It's true that your score rises with the number of words you know, but the method you memorize them with makes a huge difference to the result, even for the same amount of study time.
There's no exact official figure published. Numbers like 'X words gets you level Y' are weakly grounded, so don't set them as a goal.
A more reliable gauge is past papers. Marking the words you don't know on a past exam paper immediately shows you what you're missing.
Different sections need different vocabulary. Reading Q42–50 needs abstract vocabulary from fiction and opinion pieces; Listening Q45–50 needs academic vocabulary from lectures and discussions. If Level 3 is your goal, you can lower the priority on vocabulary in these ranges.
Just reading only creates a 'feeling like you know it' — you still can't actually pull the word out and use it. You need retrieval practice: cover the meaning and try to recall it yourself.
Spacing out your reviews sticks better than cramming them all together. This is a result confirmed across many experiments.
Don't memorize words in isolation — memorize whole phrases. If you only memorize '지원하다' (to support/apply), you won't know what particle goes with it. Storing it whole, like '장학금을 지원하다 (to fund a scholarship) / 회사에 지원하다 (to apply to a company),' means it comes out ready-made in writing too.
This site's study-method card, 'Why doesn't re-reading a word list help you memorize it?,' covers the evidence and method in more depth.
You don't need to be able to write the Chinese characters. But knowing how Sino-Korean words are built lets you guess words you don't know.
For example, words containing '학(學)' relate to learning — 학교 (school)·학생 (student)·학습 (studying)·유학 (studying abroad)·입학 (entering school). '료(料)' relates to fees — 재료 (material)·수수료 (fee/commission)·무료 (free of charge).
This is a big advantage if you already know Chinese or Japanese. Most of the abstract vocabulary in the later reading passages is Sino-Korean, so having this sense means you get stuck less on unfamiliar words.
Distinguish them by 'what they're used with,' not by meaning. Dictionary definitions can look similar even when the words actually pair with different things.
'고치다' is used for objects and habits, '수리하다' for machines and facilities, '치료하다' for illnesses. They all roughly mean 'to fix,' but what they pair with is different.
Reading Q3–4 (finding the expression closest in meaning to the underlined word) tests exactly this. Learning words as paired expressions rather than in isolation makes this question type easier.
Idiomatic expressions show up in Reading Q21–22. But if Level 3 is your goal, they're not a high priority.
Idioms give the wrong answer if you translate them literally. '발이 넓다' (lit. 'has wide feet') means knowing a lot of people, and '손이 크다' (lit. 'has big hands') means being generous with spending.
Narrow it down to the ones that come up often on the exam. Idioms built around body parts (eyes, hands, feet, ears, mouth) come up especially often.