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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.

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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.

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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.

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Here is a typical Proportion question withÂ percentageÂ change:

Example 1:

Given that yÂ is directly proportional to the square of x. When xÂ is increased by 200%, calculate the percentage increase in y.

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Step 1: Always write down the relationship as per given in the question:

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Step 2: Convert the percentage change into a numerical multiplier:

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Step 3: Derive the corresponding change in y, given the relationship and the change in x:

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Step 4: Calculate percentage change in y.

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Practice Questions:

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1) It is given that yÂ is directly proportional to square of x. When xÂ is increased by 150%, calculate the percentage increase in y.

(Ans: 525%)

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2) it is given that yÂ is inversely proportional to square root of x. When xÂ is increased by 200%, calculate the percentage change in y.

(Ans:-42.3%)

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3) it is given that yÂ is inversely proportional to cube of x. When xÂ is reduced by 50%, calculate the percentage change in y.

(Ans: 700%)

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4) it is given that GÂ is directly proportional to cube of M. When MÂ is reduced by 20%, calculate the percentage change in G.

(Ans: -48.8%)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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"Expect problems and eat them for breakfast" Â Â Â ~ Alfred A. Montapert

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