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Countdown to Exams - Day 72 - Rates of change

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 49 - Contextual graphs

Countdown to Exams - Day 49 - Contextual graphs

In today's blog post, we take a look at everyday Contextual graphs and how to interpret the data within them. We take a look at Distance-time graphs initially where the gradient of the graph is calculated to be the speed. If your graph is non-linear then you ay have to use a tangent to work out the speed of an object at a specific point. You will also need to use the Speed/Distance/Time formula triangle to help with calculations. We then move onto Velocity-time graphs where the same principles occur except the gradient of the line is now acceleration and the area under the graph can be calculated to give the distance traveled. Finally, we finish off on financial graphs where we can do cost comparison or currency conversions by reading off the graph.

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Countdown to Exams - Day 47 - Equation of a straight line

Countdown to Exams - Day 47 - Equation of a straight line

Today we are looking the Equation of a straight line. Before we move onto the more complex straight line graphs, we must understand the equations of horizontal and vertical lines.

A horizontal line has the equation y =? where ? is the point the line crosses the y-axis. A vertical line has the equation x =? where ? is the point where the line crosses the x-axis.

All straight line graphs follow the general rule y = mx+c where m is the gradient (steepness) of the line and c is the y-intercept. You will need to be able to calculate gradients effectively and substitute into the general rule to find the y-intecept if you are given some coordinate points.

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