Continuing from where Season 1 left, the story continues with a more in depth into the characters but with the same humor narrative as before. 
(Source: Anime News Network)

Continuing where season 1 left off, everyone in Class F is bemoaning the horrible equipment they have. There is a school festival going on though, and if they make enough money they'll be able to buy better school supplies, and as always Akihisa is ready to do anything that might help out Himeji. This is especially important though, because Himeji's father is worried about her placement in Class F and is thinking about transferring her to another school. 
(Source: Anime News Network)

The protagonist is a guy who is among the stupidest of the stupidest in the school. In this school, your grades can, under the supervision of teachers, take a virtual form to do combat! However, if you leave an examination half way, you get zero marks. A bright and cute girl, Mizuki Himeji, was having a high fever during the examination. Despite her potential to be the second highest scorer in the level, she obtained zero marks for having left due to her illness and is thus allocated to the worst class, class F. 
Grades mean almost everything. For Class A, they have a smart-looking teacher, a plasma TV as big as the entire wall as their blackboard, personal laptops, personal air-cons, refrigerators, adjustable seats and all kinds of different appliances. Within the refrigerator, there are all kinds of drinks and snacks. Their ceiling is made of glass, the wall lets them put up high-class drawings and plants. As for Class F, the worst class...They have Japanese desks and seat paddings. Their blackboard is dirty and there is no chalk even! Someone complains that the leggings of his desk is broken, so the teacher asks "Didn't we distribute some glue to stick wood together? Glue it back yourself later." Another complains that wind is blowing in from the broken window. The teacher says "I got it. I will apply for plastic bags and invisible glue to fix it later." There are spider webs everywhere, not a patch of the wall is clean. A unique moldy smell spreads across the entire room, it must be from the old tatamis used to tile the floor. This is the status of class F. 
The protagonist feels displeased at such an arrangement, and seeks help from his friends to try to make a change through summoning war!! And they devise all kinds of plans to try to beat the famous class A, intending to get class A's classroom and equipment if they win!! 
(Source: Baka-Tsuki)

Spin-off of Baka to Test to Shoukanjuu that has been serialized on Famitsu Comic Clear website since 2010. 
These specials are included in the Baka to Test Ni! BD/DVD releases.

A short special included on the second volume of Baka to Test to Shoukanjuu Ni! Blu-ray/DVD release.

The story centers around Akihisa Yoshii, the "baka" of the title. His academy rigidly divides up the student body into classes based on the results of tests. The prodigies are in the A class with reclining seats complete with air conditioning, but Akihisa is in F class, the lowest rung of the school ladder which is furnished only with low, decrepit tables and worn-out straw tatami mats. A girl named Mizuki Himeji is actually one of the smartest girls in Akihisa's sophomore year, but she had a fever on test day and was pigeonholed into the F class. Besides Mizuki (who Akihisa secretly adores), the F class also has Yuuji Sakamoto, the class president who has been Akihisa's friend and partner-in-crime since the freshman year. 
The school happens to have developed experiments to summon fantasy creatures, and Akihisa decides to rally F class to take on the higher-tiered classes and seize their perks. The F class uses the summoned creatures in an all-out battle for school supremacy.

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