'Whatever' means 'whichever thing/job' etc. 'Whichever' would only work if followed by another noun. For example, "Then you can be refreshed enough to start WHICHEVER JOB is next on your to-do list." Alternatively, you could say 'whichever task' or 'whichever chore', or another noun with a similar meaning. 'Whichever' doesn't work on its own - we need to know 'whichever...what?'.

Unfortunately, this is not a good question, because there are multiple reasonable answers. "Whatever" works if the to-do list is unknown to the speaker. "Whichever" works if the to-do list is known to the speaker. For an exam, "whatever" is the expected answer. WHICH X and WHAT X (which and what are determiners) Which X usually refers to one X of a small, well-known set (such as items on a menu). ex: "Which day will you go to the movies? " (Which day of the well-known set of Monday, Tuesday, ... ?) What X usually refers to one X of a large set or not well-known set. ex: "What type of movies do you like most?" (Which type of the many types of movies do you like most? WHICHEVER and WHATEVER (whichever and whatever are pronouns) Whichever and whatever can mean "any X, it doesn't matter." Because of this, the question is a poor question because both are reasonable choices. By extension to which and what, whichever can mean "any X from the well-known set" and whatever can mean "any X from the not well-known set." "Would you like to go to the beach or to the movies?" "I don't care. You choose whichever you prefer." "What would you like to do today?" "I don't care. You choose whatever you prefer." More information: The Oxford Learner's Dictionaries are an excellent resource. whichever determiner pronoun https://www.oxfordlearnersdictionaries.com/definition/english/whichever?q=whichever Pensions should be increased annually in line with earnings or prices, whichever is the higher.