You are pressed for time now. Don't worry about other instruments, even if you can, you won't need this instrument without taking the exam. But it is necessary to know the keyboard. But it takes a long time to practice, and it's definitely too late now. I suggest you know some basic knowledge. Don't spend too much time on it.
Basic music theory and audition are the focus of the exam, so you must find a professional teacher and make up lessons quickly.
Vocal music is also very important, so we must lay a good foundation. If you start studying now, you can't reach a particularly high level at once, so a solid foundation is the magic weapon to pass the exam.
The question of cost has a lot to do with the teacher you invited and the school you took the exam in. Generally, art colleges enroll students after the Spring Festival, but you should get to know the school on the spot in the first half of the semester, which belongs to your examination fee. Also, just don't think that you don't need a good teacher to learn the basics. The foundation determines your future development, and buildings with weak foundations will collapse.
Don't believe the so-called art school, saying that you can go to college to study music without foundation. That kind of school enrollment is just to cheat money, and most countries admit that they need self-study exams and adult college entrance examinations, and there is no requirement for college entrance examination results, so the diplomas they get are naturally worthless.
My understanding of shortcuts in art colleges: after all, the exams in art colleges are artificial, not as fair as the machine-readable cards in the college entrance examination. The training organized by the school is actually a means of charging in disguise. Not participating is largely equal to not having a chance. Therefore, if the economy permits, we should give due consideration to such activities. For the professional exam, the examiner said that he passed. Many people will go to the examiner for tutoring. If time is tight, you can consider it. However, the prices are very high, ranging from 300- 1800 before the exam. You should seriously consider it yourself.
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I hope my answer is helpful to you.