Nominalization: は vs. が
The sentence "She takes notes quickly" is translated
かのしょは ノートをとるのが はやいです。
I was surprised that はやい demands が (yes, I know that 好き and きらい do too but たのしい for example does not).
So (cue Whitney Houston): how will I know? (And no, "trust your feelings" would not be a useful answer here.)
P.S. I'm asking you coz you know about these things.
There are some typos in your sentence:
or with pure hiragana:
かのじょは ノートを とるのが はやいです。
Other than that I am not sure, if I understand your question correctly: What do you mean by は vs. が? Because there is already the topic かのじょ, there cannot be a second は (exception would be for example a sentence which contains a quote).
ManuelNARAU is correct, if you want to say "She is fast at taking notes." You would say "かのじょは ノートを とるのが はやいです。"
The particle が in this case is modifying the topic. When you see this sentence pattern "(verb)のが(adjective)です。" One is saying "The action of (verb) is (adjective.)" "の" is used as a modifier to go with verbs that are in the casual/dictionary form of the verb. And "が" is used to modify the verb, giving it the rules that would apply to a noun.
１）にほんご が すき です。 「日本語が好きです。」 "(I) like the Japanese language."
２）にほんご を べんきょう する のが たのしい です。 「日本語を勉強するのが楽しいです。」 "Studying the Japanese language is fun."
The particle が can also be used as a way to emphasis that "she" is fast at taking down notes, as opposed to talking about others.
For example, if this female is in a room filled with other people taking notes, she is the one that is faster at writing them down, compared to the others taking notes in the room or as the topic of conversation.
Another example of this, that I have seen in Japanese textbooks for English speakers, is:
Q: だれは がくせい ですか？ 「誰は学生ですか？」 "Who (among you) is a college student?"
A: わたしが がくせい です。 「私が学生です。」 "I am a college student (among all of us.)"
Sorry for the long post, but I hope that this can help you and others.
Hi Kimiko, Thank you for all the examples! I remember that there are quite a lot of example sentences in the Duolingo app where the particle after the nominalization is not が but は - I don't have an exact quote ready but it might be something like
So that's why I was confused by the "She takes notes quickly" sentence, and the fact that there they used が instead.
"giving it the rules that would apply to a noun" is a helpful way to think about this - I'm pretty sure I have also come across one or two sentences where the nominalization ended in のを because the phrase was treated like an object.