A thing I have noticed with the A Level textbooks (I use the Edexcel books published by Pearson) is that there are very few derivations of results, with them preferring to just present a formula for the student to use.

I don’t understand why this is the case… I get that there is a lot of content to be covered in a relatively short time (maybe this will improve with going back to terminal exams) but aren’t students missing out on some really important concepts by not including derivations.

I’m sure many teachers do show derivations, but why are they not in the text books we expect students to use to help their studying?

I recently asked my Year 12 FP1 students to derive an expression for the inverse of a general \( 2 \times 2 \) matrix, in terms of the entries of the matrix that you are trying to invert. Of course, a straight forward way to do this is to use the definition of the matrix inverse to derive 4 equations with 4 unknowns which can be solved in two pairs to obtain the entires of the inverse matrix in terms of the original matrix.

I was surprised to find that no one managed to do it. Perhaps the amount of letters floating around put them off, but I think this kind of exercise is important for building confidence and developing fluency with methods used in other modules.

I typed up a solution for them, if it is of interest to anyone it is available on my website here. Of course there are likely to be typos…..

I’d be interested to hear other peoples views / experiences of derivations with A Level maths.

*Related*

Nice post. I agree, those textbooks are rubbish. The best a level ones are the Collins ones, but even they are majorly lacking. I’m hoping that the new a level, with its increased rigour, will lead to better source material.

I still think the Bostock and Chandler ones are really good. Im not sure if you can still get them, but my A Level teacher recommended them when i was studying. I think thry are from the previous time the exams were terminal. The current Pearson ones are even worse than the Edexcel ones i used.