Modelling using First Order Differential Equations (Edexcel A-Level Further Mathematics): Quizzes

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Modelling using First Order Differential Equations
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Which contexts use first-order differential equations for modelling?

Kinematics, population, reactions

How is acceleration aa expressed using velocity vv and displacement ss?

a=vdvdsa = v \frac{dv}{ds}

What is the differential equation for population growth with rate proportional to population?

dPdt=kP\frac{dP}{dt} = kP

In dPdt=kP\frac{dP}{dt} = kP, what does k<0k < 0 indicate?

Exponential decay

What is Newton's Law of Cooling equation for temperature TT with ambient temp TaT_a?

dTdt=−k(T−Ta)\frac{dT}{dt} = -k(T - T_a)

For motion with resistance, what is the terminal velocity from v=mgk+Ce−kmtv = \frac{mg}{k} + Ce^{-\frac{k}{m}t}?

mgk\frac{mg}{k}

What is the solution to dPdt=kP\frac{dP}{dt} = kP with initial condition P(0)=P0P(0) = P_0?

P(t)=P0ektP(t) = P_0 e^{kt}

What is the integrating factor for dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x)?

F(x)=e∫P(x)dxF(x) = e^{\int P(x) dx}

What is a common mistake when solving differential equations?

Forgetting constant of integration CC

What equation models an object's motion with resistance proportional to velocity vv?

mdvdt=−kvm \frac{dv}{dt} = -kv

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Flashcards by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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