How do we know that Joseph didn't study all of Taharos before he was sold to Egypt? The Baal Haturim (Gen. 37:3) writes as follows:
According to the Baal Haturim, Yaakov Avinu learned with Joseph 5 orders of Mishnayos, all of which are alluded to with the defective spelling of Zekunim, which is interpreted through means of Rashei Teivos. As the Baal Haturim understands, Yaakov learned with Joseph, Zera'im, Mo'ed, Nashim, Nezikin (which is alluded to in the Notrikon "Yeshu'os", see BT Shabbos 31a) and Kodshim. But what is strange with this Notrikon, is that there's one order that's missing! The order of Taharos, which includes the discussions of Halachic impurity and purity, is not in the list! It is all the more strange, because the Baal Haturim actually stresses the defective spelling of זקנים. If it would have been spelled in full (plene spelling), it would've had an extra vav, which could have been understood as alluding to Ve'da'as (ודעת) which corresponds with Taharos (see BT ibid.)! By citing the Ksiv (the way the word is written) instead of the Kri (the way the word is read), the Baal Haturim actually undermined his Notrikon!
I saw an answer to the above question in a very recently published sefer named Imerei Menachem. It's a peculiar answer, and anachronistic (an understatement). But it has a surprising source.
Trans.: The world asks why Yaakov didn't learn Taharos with Joseph. - In the name of my spouse, may she live, since Joseph was still not married than, and it is not customary to learn all of the order of Taharos with an unmarried person. Meaning: tractate Niddah which is in Seder Taharos is off-bounds for unmarried teens in the Chasidish world, and if you will remember correctly, you will know that Yaakov came from a prominent Chasidishe family. therefore, of course Taharos can't be included in the Notrikon, because Joseph was still not in a position to finish it!