By now, you've seen pretty much all the sharps and flats by their alternative names. Of course, that also means you've played all twelve notes of the chromatic set. Here's a rising chromatic scale and then a falling one . . .
The conventions regarding the notation of chromatic scales are quite involved. For now, you'll find that using sharps in rising passages and flats in falling passages helps avoid unnecessary accidentals. The crucial thing is to be able to recognise and play the chromatic scale over the range of your instrument so practice the above, extending into lower and higher octaves wherever you can.
The ragtime tune below includes a chromatic run but also some rhythms that will be worth preparing.
Count, clap & loop these rhythms before you attempt the tune.
There are some familiar patterns but also some ties in unfamiliar places.
Aim for 120bpm
Check those? Four bars of each rhythm . . .
. . . by Irene Giblin.
Aim for 144bpm
Follow the 'adjacent fingers for adjacent notes' rule but, in bars 1, 2. 9 & 10, this will obviously apply chromatically.