Parametric equations · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Parametric first and second derivatives — objective 1

Maths4U Original · Short practice

\(x=t^2+11,\ y=t^3+2t\), for t>0. Evaluate the requested quantities at \(t=2\).

Find \(\displaystyle \frac{dy}{dx}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Parametric first and second derivatives — objective 1

Maths4U Original · Short practice

\(x=t^2+12,\ y=t^3+3t\), for t>0. Evaluate the requested quantities at \(t=3\).

Find \(\displaystyle \frac{dy}{dx}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Parametric first and second derivatives — objective 2

Maths4U Original · Short practice

\(x=t^2+12,\ y=t^3+3t\), for t>0. Evaluate the requested quantities at \(t=3\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Parametric first and second derivatives — objective 2

Maths4U Original · Short practice

\(x=t^2+13,\ y=t^3+4t\), for t>0. Evaluate the requested quantities at \(t=4\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Parametric first and second derivatives — objective 3

Maths4U Original · Short practice

\(x=t^2+13,\ y=t^3+4t\), for t>0. Evaluate the requested quantities at \(t=4\).

Find the tangent y-intercept.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Parametric first and second derivatives — objective 3

Maths4U Original · Short practice

\(x=t^2+14,\ y=t^3+1t\), for t>0. Evaluate the requested quantities at \(t=1\).

Find the tangent y-intercept.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Parametric first and second derivatives — objective 4

Maths4U Original · Short practice

\(x=t^2+14,\ y=t^3+1t\), for t>0. Evaluate the requested quantities at \(t=1\).

Find the normal gradient.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Parametric first and second derivatives — objective 4

Maths4U Original · Short practice

\(x=t^2+15,\ y=t^3+2t\), for t>0. Evaluate the requested quantities at \(t=2\).

Find the normal gradient.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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