WAEC Further Mathematics questions: Differentiation

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

1. Question 1· Differentiation· WAEC

   Differentiate (x² + 1)⁴ with respect to x.

   • A8(x² + 1)³
   • B4(x² + 1)³
   • C4x(x² + 1)³
   • D8x(x² + 1)³

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   Explanation and discussion

2. Question 2· Differentiation· WAEC

   The radius of a circle increases at 2 cm/s. How fast is the area increasing when the radius is 5 cm?

   • A20π cm²/s
   • B10π cm²/s
   • C25π cm²/s
   • D4π cm²/s

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3. Question 3· Differentiation· WAEC

   If y = 4x³, then dy/dx is

   • A12x²
   • B4x²
   • C12x³
   • Dx⁴

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   Explanation and discussion

4. Question 4· Differentiation· WAEC

   Find the equation of the tangent to y = x² at the point (2, 4).

   • Ay = 4x + 4
   • By = 2x
   • Cy = 4x − 4
   • Dy = 4x − 12

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5. Question 5· Differentiation· WAEC

   Find the maximum value of y = 6x − x².

   • A9
   • B3
   • C6
   • D18

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6. Question 6· Differentiation· WAEC

   If y = sin x, then dy/dx is

   • Asin x
   • B−cos x
   • Ccos x
   • D−sin x

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   Explanation and discussion

7. Question 7· Differentiation· WAEC

   Differentiate y = 5x³ − 4x + 7/x with respect to x.

   • A15x² − 4
   • B15x² − 4 + 7/x²
   • C15x² − 4 − 7/x²
   • D5x² − 4 − 7x

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8. Question 8· Differentiation· WAEC

   Find dy/dx if y = (2x + 1)³.

   • A6(2x + 1)²
   • B3(2x + 1)²
   • C2(2x + 1)²
   • D6(2x + 1)³

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9. Question 9· Differentiation· WAEC

   Differentiate (3x − 1)/(x + 2) with respect to x.

   • A3/(x + 2)²
   • B5/(x + 2)²
   • C7/(x + 2)²
   • D−7/(x + 2)²

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10. Question 10· Differentiation· WAEC

    If y = (2x + 1)³, then dy/dx is

    • A6(2x + 1)²
    • B3(2x + 1)²
    • C2(2x + 1)³
    • D6(2x + 1)

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11. Question 11· Differentiation· WAEC

    The displacement of a particle is s = t³ − 6t² + 9t metres. Find its velocity at t = 2 seconds.

    • A2 m/s
    • B3 m/s
    • C−3 m/s
    • D0 m/s

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12. Question 12· Differentiation· WAEC

    Find the turning point of the curve y = 2x² − 8x + 5.

    • A(2, −3)
    • B(−2, 29)
    • C(2, 5)
    • D(4, 5)

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13. Question 13· Differentiation· WAEC

    Find the gradient of the curve y = x² − 3x + 2 at the point where x = 4.

    • A2
    • B6
    • C13
    • D5

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14. Question 14· Differentiation· WAEC

    The displacement of a particle is s = t³ − 2t. Its velocity at t = 2 s is

    • A10
    • B4
    • C8
    • D6

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15. Question 15· Differentiation· WAEC

    The curve y = x² − 6x + 5 has a turning point at x =

    • A5
    • B6
    • C3
    • D−3

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16. Question 16· Differentiation· WAEC

    Differentiate y = x² sin x.

    • A2x sin x + x² cos x
    • B2x cos x
    • C2x sin x − x² cos x
    • Dx² cos x

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17. Question 17· Differentiation· WAEC

    Find dy/dx if y = sin 3x.

    • A3 sin 3x
    • Bcos 3x
    • C−3 cos 3x
    • D3 cos 3x

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18. Question 18· Differentiation· WAEC

    The gradient of y = x² − 3x at x = 2 is

    • A−2
    • B1
    • C4
    • D7

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