Date | May 2022 | Marks available | 4 | Reference code | 22M.1.AHL.TZ2.14 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Estimate | Question number | 14 | Adapted from | N/A |
Question
The shape of a vase is formed by rotating a curve about the y-axis.
The vase is 10 cm high. The internal radius of the vase is measured at 2 cm intervals along the height:
Use the trapezoidal rule to estimate the volume of water that the vase can hold.
Markscheme
V=π10∫0y2 dx OR π10∫0x2 dy (M1)
h=2
≈π×12×2×((42+52)+2×(62+82+72+32)) M1A1
=1120 cm3 A1
Note: Do not award the second M1 If the terms are not squared.
[4 marks]
Examiners report
This was a straightforward question on the trapezoidal rule, presented in an unfamiliar way, but only a tiny minority answered it correctly. It may be that candidates were introduced to the trapezium rule as an approximation to the area under a curve and here they were being asked to find an approximation to a volume and they were unable to see how that could be done.