In #MathsToday #FurtherMaths we finished mechanics with a look at the bowl questions. I think this one has to be in the conversation if I were asked for the most difficult FM questions I've seen.

I'm brushing up on my forming and solving of first order ordinary differential equations. I'm unsure on these ones from the AQA teaching guidance. Does anyone fancy a go? @susanwhitehouse.bsky.social @ecrmaths.bsky.social @missradders.bsky.social @sheena2907.bsky.social @drbennison.bsky.social

In #MathsToday year 8 took this question entirely seriously!

In #MathsToday we took on this epic from AQA M1 2016. Using an integration approach as per the current spec the students had a lot of success. Noticing that the ratios of i and j parts of the velocities are equal when the choppers are parallel is the key.

I'm doing this question from the AQA maths teaching guidance. I've looked on exampro and it is an old exam question, but they have tacked parts a and b on to the start. However, I think that this means that they have messed up as the amplitude is 0.4m in parts and ab then becomes 2.59m later on.

In #MathsToday a year 11 realised that you could use angle at centre to answer this circle theorems question in one step.

This is what we use

Doing second order differential equations. The textbook uses this question and solution to present the rationale for using y= e^mx(Asin(nx) +bcos(nx)) when the auxiliary equation has complex roots. However, it looks like a fudge as it means tat alpha has to be real and beta imaginary. #MathsToday

In #MathsToday we did this one from the AQA teaching guidance on series expansions and limits. Nice question where several stages unfold as you go.

In #MathsToday I decided to finish the graph sketching lesson by turning the question on its head and having them work out the equation from the sketch. Which is more interesting to me and more motivating to them.

Converting parametrics to Cartesians. Having trawled through the textbooks I think this is the toughest one, the boss question as we are now calling them. #MathsToday

Does this constitute a proof that the product of gradients of perpendiculars is -1?

Here it is:

In #MathsToday we used quadratic sequences and sum of series formulae to find the weight of Nelson's balls.

Here you go. :)

In #MathsToday we did this doozy from the AQA teaching guidance. Made the point that we move from the complicated to the simple but it wasn't easy.

When teaching mechanics questions like this I have typically set up the process by doing multiple questions with just numbers for every value. Then I would drop a question like this which requires them to do the same kind of thing, but then put all the algebra together themselves at the end.