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## Countdown to Exams - Day 72 - Rates of change

In today's blog, we look at the topic of Rates of change. With linear functions (straight line graphs) the rate of change can be interpreted from the gradient of the function. It is interpreted as an amount of y per amount of x (e.g. Dollars per hour, Metres per second). When dealing with non-linear functions there are two rates of change you could calculate.

The average rate of change; here you create a chord between two intervals and then calculate the gradient of the cord and interpret as a rate of change. The disadvantage of this is that it doesn't truly reflect the nature of the graph.

The other rate of change is an instantaneous rate of change; here you are working out the rate of change at a specific point. Create a tangent at the point, calculate and interpret the gradient as a rate of change. This will give a more accurate representation of what is happening but more tangents will be required to deliver the bigger picture.

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## Countdown to Exams - Day 35 - Proportion

On Day 35, we are focusing on Proportion. Remember that there are two types of proportion; Direct and Inverse. As one value increases, the other increases at the same rate is an example of direct proportion (buying cups of coffee). As one value increases, the other decreases at the same rate is an example of inverse proportion (adding more people to paint a wall). When you are asked more challenging questions you will have to work out what the rate of change is (written with a k).

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## Countdown to Exams - Day 34 - Ratio

Today we are focusing on Ratio. We start off with an introduction to ratio and how to write ratios (paying attention to sentence structure) and simplify them (much like fractions). We then look at sharing quantities in a given ratio (almost like sharing out profits to shareholders). Make sure you follow the three step process here. A key thing to note here is when you have your answer, do not simplify it as it will take you back to your original ratio. Only simplify ratios when asked.

Ratio is commonly used in map and bearing questions and we cover this element as well using a scale factor multiplier.

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## Countdown to Exams - Day 33 - Simple interest, Compound Growth and Decay

Day 33 looks at Simple interest, Compound Growth and Decay. Here we take an in depth look at the formulae required to carry Simple interest problems first of all (IPRY) It is important that you convert the percentage to a decimal (rate). If you were to do this manually, find the percentage of the amount then multiply by the number of years.

The second half looks at Compound Growth and Decay. Here the rate is added/subtracted from one to create a multiplier and a version of the IPRY formula is used. Remember here, years is written as a power.

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## Countdown to Exams - Day 32 - Percentages and percentage change

The focus for today is on Percentages and percentage change. You should be confident with common conversions as seen in the table as well as converting percentages into a fraction or decimal using the conversion flow chart. We then take a look at increasing/decreasing an amount by a percentage manually using two methods (Unitary method and Decimal method)

A calculator method is explored at the end and shows a quick way to increase and decrease an amount quickly using a multiplier factor. This method will help to work out original price problems. Finally we recap the formula used to calculate the percentage change between two values.

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## Countdown to Exams - Day 31 - Quantities as fractions/percentages of each other

For day 31 we take a look at being able express quantities as fractions of each other and how to calculate a fraction of an amount. We then move onto expressing quantities as percentages of each other and how to find a percentage of an amount.

A nice way to think about these sorts of a problem is to treat it like a test score where the first value is your score (numerator) and the second value is how many marks there were.

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