Swiss Travel Pass discounts

Without a Swiss Travel Pass, it appears that a single adult would pay 50 CHF to go from Zurich to Bern in August, 262 CHF to go from Bern to Gornergrat and return, 261 CHF from Bern to Jungfraujoch and return, and 50 CHF from Bern to Geneva (all 2nd class). A Swiss Travel Pass for 8 days (2nd class) costs 363 CHF, a considerable saving. However, it seems that the trips to Gornergrat and Jungfraujoch may not be free with the pass (only 25% seems to be the discount for Jungfraujoch, and I'm not sure about Gornergrat). Can you please explain how much extra I would need to pay for these two trips if I have a Pass? And a trip from Bern to Interlaken if I have a pass? Free? What about Bern to Lucerne and then up Mt Pilatus? Are those trips covered free by the Travel Pass?

Thanks Arno

You're welcome! Yes, the trip is basically covered to Geneva. A bit more perhaps, depending on your route as there are a few bus lines from Geneva to the border (see the map), but I would recommend to keep things simple: free to Geneva, and from there, you need a ticket into France.