Forming differential equations and connected rates of change

Forming differential equations and connected rates of change Quiz

Spec 5.2 · Edexcel International A Level Maths: Quiz

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  1. 1. The rate of increase of a population PP is proportional to PP. Which differential equation models this?

    • A. dPdt=kP\frac{dP}{dt}=kP
    • B. dPdt=kP\frac{dP}{dt}=\frac kP
    • C. dPdt=kt\frac{dP}{dt}=kt
    • D. dPdt=Pk\frac{dP}{dt}=\frac Pk

  2. 2. A bath empties so that its volume VV decreases at a rate proportional to h\sqrt h, where hh is the depth. Which is correct for k>0k>0?

    • A. dVdt=kh\frac{dV}{dt}=k\sqrt h
    • B. dVdt=−kh\frac{dV}{dt}=-k\sqrt h
    • C. dVdt=−kh\frac{dV}{dt}=-\frac{k}{\sqrt h}
    • D. dVdt=−kh2\frac{dV}{dt}=-kh^2

  3. 3. A cube has edge xx cm increasing at 0.20.2 cm s−1^{-1}. Find dVdt\frac{dV}{dt} when x=4x=4.

    • A. 12.812.8 cm3^3 s−1^{-1}
    • B. 2.42.4 cm3^3 s−1^{-1}
    • C. 4848 cm3^3 s−1^{-1}
    • D. 9.69.6 cm3^3 s−1^{-1}

  4. 4. A sphere's surface area increases at 1010 cm2^2 s−1^{-1}. Find drdt\frac{dr}{dt} when r=5r=5 cm.

    • A. 4π4\pi
    • B. 40π40\pi
    • C. 14π\frac{1}{4\pi}
    • D. 140π\frac{1}{40\pi}

  5. 5. VV depends on rr and rr depends on tt. Which relation is correct?

    • A. dVdt=dVdr÷drdt\frac{dV}{dt}=\frac{dV}{dr}\div\frac{dr}{dt}
    • B. dVdt=dVdr×drdt\frac{dV}{dt}=\frac{dV}{dr}\times\frac{dr}{dt}
    • C. dVdt=drdV×drdt\frac{dV}{dt}=\frac{dr}{dV}\times\frac{dr}{dt}
    • D. dVdt=dVdr+drdt\frac{dV}{dt}=\frac{dV}{dr}+\frac{dr}{dt}

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