You get XP for playing in Single Player mode.
For the first batch of questions (the first 4 questions before your first Wildcard), you get 10 XP for each question. That number increases by 1 for every batch (between wildcards), maxing out at 30 XP for each question. The XP for wildcards follows the same formula, but is always multiplied by 2.
Question 1 - 4: 10 XP each
Question 5: 20 XP
Question 6 - 9: 11 XP each
Question 10: 22 XP
Question 11-14: 12 XP each
Question 15: 24 XP
Etc., until the cap at 30 XP for regular questions and 60 XP for Wildcards.