Maths

I divide school Maths into Lower School, Middle School and Upper School. 

I am interested in Lower School becasue it is generally not limited by KeyStage 3. As I have written in the general text at the head of that section, I spent several years with huge freedom to teach whatever I thought was appropriate to the class in Year 8. Some of the students hated that apparent lack of structure, hated the demands I made of them to think – and some of them loved it, turning that learning to great advantage later in school.

The Middle School is, it seems to me, entirely defined by KeyStage 4. It is therefore by my lights entirely boring and very much better covered in content by other sites. The best I could offer would be revision content aimed at improving specific skills within a GCSE context. I am not interested in this. School experience has taught me that the kids are not interested either. They say they are (Y9 say they will be, Y12 say they would have been) but no-one in or teaching Y10/11 actually does anything much about wider study, since all their teaching is directed at the target of GCSE examinations. Spare capacity is soaked up by other subjects, and those with capacity for significantly mnore work simply collect another subject. Therefore, students looking for challenge in Y10 and Y11 are encouraged to prove to themselves that the Lower School content is indeed as easy as they think and if so, to move on to the Extension Work. For those in Y7-9, there is very little point in chasing the Y11 and Y12 content in advance of sitting the GCSE exams. For those in Y10 and 11, there is similarly very little point in chasing sixth-form content.  I strongly doubt there are many who would have the sense to look at content of any source in the gap between exams and starting Y12, but anyone reading this needs to be aware that there is a large amount of GCSE content simply assumed to be perfect for the purposes of doing A-level content. If you want to make your life simpler, do the boring bit and make your algebra and numeracy reliable.  However, the FPM section "Further Pure @BSB” just might give Y10/11 what they feel they want. A hard course.

The Upper School—AS level, A2 level and Further Maths—is a very large field and I have subdivided that by topic title (Pure, Stats, Mechanics, ignoring other applied topics I do not feel competent to advise upon)  and, in some cases, by the board I was considering / teaching at the time. The applied topics not in the usual A-level syllabus may be found under the Further Matrhs umbrella. I do not claim to be consistent in how I chose to spread this around.


In general, I do not attempt to replace or reproduce the content of a good textbook. I do attempt, in places, an explanation I found worked in the classroom (example, inertia) and on occasion I use what I think of as university level language to present a topic I think should have been already covered slowly in class, or at the other extreme covered only by a student working on their own. I make some effort to point out places where I found classes ‘lost the plot’; while that may have been my fault, I felt at the time that this was more to do with misconceptions. I have also included topics I think belong within school but which for various reasons are no longer included for study at school. Examples of this include the several pages placed in Finance/Science and in Extension Work, dimensional analysis in FM, and exploration of errors consequent on a lack of precision, scattered throughout.

DJS 20171113
 on uploading afresh after switching software packages


Notes:       !! in the page title means there is something missing, like a diagram or a matrix
            x or XX in the title means that the editing is incomplete

Some pages have answers hidden on the page. Some pages have no answers. Some pages have answers to some questions. No pages have answers by me held on paper. People who care to write (email or paper) with worked answers will be publicly applauded (on here). The very few who wish to discuss a question will be met with enthusiasm. I’d welcome discussion as to what was meant by my use of language and improvements to that will probably also end up being applauded on site.

Where I have stolen/copied a question I have said so. Where I have based a question on another Question I have indicated this. All other questions are mine; similairity to questions you find elsewhere is not deceit but synchronicity. Otr perhaps someone has followed my lead….


The move to SandVox from iWeb, particulalry the way Sandvox allows indexes, has reduced the total number of pages. My count for the Maths section is not just over the 100.

© David Scoins 2017