9231 FP2 · Notes & worked examples
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
Maths4U Original · Short practice
On \(0\le x\le 3\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 12)^{\frac{3}{2}}\).
Find its arc length.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
On \(0\le x\le 1\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 13)^{\frac{3}{2}}\).
Find its arc length.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Maths4U Original · Short practice
On \(0\le x\le 1\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 13)^{\frac{3}{2}}\).
Find \(\displaystyle \frac{S}{\pi}\) for the curved surface produced by revolution about the x-axis.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
On \(0\le x\le 2\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 14)^{\frac{3}{2}}\).
Find \(\displaystyle \frac{S}{\pi}\) for the curved surface produced by revolution about the x-axis.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Maths4U Original · Short practice
On \(0\le x\le 2\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 14)^{\frac{3}{2}}\).
Find \(\displaystyle \frac{V}{\pi}\) for the solid formed from the region under the curve.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
On \(0\le x\le 3\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 15)^{\frac{3}{2}}\).
Find \(\displaystyle \frac{V}{\pi}\) for the solid formed from the region under the curve.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Maths4U Original · Short practice
On \(0\le x\le 3\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 15)^{\frac{3}{2}}\).
Find the gradient at the right endpoint.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
On \(0\le x\le 1\), the curve is \(\displaystyle y= \frac{2}{3}(x+ 16)^{\frac{3}{2}}\).
Find the gradient at the right endpoint.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.