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Showing posts from December 25, 2022

### Differentiation: problem solving

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Snell's Law When light refracts from one medium to another, the ratio of sine of the angles is equal to the ratio of refractive index of each corresponding medium. Snell's Law implies that light, when refracting from one medium to another, takes the shortest path. We can show by differentiation that when the light takes the shortest path, it obeys Snell's Law, verifying the 400-year-old law discovered by the Dutch astronomer and mathematician.

### Pascal's Triangle in Python for Computer Science: GCSE, IGCSE and A Level

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Pascal's Triangle with Python The above simulation is produced in Python with aid of three functions. They are as follows: Factorial function A function to generate combinations - nCr A function to produce the Pascal's Triangle You can practise it interactively with the following simulation. Please make sure you keep the number of rows below 10 so that the format of the output stays the way it should. The number of rows is the only parameter that Pascal(n) function needs.

### Straight Line Graph Generator for Maths Teachers: GCSE, IGCSE, GCE O Level, GCE A Level, A Level

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Created with GeoGebra, this applet lets you generate straight line graphs at random, displaying the corresponding equation for each. In addition, you can find a parallel line - and its equation - for each line. Moreover, for each generated line, a random point is created. Then, the perpendicular line that goes through the point in question can be created too. It is ideal for teachers at GCSE, IGCE, GCE O Level, GCE A Level and of course, A Level. The interactive simulation of the above is as follows: you can generate unlimited number of lines for practice for you students: just press the button - Draw Line - to create random lines.