Eliot is probably one of the toughest writers to emulate. He has a distinct style because he possessed a broad understanding of Classical allusion within an arsenal of literary understanding. In his style was also a desire to construct work that was consciously different from Romantic traditions, as well as the need to use his techniques such as stream of consciousness in developing work products that had social meaning. Accordingly, it will be difficult to "write stream of consciousness like Eliot." Stream of consciousness was the vehicle that Eliot used to convey universal truths of being in the modern world. This is what makes Eliot such a difficult writer to replicate.
You might be able to find a starting point in embracing Eliot's style in "The Waste Land." One of the basic points is to understand that nearly everything that Eliot puts on the page has some larger meaning. For example, "April is the cruelest month" is an inversion of the Chaucerian notion of hope and redemption found in the April of his Prologue to The Canterbury Tales. Perhaps, this can open your piece on Algebra. Since most final exams take place in May, April could be the month in which there is incessant cramming of concepts and the most intense of content becomes available. With this stream of consciousness invocation, an opening to your poem can be the following:
April is the most brutal month, breeding equations out of the scratched out paper, mixing laughter and forgetting, filling FOIL and balancing sides.
In this opening, there are a couple of elements that can be reflective of Eliot's style. The first would be the idea of Algebra representing illegitimate and cancerous growth. The equations that grow from the "scratched out paper" helps to bring out the bleakness and sense of despair in Eliot's work. That which grows is not meant to regenerate life, but actually kill it. The view of disliking algebra and Eliot's views are similar. Something bred from barrenness can be reflective of algebra's effect on the individual. I threw in an allusion or reference to Kundera's The Book of Laughter and Forgetting to reflect Eliot's "mixing memory and desire." Kundera's book is something that I see as very hopeless and bleak as a statement of life under Communist rule, an oppressive condition that you might be able to evoke out of how you see Algebra. Any literary allusion that you can use to convey your own belief could work here, as well. Finally, the inclusion of "FOIL" and "factoring" help to echo "filling dull roots with rain." Eliot's use of rain as saturating roots that are dull can mirror how the FOIL method of factoring as well as balancing sides of an equation oversaturate the mind.
In the end, this is only a guide. Being able to take sections of Eliot's work that is rooted in allusion, narrative experimentation, and stream of consciousness and applying the same principles to the deadening world of Algebra might be a path for you to follow. The dislike you hold towards Algebra is similar to how Eliot sees the world as a mass of disillusionment and decay. Being able to tap into this and mirroring its application to Algebra might result in an interesting work sample.
I see that the previous answer gave lots of helpful advice about how to write specifically like Eliot. On the other hand, if you are merely going for a stream of consciousness piece, basically the best advice is just to let your mind loose. Don't worry too much about whether there is a specific structure to your piece. Write down what you are thinking at the moment but do try and relate back to your topic - Algebra 2. By "let your mind loose", I mean that you do not need a strict organizational structure to the essay. Additionally, longer sentences (and dare I say, run-on sentences) give the impression of long, continuous thought that better fits the stream of consciousness writing style. For example, maybe you are discussing how Algebra 2 is very complicated (as one of your reasons for disliking the subject) and then dive headlong into a mid-length narrative about a specific example of when you felt the subject was superbly difficult and then you follow that up with another reason and another example. As you can see from the previous sentence, these long sentences give the sense that you are propelling forward without rest and making your argument while seeming like you are saying whatever comes to mind.