I think this could save teachers 200+ hours of preparation time in delivering an IB maths course – so it should be well worth exploring! You can see some of examples of the content in the Teacher resources section of this site – which has a lot of worksheets and ideas for IB maths teachers. There’s a really fantastic website been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications. There is a beautifully designed and comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank 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. The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers. These all have worked solutions and allow you to focus on specific topics or start general revision. This also has some excellent challenging questions for those students aiming for 6s and 7s.Įach course has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories. 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. To keep in the spirit of discovery I also just took this diagram as a starting point and tried to prove this myself, (though Einstein’s version turns out to be a bit more elegant)! There are many ways to prove Pythagoras’ theorem – Einstein reputedly used the sketch above to prove this using similar triangles. Step 1: Finding some links between triangles
We can see that our large right angled triangle has sides a,b,c with angles alpha and beta. Hopefully it should also be clear that the two smaller right angled triangles will also have angles alpha and beta. Therefore our triangles will all be similar. Step 2: Drawing a sketch to make things clearer: It should also be clear that the area of the 2 small triangles will be the same as the area of the large triangle. We also can make the following equation by considering that triangles 2 and 3 are similar So, let’s do that first.Īs the area of the 2 small triangles will be the same as the area of the large triangle this gives the following equation: It always helps to clarify the situation with some diagrams.
We can now substitute our previous result for x into this new equation (remember our goal is to have an equation just in terms of a,b,c so we want to eliminate x and y from our equations).
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