Example 1: Volume of revolution in 2017 alevel P2 4b
Let a=2 so we can visualise the shape of the graph
Example 2: Solution curve for Differential equation. 2014 alevel P1
This is solution for part iv.
It can be sketched without expressing the solution in the form x=f(t)
GC can be used to check the solution to differential equation.
Example from 2014 P1 Q10
Suppose we want to check whether the following solution to 10 iv is correct:
Enter the following in GC
Since Y2 and Y3 gave the same values, the solution is correct.
The following example illustrates how we can use GC in Differential equations, and avoid the need to do integration to solve differential equation.
Solution for part ii
Many students viewed Paper 1, question 3 as the top killer question in the 2015 alevel h2 math 9740 paper.
This question is a new style of question in alevel, and is likely to come out in 2016 prelim and future Alevel.
The following questions serves as a good practise:
These questions by students illustrate the common misconceptions on volume of revolution:
Further queries by student
Misconception: Since the region is bounded on both sides of the Y-axis, the volume of revolution needs to be multiplied by 2 when integrate one side.
Clarification: The volume of revolution is the same whether one side of the region is rotated or both sides of the region are rotated. The swept volume of one side or both sides are the same.
Notice that for part i, the volume needs to be multiplied by 2, whereas for part 2, there is no need.
Student’s queries on part ii:
Misconception: That the volume achieved by rotating only 180 degrees is half of the volume of rotating 360 degrees.
Clarification: Since the graph is bounded on both sides, just need to rotate by 180 degrees to obtain the full swept volume. If it is bounded by one side, then need to rotate by 360 degrees to obtain the full swept volume.