# Category: Calculus

## How to graph X given Y

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)

## Checking Differential equation using GC

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.

## Using GC in Differential Equations

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**

## Top killer question in 2015 alevel

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:

**Question 1**

Ans: 1.90235

**Solution**

**Question 2**

**Solution**

## Common misconception on Volume of Revolution

These questions by students illustrate the common misconceptions on volume of revolution:

**Question 1**

My Solution

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.

**Question 2**

Solution

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.