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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 50 - Quadratic and Cubic graphs

Countdown to Exams - Day 50 - Quadratic and Cubic graphs

Today we take a look at Quadratic and Cubic graphs. It is important to understand the shape of these graphs and identify where they cross the x and y axes as you will be asked questions about this. Sometimes you will be required to fill in a table of values and then plot the graph. Take care plotting the points and always check the shape of your graph. If it is a quadratic, is it symmetrical?

It is always worthwhile double/triple checking your work here to ensure accuracy.

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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 48 - Midpoints, Parallel lines and Perpendicular lines

Countdown to Exams - Day 48 - Midpoints, Parallel lines and Perpendicular lines

In today's blog, we take a look at Midpoints, Parallel lines and Perpendicular lines. We take a look at finding the midpoint between two coordinate points by taking the average of the x values and an average of the y values. We then take a look at parallel lines (two or more lines that always remain the same distance apart) and establish that parallel lines share the same gradient but will have a different y-intercept.

Finally, we finish off with perpendicular lines (two lines intersect to create a right angle) and establish that the gradients of perpendicular lines are negative reciprocals of each other (their products = -1)

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Countdown to Exams - Day 24 - Scatter graphs

Countdown to Exams - Day 24 - Scatter graphs

The focus for today is Scatter graphs. A scatter graph is used to show if two sets of data are related (correlated). There are three types of correlation to watch out for; Positive, Negative and No correlation. Sometimes you will be asked to plot points on a graph, be sure to plot these points like coordinates and try to do it as accurately as possible.

When asked to extract and estimate information from the scatter graph you will normally be marked on constructing a line of best fit so don't forget to do this.

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Countdown to Exams - Day 22 - Quartiles and box plots

Countdown to Exams - Day 22 - Quartiles and box plots

For day 22 we extend beyond plotting cumulative frequency graphs and look at Quartiles and box plots. Once the graph has been created, we tend to examine it in more detail by looking at the quartiles which are situated at 25%, 50% (the Median) and 75%. An important area we analyse is the Inter Quartile Range (IQR), this tells about the spread of data of the middle 50% of the data.

A box plot is extracted from a cumulative frequency diagram and is made up of five key elements; Highest and lowest value, Upper and lower quartile (75% and 25%) and the median. These become useful when we want to compare tow or more sets of data.

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Countdown to Exams - Day 21 - Cumulative frequency tables and graphs

Countdown to Exams - Day 21 - Cumulative frequency tables and graphs

On day 21 we move on and have a look at Cumulative frequency tables and graphs. This is essentially a running total where we add up the frequencies as we go along. It is important to check to see if your final value of the cumulative frequency matches the total frequency (normally given in the question).

When constructing a cumulative frequency graph, it is important to plot each point at the end of each group and join the points up with a nice smooth curve ('s' shaped). The graph is used to estimate numbers above and below certain values.

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Countdown to Exams - Day 20 - Representing Data

Countdown to Exams - Day 20 - Representing Data

The focus for today's snapshot is Representing data. Once data has been collected, diagrams are used to represent the data so that it is easier to extract the key points from the data without having to look at all the numbers etc. The most common diagrams that are used are Pie charts, Bar charts, Line graphs and Pictograms. It is important that you follow the rules regarding the construction of the diagrams.

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