Parametric Differentiation (Edexcel A-Level Mathematics): Quizzes

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Parametric Differentiation
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What is the formula for dydx\frac{dy}{dx} in parametric differentiation?

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} in parametric form?

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

If dxdt=−sin⁡θ\frac{dx}{dt} = -\sin\theta, what is dtdx\frac{dt}{dx}?

−1sin⁡θ\frac{-1}{\sin\theta}

If dydt=6\frac{dy}{dt} = 6 and dxdt=2\frac{dx}{dt} = 2, what is dydx\frac{dy}{dx}?

33

If the tangent gradient is −5-5, what is the gradient of the normal?

15\frac{1}{5}

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

−5-5

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

y=−5x+52y = -5x + 5\sqrt{2}

For x=1t+1x = \frac{1}{t+1}, y=t−1y = t-1, if y=3xy = 3x intersects at t=−2t = -2, what is the other tt value?

22

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

For x=1t+1x = \frac{1}{t+1}, y=t−1y = t-1 at t=−2t = -2, what is the gradient of the normal?

11

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