Parametric Equations (AQA A-Level Mathematics): Quizzes

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Parametric Differentiation
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What is the chain rule formula for parametric differentiation?

dydt×dtdx=dydx\frac{dy}{dt} \times \frac{dt}{dx} = \frac{dy}{dx}

How is dydx\frac{dy}{dx} calculated from parametric equations?

dydx=dydtdxdt\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}

What is the formula for the second derivative d2ydx2\frac{d^2y}{dx^2}?

ddt(dydx)dxdt\frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}

What properties can parametric differentiation calculate?

Slope, concavity, and other properties

What is the first step in parametric differentiation?

Differentiate xx and yy wrt tt

For x=cos⁡θx = \cos\theta, y=5sin⁡θy = 5\sin\theta at θ=π4\theta = \frac{\pi}{4}, find dydx\frac{dy}{dx}.

−5-5

For x=cos⁡θx = \cos\theta, y=5sin⁡θy = 5\sin\theta at θ=π4\theta = \frac{\pi}{4}, what is the point?

(22,522)(\frac{\sqrt{2}}{2}, \frac{5\sqrt{2}}{2})

What is the tangent equation at (22,522)(\frac{\sqrt{2}}{2}, \frac{5\sqrt{2}}{2}) with gradient −5-5?

y=−5x+52y = -5x + 5\sqrt{2}

If the gradient of the tangent is −1-1, what is the gradient of the normal?

11

For x=1t+1x = \frac{1}{t+1}, y=t−1y = t-1, what is the Cartesian equation?

y=1x−2y = \frac{1}{x} - 2

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