Finding a curve from its gradient

Finding a curve from its gradient Quiz

Spec 5.2 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. dydx=4x−1\frac{\mathrm{d}y}{\mathrm{d}x}=4x-1 and the curve passes through (0,3)(0,3). Find yy when x=1x=1.

    • A. 22
    • B. 44
    • C. 66
    • D. 33

  2. 2. dydx=2x\frac{\mathrm{d}y}{\mathrm{d}x}=2x and the curve passes through (1,5)(1,5). Find the equation of the curve.

    • A. y=x2y=x^2
    • B. y=x2+5y=x^2+5
    • C. y=2x2+3y=2x^2+3
    • D. y=x2+4y=x^2+4

  3. 3. dydx=6x2−2\frac{\mathrm{d}y}{\mathrm{d}x}=6x^2-2 and the curve passes through (2,10)(2,10). Find cc in y=2x3−2x+cy=2x^3-2x+c.

    • A. −2-2
    • B. 22
    • C. 1212
    • D. 1010

  4. 4. dydx=x\frac{\mathrm{d}y}{\mathrm{d}x}=\sqrt{x} and the curve passes through (4,10)(4,10). Find cc.

    • A. 163\frac{16}{3}
    • B. −143-\frac{14}{3}
    • C. 143\frac{14}{3}
    • D. 463\frac{46}{3}

  5. 5. Why is a point on the curve needed as well as the gradient function?

    • A. To check the derivative is correct
    • B. The gradient function fixes the curve only up to a vertical shift, so a point fixes cc
    • C. To find the second derivative
    • D. Because the gradient is undefined without a point

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