@sxpmaths More for Further but:
Factorising out fractions eg taking out a 1/6 if we have 2/3 of something - 1/2 something squared - 5.
Mathematical induction, simplifying calculations (don’t buy the “they have a calculator” we’re aiming to make them better mathematicians not just get A*s)
Thanks Silverstein for spending 1,016 minutes with me in 2022. I couldn’t stop listening to Smile in Your Sleep. #SpotifyWrapped https://t.co/qBtDTzbxaA
@TLMaths Thank you, on behalf of all my own students and my dpt’s students, thank you. The hours you have poured into your videos and cataloguing them on your site has huge impact for the learning, and subsequent outcomes, for so many. Thank you ❤️
@TLMaths The general shape can be explained by the the cosθ contributing “more” to r=a -π/2<θ<=π/2, maxing at θ=1 and detracting from r=a π/2<θ<=3π/2 also worth noting the shape lays over itself every 2π due to period of cosine. for Type 1 eqn’s y(=rsinθ)=0 has 3 roots and dx/dθ has
@TLMaths Also, without negative r you don’t get the loop scenario 🙂 in 1 you’re firing out towards the left but sometimes misfiring and heading back, as the cosine term is negative for π/2<θ<3π/2, and the term’s magnitude is greater than a for part of it
@TLMaths 4 roots. 2 y=0 has 2 roots and dx/dθ has 3 roots. 3 y=0 has has roots and dx/dθ has 4 roots. Perhaps always worth challenging students to sketch the cases from these properties before showing as they then tend to “get” more of what we’re saying when we go through it