## Polynomial March

This is far too late but I figure the questions can be used any month really….

Download March’s question-a-day sheet, focussed on polynomials, including quadratic functions, factor theorem and the binomial theorem with positive integer powers.

The file is available here.

## Substitution April

My students seem to like these, so the plan is to do one for each month of the year. The idea will be that Year 12c start with one in June and then do one a month up till their exams in Year 13. I have January, February and March to share (sorry I should have done this at the time) but for now here is April’s calendar. It is designed around the method of Integration by Substitution so for each day there is an integral to do.

Answers will be uploaded in a few days when I have scanned them in.

UPDATE: solutions now available here.

UPDATE: A correction to my solution for Question 23 from Susan Whitehouse (@WhiteHughes

## Year 13 Exam Question a Day – updated to April

Those of you who have downloaded my Year 13 daily exam question resource that I posted a couple of weeks ago may be pleased to know that it has now been updated to include a question from the SAMS for every day in April.

April covers the topics below:

## Year 13 Revision Plans

I normally don’t structure my student’s revision much, however this year some of my students asked if I could provide them with guidance on what topics to revise in a given week.

Because of this I have written a revision plan, an excerpt of which is shown below.

I have also done one for Further Maths. As this is more bespoke and tied to our options (Statistics and Mechanics) for AQA I haven’t uploaded it – if anyone would like it as well please get in touch.

## Damped SHM

A very quick post early this morning to share a card sort I made for damped simple harmonic motion as a fellow twitter user has requested it.

I made this about a month ago, but like everything I need to get better at sharing things in a timely fashion…

I enjoyed teaching the damped simple harmonic motion content as it is much more realistic than the idealised SHM equations. It also provided good practice of modelling, solving ODEs, using ICs, sketching graphs and interpreting graphs / solutions in context.

Each set should contain an equation, a solution, a solution plot and some conditions.

## Year 13 Exam Question-a-Day

This is going to be the first of a few posts this week, finally sharing things that I should have shared since the beginning of the year. Many of them are things that I think will be helpful for A-Level revision.

The first is the Exam Question A Day booklet I have put together for my Year 13 classes. I am really pushing the “do a bit of maths every day” mantra this year, and for some it seems to be having a positive impact 🙂

Every question in this is taken from the SAMs for AS or  A-Level Mathematics and so don’t use any of the questions contained in the practice paper sets that are kept secure by each of the exam boards, so secure mocks aren’t affected etc. I have used questions from each of the 4 boards – AQA, Edexcel, OCR, OCR (MEI) – as maths is just maths after all.

At the moment the file contains questions for February and March. The questions for April will be added by the end of this month – keep an eye out for the post about this.

The topics covered in the February and March questions are shown below:

## 12 Days of Christmas: Day 12 – Perils of Real Life Situations

As this is an extremely late post for the last of the “12 Days of Christmas” series it is very brief.

I received this card just after New Year from my aunt:

I’ve seen this before but I still find it fairly funny and it is a useful reminder of the problems with trying to shoehorn a physical / applied situation onto a maths problem!

## 12 Days of Christmas: Day 11 – Further Maths Polynomials Cardsort

Over the last couple of years I have particularly enjoyed teaching and writing interesting questions that concern Vieta’s Formulae. These relate the sums of products of roots of polynomials to the coefficients of the polynomial.

I have always liked these, and have a very vivid memory of a Russian lecturer in one of my first undergraduate lectures expressing surprise that we weren’t formally taught them as part of the normal A-Level in Maths. He confidently told us that in Russia they are done in primary school!

Last year I created a card sort for this topic which turned out to be trickier than I anticipated. It has taken two different classes now a whole lesson to complete but it has generate some fantastic mathematical discussions.

If you download the file to use in the classroom from here I would love to know what you think.

## 12 Days of Christmas: Day 10 – Thirdsday

Sometimes being late with posting has it’s advantages!

Thursday 3rd January was deemed a day to celebrate the number 1/3. It was named Thirdsday by James Propp (@JimPropp) who has written a fascinating and very detailed post about why he thinks 1/3 deserves more recognition and some interesting facts about 1/3 here.

Since this post lots of cool things have been written on the theme of Thirdsday and Matt Parker (@standupmaths) has produced an excellent video:

Unfortunately being late to posting also has its drawbacks. I was going to talk about the classic geometric series

$$\frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \frac{1}{256} +\cdots$$

which converges to a third. However the excellent Zoe Griffiths st Think Maths has already published a lovely classroom activity involving this.

Over at The Aperiodical they have rounded up some nice Thirdsday related posts.

I’ve put a reminder in my phone to spend some time preparing a more interesting post in time for the next Thirdsday – 3/1/30 Keep an eye out for that…

## 12 Days of Christmas: Day 9 – Peppa Pig Maths

Watching an episode of Peppa Pig this morning (Season 3, Episode 11) I was quite excited to see the quadratic formula on a board at Daddy Pig’s work.

I found it interesting that they wrote it with the $$\bigtriangleup$$ notation. I always introduce this notation for the discriminant but have never actually used it in the quadratic formula.