While this may not be the case in the Starter Set you are looking at, in the official rules (the Player's manual), First-class attendees (PHB 114) are given a spell book that contains 6 spells. Then they can prepare a number of spells equal to your level of assistant + Int modifier to cast (in this case, 4) using its two first level spell slots.
Spellcasting / Spellbook
On the first level, you have a spellbook that contains six first-class assistants
spells of your choice.
Spell casting / spell casting and casting
You prepare the list of assistant spells available to you.
to emit. To do so, choose a number of wizard spells from your spellbook
equal to your intelligence modifier + your assistant level (minimum
of a spell).
Without seeing the source he refers to, it seems that the 6 spells listed are his 6 initial spells in his spell book, of which the player must prepare 4 spells each day to have them available to cast. Detect magic, being a ritual spell, can still be prepared and launched as a standard action using one of the two spell slots, or it can be launched as a ritual, in which case it is not necessary to be prepared and it takes an additional 10 minutes to cast.
In summary, as far as I can determine, the character sheet is correct.