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Modeling hours of daylight

Desmos has a nice student activity (on teacher.desmos.com) modeling the number of hours of daylight in Florida versus Alaska – which both produce a nice sine curve when plotted on a graph.  So let’s see if this relationship also holds between Phuket and Manchester.

First we can find the daylight hours from this site, making sure to convert the times given to decimals of hours.

Phuket

Phuket has the following distribution of hours of daylight (taking the reading from the first of each month and setting 1 as January)

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Manchester 

Manchester has much greater variation and is as follows:

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Therefore when we plot them together (Phuket in green and Manchester in blue) we get the following 2 curves:

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We can see that these very closely fit sine curves, indeed we can see that the following regression lines fit the curves very closely:

Manchester:

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Phuket:

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For Manchester I needed to set the value of b (see what happens if you don’t do this!) Because we are working with Sine graphs, the value of d will give the equation of the axis of symmetry of the graph, which will also be the average hours of daylight over the year.  We can see therefore that even though there is a huge variation between the hours of daylight in the 2 places, they both get on average the same amount of daylight across the year (12.3 hours versus 12.1 hours).

Further investigation:

Does the relationship still hold when looking at hours of sunshine rather than daylight?  How many years would we expect our model be accurate for?  It’s possible to investigate the use of sine waves to model a large amount of natural phenomena such as tide heights and musical notes – so it’s also possible to investigate in this direction as well.

IB Revision

If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources:

Screen Shot 2018-03-19 at 4.42.05 PM.pngThe Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and each area then has a number of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

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The Practice Exams section takes you to ready made exams on each topic – again with worked solutions.  This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.

I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think.

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