Starter for AS level class before moving on to transformations of graphs. Sketch a quadratic and mark its turning points. Extension: are all quadratics a translation of y = x²? It made a nice discussion which led us nicely into why f(x *+* 3) is a translation by (3 0), to the *left*.

#mathstoday

What is a good student? Does it mean you know everything exactly when you're supposed to know it because that's when everyone else knows it?
Or
Is it being open to learning new things?? Join "lucky 10,000 club", learned a new thing today, it's your time to shine!!
@themathguru.bsky.social #ATMNE25

I love breaking the unspoken rule about fraction diagrams (all pieces congruent, not just equal in area). Here are a few of my favourite non-standard representations. A one radian sector fills half the unit square, the curves y = x² and y = √x enclose 1/3 of the square. Can you come up with more?

Thank you!

I wonder if there's a construction-type argument that leads to their solution. I often find with these types of problems that trying to draw them leads to an algebraic argument.

Nothing wrong with a sledgehammer approach! The sol. using compound angle formulae came to me by considering the small square as fixed, and a lazer shooting to a point U, which then determines the size of the larger square. Rotating up 45 deg, I now need need to touch the top of my new square...

Spending time 'guessing' the solutions to simultaneous equations so that students learn what finding the solution means before moving on to more formal methods. It's amazing how complex an equation they manage to 'guess' the answer to without a formal method when left the time to puzzle #mathstoday

I also did it this way. Could you please share their model solutions?

That's really nice. Did you do it purely thinking about substitution or by looking at graphs? It can lead to a rabbit hole of "continuous functions are one-to-one iff strictly monotonic" etc etc which can be fun! And potentially their first sight of what university maths will look like.

Nice little activity with further today, give them a function, eg f(x)=x²+1, {x:x<3}, and they have to say whether it is many to one or one to one, and if it is many to one a reason why (eg in this case f(-2)=f(2)), & if it is one to one to give the inverse function #alevelmaths #mathstoday