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If I have a 1st level wizard with an Intelligence modifier of +3 (and therefore 6 spells known in my spellbook, plus all the cantrips for my chosen school of magic), exactly how many spells could I prepare to cast if I were a universalist school wizard?

I realize this may seem a simple question but, after a lot of searching on the internet I have found many conflicting responses.

Am I correct, for example, in assuming that I could prepare a total of 3 cantrips and 2 1st level spells per day maximum (plus I'd also get the hand of apprentice ability x6 uses day and my arcane bonded item for 1 free choice of spell cast from spellbook)?

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    \$\begingroup\$ Thank you for clarifying the system! You can also take the tour as an introduction to the site and check the help center for further guidance. Good luck and happy gaming! \$\endgroup\$ – Sdjz May 29 at 18:57
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Your assessment is mostly correct

First, a minor correction to your assumption regarding the spellbook you start with. Note what is said under spellbooks

A wizard begins play with a spellbook containing all 0-level wizard spells (except those from his opposed schools, if any; see Arcane Schools) plus three 1st-level spells of his choice. The wizard also selects a number of additional 1st-level spells equal to his Intelligence modifier to add to the spellbook.

As a universalist wizard, you have no opposed schools so your spellbook would initially contain all cantrips, plus 6 1st-level spells as you noted (3 base + 3 from your intelligence modifier)

Spells prepared per day

For the number of spells you can prepare each day, you should consult the wizard table and note that a 1st level wizard can prepare 3 0-level spells and 1 1st-level spell.

Further, by checking the Ability Modifiers and Bonus Spells table, you can see that an ability score modifier of +3 grants you an extra 1st level spell per day, bringing your total to 3 0-level spells and 2 1st-level spells.

As a final note, your statements regarding the bonded item and hand of the apprentice are also correct.

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A prepared spellcaster such as a wizard can prepare a number of spells per day based on their level, then adds additional spells based on the ability modifier that controls their spellcasting, in this case intelligence. By default a 1st-level wizard gets three cantrips and one 1st-level spell as a baseline. Under the ability score table in the front of the book a score of 16-17 gives one bonus 1st-level spell, one bonus 2nd-level spell and one bonus 3rd-level spell. You are only allowed to use bonus spells of a level that your character can already cast, so you add the additional 1st-level spell, but ignore the 2nd and 3rd until you level up. So you are correct, a 1st-level wizard with an intelligence score of 16 can prepare three cantrips and two first-level spells.

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