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VICMath MethodsQuick questions

Unit 1

Quick questions on Rates of change and the derivative: VCE Math Methods Unit 1 Year 11

8short 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 tangent?
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The line touching the curve at one point with the same gradient as the curve.
What is normal?
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Perpendicular to the tangent at the same point.
What are power rule applied to non-power functions?
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The power rule applies to xnx^n. It does not directly apply to exe^x, sin⁡x\sin x, or ln⁡x\ln x (those are introduced in Unit 3).
What is tangent gradient confused with the function value?
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f(a)f(a) is the function's value at aa. f′(a)f'(a) is the gradient at aa. Different objects.
What is wrong normal gradient?
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Normal gradient is −1/m-1 / m where mm is the tangent gradient. Sign and reciprocal both matter.
What is q1?
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Find the gradient of the chord of y=x2y = x^2 between x=2x = 2 and x=5x = 5. [2 marks]
What is q2?
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For f(x)=x3−6xf(x) = x^3 - 6x, find f′(x)f'(x) and the gradient of the tangent at x=2x = 2. [3 marks]
What is q3?
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A car's position is s(t)=t3−9t2+24ts(t) = t^3 - 9t^2 + 24t metres. (a) Find s′(t)s'(t). (b) Find the times when the velocity is zero.

All Math MethodsQ&A pages