Motion and Rates (HSC SSCE Mathematics Advanced): Quizzes

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Rates and Integration
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What is the relationship between integration and differentiation?

They are inverse operations

What must always be included when integrating a rate function?

Constant of integration CC

For dVdt=1500+30t\frac{dV}{dt} = -1500 + 30t, when does water stop flowing?

t=50t = 50 seconds

Why is the rate dVdt\frac{dV}{dt} negative when water drains from a tank?

Volume is decreasing

On a rate graph, when dPdt=0\frac{dP}{dt} = 0, what does this indicate for PP?

Stationary point

When is a quantity decreasing based on its rate graph?

When rate is negative

If rate changes from positive to negative at t=4t = 4, what occurs there?

Maximum of the quantity

What is eax+bdx\int e^{ax+b} dx equal to?

1aeax+b+C\frac{1}{a}e^{ax+b} + C

For rate dVdt=3e0.02t\frac{dV}{dt} = 3e^{-0.02t}, is the rate always positive?

Yes, always positive

For V=150(1e0.02t)V = 150(1 - e^{-0.02t}), what happens as tt \to \infty?

V150V \to 150 megalitres

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