Ask any secondary 2 student in Singapore which is the toughest math topic and most of them will tell you it is Direct/Inverse Proportion. Overall, this is actually a very easy chapter, except for a particular kind of question: Questions with percentage increase and proportions.
So why do students find this kind of question difficult? The biggest hurdle is to get over the fact that each algebra alphabet (x or y) can represent more than 1 value. In secondary 1, they have been drilled to solve for x and each x would give a specific value for each question. Now, they have to abandon that understanding and accept the fact that the values of x and y can both change in a single question. Once students are able to get over this fact, understanding direct/inverse proportions would become a whole lot easier.
For students who find it difficult to understand percentage change questions, do read on. I have broken down a typical proportion/percentage change question into 4 steps to make it more digestible for my beloved students.
Here is a typical Proportion question with percentage change:
Given that y is directly proportional to the square of x. When x is increased by 200%, calculate the percentage increase in y.
Step 1: Always write down the relationship as per given in the question:
Step 2: Convert the percentage change into a numerical multiplier:
Step 3: Derive the corresponding change in y, given the relationship and the change in x:
Step 4: Calculate percentage change in y.
1) It is given that y is directly proportional to square of x. When x is increased by 150%, calculate the percentage increase in y.
2) it is given that y is inversely proportional to square root of x. When x is increased by 200%, calculate the percentage change in y.
3) it is given that y is inversely proportional to cube of x. When x is reduced by 50%, calculate the percentage change in y.
4) it is given that G is directly proportional to cube of M. When M is reduced by 20%, calculate the percentage change in G.
"Expect problems and eat them for breakfast" ~ Alfred A. Montapert
Specialist Math Tutor