Sorry for the horribly worded title.
Per the PHB: Wizards can prepare a number of spells equal to their Int Modifier + their wizard level.
I have a necromancer who just hit 4th level and used the ability score increase to push her Int to 20 (+4). So she would have 8 spells she could prepare.
However in the spell slots per level chart she has four 1st level slots and three 2nd level slots.
So what could she level could she use that spare slot for?
Thanks!
[First off: if you have an INT of 20, you have a +5 modifier, not a +4. So a 4th level wizard with an INT of 20 can prepare 9 spells, not 8. Now on to the main question.]
You may be thinking in terms of 3.5e style preparation rather than 5e.
In 5e, you don't have to match spells to spell slots when preparing them. A 4th level wizard with INT 20 can prepare 9 spells, and those are the spells you are capable of casting until you choose to prepare new ones after a long rest. You have four 1st level spell slots and three 2nd level spell slots to cast them in, which you can use to cast any of his prepared spells in any combination you want.
With 9 spells prepared and 7 spell slots, you won't actually end up using all the spells you prepare (I'm ignoring Arcane Recovery for the moment). However, you have those spells as options, so you can choose what you need as the situation demands it. If you need three False Lives during the day (two 1st, one 2nd), you can do that. If you never need False Life, you can use those slots for other spells. Its about versatility and options.
Now, as to what level the spells you prepare can be, that is entirely up to you. If you are certain that you will only ever use your 1st level slots for Shield but have no idea what you'll need to use your second level slots for, you can prepare eight 2nd level spells and one 1st level spell (but this is probably not the best idea). Alternatively, you could prepare nine 1st level spells and use the 2nd level slots to "upcast" those spells (such as getting more temporary HP out of False Life or getting more targets for Charm Person). Your only real limitation is that you can't prepare a spell of a level that you cannot cast (so a 4th level necromancer can't prepare a 3rd level spell).
In 5th edition, the list of spells you can prepare and the set of spell slots you get are independent things. You can prepare any 8 spells that you know. You could prepare 8 first level spells. Or 8 second level spells (don't do that).
When you cast a spell, it can be any of those 8, and you choose a spell slot to cast it with. When a spell is prepared, you can cast it as many times as you feel like expending appropriate level spell slots on it - The spell slot must be of the level of the spell or higher. If you cast a spell using a slot higher than its own, you get an increased effect (as detailed in the 'at higher levels' section of the spell description.
