Is the phrasal verb buck up used only in British English?
I’ve never heard an American use the word buck up to mean cheer up; I suspect the phrasal verb is only used in British English.
Learn English – Is the phrasal verb “buck up” used only in British English, not in American English
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When I learned this “rule” (in first grade, I believe), it was explained that and separates the whole part from the fractional part: 2⅔=two and two thirds. The word and would only represent the decimal point in decimal numbers when they are read out in the formal “fractional” reading of decimals, as 2.3=two and three tenths, or 1.75=one and seventy-five one-hundredths. That is, according to this rule, *one hundred and fifty is ungrammatical because, if it is supposed to mean 150, it should be one hundred fifty, and if it is supposed to be mean 100.50, it should be one hundred and fifty one-hundredths. The rationale behind the rule is that you should only have one and in a phrase, so if the number were 403⅞, you wouldn’t say four hundred and three and seven eighths.
Of course, most of the time the decimal point is read as point: 2.3=two point three; 1.75=one point seven five or one point seventy-five; 100.50=one hundred point five zero, one hundred point five oh, or one hundred point fifty. The fractional reading of decimal numbers also starts to become a bit ridiculous if there are more than three digits after the decimal point: nobody would say 3.14159265=three and fourteen million one hundred fifty-nine thousand two hundred sixty-five one hundred millionths.
As you have undoubtedly observed, many Americans don’t follow the rule about and only being used to separate whole and fractional parts, and insert and just before the units of a number less than one hundred, although the forms without and are quite common too.
457 four hundred fifty-seven or four hundred and fifty-seven
2001 two thousand one or two thousand and one
1,000,001 one million one or one million and one
As noted in the comments, phrasal verb is a slippery term that has been variously defined. Indeed, the Cambridge Grammar of the English Language states (p274): We do not use the term 'phrasal verb' in this grammar.
However, if we follow the definition given in the foreword of the Collins Cobuild Dictionary of Phrasal Verbs, then phrasal verbs are "combinations of verbs with adverbial or prepositional particles".
So the answer to your question: "When is a phrasal verb not followed by a preposition?" is "When it is followed by an adverb(ial)." For example: to steal away, to cut back.
Other phrasal verbs have particles which can in other contexts function either as an adverb or as a preposition: to put down, to get across, to come about.
The last group contains particles that can only function elsewhere as prepositions: to make do with, to get at, to make of.
The question in your title is a complex one. The textbook that you refer to should be able to help you answer it.
Best Answer
Answer: nope!
Your impression appears to be an instance of the locality illusion, in which if you yourself don’t use something you overly generalize personal disuse to a much broader community via negative confirmation bias. It’s a form of cognitive bias that leads you to draw the wrong conclusion.
In Corpora
For while BNC, the British National Corpus, shows 18 hits, such as:
But COCA, the Corpus of Contemporary American English shows 135 hits, including many from the last few years:
In the OED
It appears to be common enough. The OED lists ten completely different entries for the verb to buck, ten different headwords. This one, the buck up version, is marked dial. or colloq. and dates from 1854. It has two primary senses, the first as a synonym for dress up with only a pair of citations from the 19th century, and the second with two subsenses, each with many citations, quite a few from the 20th century:
As for popularity, it’s in their “Frequency Band 4”:
One of the earlier citations is from Barrere and Leland Dictionary of slang, jargon and cant published in Edinburgh in 1889 and 1890 (2 volumes), and an even earlier gloss for it is given in the 1875 Lancashire Glossary.
In Google ngrams
Here’s a Google ngram comparing US usage with UK usage:
There might be a bit more relatively frequency in Britain during the 1980s than in America, but for the most part, the two corpora show the same relative frequency throughout their active life.
Conclusion
So the term may well originate in the 19th century from one or another dialect from the North of England or from Scotland, but the 20th-century citations given are not particularly regional, and the abundance of recent examples in COCA shows that this sense of to buck up is alive and well in contemporary American English.
You just haven’t personally heard or read it used — like I said, that’s probably just the locality illusion fuelling negative confirmation bias.