Hmm, I'll have a go but obviously literally lauren will answer better

Sure, a 'hook'-style sentence at the beginning and an interesting intro is a real help, as first impressions on the examiner are important; I've heard that examiners often have an idea of the mark they'll give you by the end of the intro. For text response, I developed a first sentence that I threw into most responses, tailored slightly to flow better into the essay topic - looking back at it now, it was probably too long and excessive, but my teacher liked it and I could normally get it to flow relatively well. Something like 'By replacing agrarian lifestyles with machinery, the 1800s Ind. revolution created rapid population increase in Victorian London, widening the gulf between rich and poor. Witnessing the ____ [something related to the topic, e.g. upper classes' increasing focus on selfish gain], Charles Dickens in his novella
A Christmas Carol portrays the/challenges the... etc.'
So I'd try writing a few of these intro sentences; spend a while with your teacher/tutor perfecting them. Then practise using them, because if you can't get them to flow nicely into the topic without it sounding disjointed or irrelevant, they're worse than useless. You don't want to risk sounding formulaic, or having an intro three times as long as you need. Sometimes it's better to just plough in and directly address the question.
If you get too hung up on a great first line, you'll never get started! And the rest of the essay is so much more important.
Remember, an intro is just a fragment of the entire thing (especially in language analysis, where it's more a structural requirement where you dump all necessary details and show a big-picture understanding of the author's contention and overall style of arguing). More important is interesting body paragraphs, the actual analysis and discussion, where you leave the beaten track of shallow 'yes', 'yes' and 'no'. So, for text response focus your effort on breaking down prompts and coming up with more insightful, unusual discussion (covering metalanguage, themes, characters and the author's views/values). For language analysis, focus more on analysing why the author does what they do, and how it makes the audience feel/think. For context, avoid Hitler

and head for fancy metaphors, creativity, and unusual external examples. No matter how catching your intro is, it's useless if your body paragraphs are shallow, cliche, summarising, or dead boring.
Note that in Context, I do think that a catchy intro (whether expository, creative or persuasive) is VERY important. I'd definitely focus on that

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