = πr². Find the rate of change of A with respect to r when r = 7. (Take π = 22/7.)

   • A44
   • B154
   • C22
   • D14

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10. Question 10· Differentiation· JAMB

    Find the turning point of the curve y = x² − 2x + 5.

    • A(1, 4)
    • B(−1, 8)
    • C(2, 5)
    • D(1, 5)

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11. Question 11· Differentiation· JAMB

    Find the maximum value of y = 4x − x².

    • A4
    • B2
    • C8
    • D0

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12. Question 12· Differentiation· JAMB

    Find dy/dx for y = 3x² − 5x + 2 at x = 1.

    • A6
    • B1
    • C−5
    • D0

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13. Question 13· Differentiation· JAMB

    Find the derivative of sin x with respect to x.

    • A−sin x
    • B−cos x
    • Ccos x
    • Dtan x

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14. Question 14· Differentiation· JAMB

    Find the derivative of cos x with respect to x.

    • A−cos x
    • Bsin x
    • Ccos x
    • D−sin x

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15. Question 15· Differentiation· JAMB

    Differentiate y = (2x + 1)³ with respect to x.

    • A3(2x + 1)²
    • B6(2x + 1)²
    • C2(2x + 1)³
    • D6(2x + 1)

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16. Question 16· Differentiation· JAMB

    Find the minimum value of y = x² − 6x + 10.

    • A3
    • B1
    • C10
    • D−1

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17. Question 17· Differentiation· JAMB

    Find the minimum value of y = x² − 4x + 7.

    • A3
    • B2
    • C7
    • D−3

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18. Question 18· Differentiation· JAMB

    Differentiate y = (x² + 1)² with respect to x.

    • A4x³
    • B2(x² + 1)
    • C2x(x² + 1)
    • D4x(x² + 1)

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19. Question 19· Differentiation· JAMB

    Find the values of x at the turning points of y = x³ − 3x.

    • Ax = 0 only
    • Bx = 1 or x = −1
    • Cx = 3 or x = −3
    • Dx = √3 or x = −√3

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20. Question 20· Differentiation· JAMB

    A particle moves so that s = 2t³ − 3t² metres. Find its acceleration at t = 2 s.

    • A6 m/s²
    • B12 m/s²
    • C24 m/s²
    • D18 m/s²

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