Constructing differential equations

Constructing differential equations Quiz

Spec G6 · AQA A-Level Maths: Quiz

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  1. 1. The rate at which a metal cools is proportional to the temperature TT above room temperature 2020. Which equation models this, with k>0k>0?

    • A. dTdt=k(T−20)\frac{dT}{dt}=k(T-20)
    • B. dTdt=−k(T−20)\frac{dT}{dt}=-k(T-20)
    • C. dTdt=−kT\frac{dT}{dt}=-kT
    • D. T=−k(T−20)T=-k(T-20)

  2. 2. A population PP grows at a rate proportional to PP and 55 individuals per year are harvested. Which equation models this?

    • A. dPdt=kP−5\frac{dP}{dt}=kP-5
    • B. dPdt=5kP\frac{dP}{dt}=5kP
    • C. dPdt=k(P−5)\frac{dP}{dt}=k(P-5)
    • D. dPdt=kP+5\frac{dP}{dt}=kP+5

  3. 3. The area AA of an oil spill increases at a rate proportional to the square root of AA. Which equation models this, k>0k>0?

    • A. dAdt=kA2\frac{dA}{dt}=kA^2
    • B. dAdt=kA\frac{dA}{dt}=\frac{k}{\sqrt A}
    • C. dAdt=kA\frac{dA}{dt}=k\sqrt A
    • D. A=ktA=k\sqrt t

  4. 4. A particle of mass 22 kg moves in a line under a resistive force of 0.5v0.5v N only. Which equation gives its velocity?

    • A. dvdt=0.5v\frac{dv}{dt}=0.5v
    • B. dvdt=−0.25v\frac{dv}{dt}=-0.25v
    • C. dvdt=−v\frac{dv}{dt}=-v
    • D. dvdt=−0.5v\frac{dv}{dt}=-0.5v

  5. 5. With dQdp=−0.15Q\frac{dQ}{dp}=-0.15Q, find dQdp\frac{dQ}{dp} when Q=20Q=20.

    • A. −0.75-0.75
    • B. 33
    • C. −3-3
    • D. 0.150.15

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