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VICMath MethodsQuick questions

Unit 4

Quick questions on Related rates and rates of change: VCE Math Methods Unit 4

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is inflating sphere (volume from radius, surface area from radius)?
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Volume: V=43πr3V = \frac{4}{3} \pi r^3, so dVdt=4πr2drdt\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}.
What is sliding ladder?
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A ladder of length LL slides down a wall. Let xx be the horizontal distance from the wall to the foot of the ladder and yy the height of the top of the ladder.
What is wrong sign on quantities that decrease?
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If the question says "water is draining at 5 L/min", dVdt=−5\frac{dV}{dt} = -5 (negative). If the question says "the ladder slides down", dydt\frac{dy}{dt} is negative.
What is not using the specific moment value?
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The question typically asks for the rate at a specific configuration (when r=10r = 10, when h=1h = 1). Substitute these values after differentiating.
What is q1?
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A circle's radius grows at drdt=3\frac{dr}{dt} = 3 cm/s. Find the rate of area increase when r=5r = 5 cm. [3 marks]
What is q2?
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A spherical balloon's volume increases at 2020 cm3^3/s. Find drdt\frac{dr}{dt} when r=5r = 5 cm. [3 marks]
What is q3?
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A 55 m ladder slides down a wall; its foot moves out at 0.50.5 m/s. When the foot is 33 m from the wall, find the rate the top descends. [4 marks]

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