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Alcumus is our online adaptive learning system, and it is the main source of practice you'll have in your course. We include Alcumus assignments in all of our introductory-level subject courses – Prealgebra 1, Prealgebra 2, Introduction to Algebra A, Introduction to Counting, Introduction to Number Theory, Introduction to Algebra B, and Introduction to Geometry.

Your Alcumus problems are tailored to you! Alcumus monitors your progress and carefully selects problems, just for you, based on your performance on earlier problems. It will check your answer, provide you with solutions, and pick more problems.

There isn't a fixed number of problems to complete within a topic, and you'll likely see different problems than most of your classmates. Alcumus chooses your problems based on your level in that topic. You'll be able to more quickly pass topics you understand well, and you'll spend more time on topics you need more practice with.

You should work through Alcumus for as short or as long a time as needed to gain an understanding of the topic. Alcumus will tell you when you've passed a topic. After passing all of the week's assigned Alcumus topics, you should then move on to the week's Challenge Problems on the Homework tab of the course homepage.

Alcumus can be used by all AoPS users. This means that you'll still have access to it after your course ends, and all of the progress you made during the course will be saved! You can always access Alcumus from this page.

How To Use Alcumus

Each week, a list of 1-3 Alcumus topics will be listed on your Homework tab. Your goal is to "pass" those topics by answering questions in Alcumus. The Alcumus bar for the topic that you are working in will turn green when it's decided that you've demonstrated enough of an understanding of the topic to "pass." It will turn blue if you go above and beyond passing to achieve "mastery" of a topic.

Alcumus is on the Course Homepage

If your class has Alcumus assignments, there will be a Tab for Alcumus on the Course Homepage. You can work on your Alcumus assignments in the Alcumus tab there.

You can also solve problems on the Alcumus page, if you prefer. When using the Alcumus page, be sure to choose the Alcumus subject associated with your class and the topics within that are assigned for the week.

Read The Solutions

You have up to two tries at each Alcumus problem. After solving correctly, giving up, or two incorrect answers, you'll be shown the correct answer and a solution. Whether or not you've answered a problem correctly, be sure to read the solutions! For questions you didn't answer correctly, read about how you could have solved the problem. For questions that you did answer correctly, read over the solution to ensure that they understand it —you might learn something, such as a new method to solve the problem. Also, the solutions provided are great examples of well-written solutions, which you can refer to when writing up your own solutions for Writing Problems.

Even More Help

If you still need help after reading this page, you can visit the Alcumus Help Page. If you have any technical questions, you can find support on the Alcumus Forum.

A Little More About How Alcumus Works

Alcumus has seven subjects: Prealgebra, Algebra, Counting & Probability, Number Theory, Geometry, Intermediate Algebra, and Precalculus. The problems in these subjects are independent, except a small number of problems are shared between Prealgebra and other subjects and between Algebra and Intermediate Algebra.

Alcumus is a complicated system. The main idea is that it considers the difficulty level of the problems it has given you and how you've answered those problems. Alcumus will primarily give you problems it thinks are just the right level for you, while mixing in some problems that are a little easier and a little harder. It then uses all of this information to determine about how well you understand the material in each topic. This level of understanding is reflected in your "rating" within the topic.

Review Problems

Alcumus will also occasionally throw in some Review Problems from topics you've already passed. Topics in mathematics typically build off of things you've studied in the past, so Alcumus wants to make sure you're holding on to all of that mathematical knowledge! You won't be able to skip these problems. Answering a review problem incorrectly could cause you to "un-pass" a topic you previously passed. If that happens, be sure to revisit that topic when you have a little time, to refresh your memory.

Hard Problems

It's OK if you find some of the problems in an Alcumus topic to be too hard. There's a Give Up button in Alcumus for a reason! If you've given a problem your very best effort, it can sometimes be a better choice to give up on the problem and carefully read over the solution than to spend hours agonizing over it. Occasionally giving up or answering a problem incorrectly will not prevent you from passing the topic. However, make sure you aren't skipping over all the hard problems.

XP, Levels, Quests, and Achievements

Alcumus also tracks a lot of other data for you. You'll find several types of "XP" (Experience Points) that you can earn in Alcumus, as well as a number of entertaining Quests and Achievements. These have no impact on progressing through Alcumus, but they sure can be fun! Learn more about these extra features on the Alcumus Help Page.

If You're Having Trouble Passing A Topic

First of all, remember that your Alcumus rating in a topic is what Alcumus believes about your ability to solve problems in that topic. When you solve a problem correctly, your rating will go up. When you solve a problem incorrectly, your rating will go down. Once you've tried enough problems, you should expect your rating to be an honest measure of your ability to solve problems in that topic.

Your Alcumus ratings may fluctuate a lot when you start a new topic because Alcumus only has a little data from you. The more Alcumus learns about you in a topic, the less your rating in that topic will fluctuate.

If your rating stops moving and you haven't passed the topic, that means that you need to try something different! Look over the suggestions below. You can also check out our When You Get Stuck guide and the Alcumus Help page for more tips.

  • Read the solutions. The problems are organized into topics for a reason. You should always be reading the solutions to problems to see if your ideas match up with ours, but you should especially be reading the solutions to problems you miss! There's likely to be something in the solution that is going to generalize to the next problem or the problem after that.
  • Go back to the book. If you keep trying at a topic for a while but haven't been able to pass, then it's probably time to take a break. The solution to every Alcumus problem also lists related textbook sections. Go back to those textbook sections and see what it is that you might be missing.
  • Don't skip all the hard problems. It will be nearly impossible to pass a topic if you are skipping a lot of problems, especially a lot of hard problems. When you encounter a tough problem, stop and try to figure it out. Even if you don't answer correctly or choose to ultimately give up, be sure to read the solution! Try to understand the important steps of the given solution —was there a step you missed? Should you go back to the textbook or ask a question on the message board to clarify something about the topic?
  • Check your difficulty level. You can find this on the Alcumus settings page. If your difficulty rating is set to "hard" or "insanely hard," consider dialing it back one step while you're working through this topic.
  • Ask questions. You can always ask your classmates and instructors on the class Message Board when you get stuck.
  • Revisit solved problems. You can look over Alcumus problems you have answered on your Alcumus Report page. Click the time-and-date stamp above any problem statement to look over the answers you gave and view the official solution.

Formatting Tips

Entering answers that aren't numbers can sometimes be tricky. Computers aren't always as good as people are at reading answers written in a format they do not expect. Sometimes, the problem statement will include instructions for how to enter your answer. ("Enter all possible values of x, separated by commas.") Sometimes, you'll be given a link to formatting tips on how to enter a particular answer. Most of those tips come from the list given below. The formatting tip you're given for a problem may or may not be relevant to the answer that you're trying to enter—we don't want to spoil that your answer should be a fraction or square root!

Here are some general tips for answering short-answer Challenge Problems:

  • Do not include units of measurement or dollar signs in your answers.
  • Express probabilities, decimal values, and ratios as simplified common fractions unless told otherwise.
  • Enter variable values without including the variable and an equals sign. For example, enter
    and not
  • Enter fractions with x as the numerator and y as the denominator either as
    or with the LaTeX code
    . For example, enter the fraction "three fourths" as
  • Enter mixed numbers only when the problem says so. Mixed numbers with z as the whole number, x as the numerator, and y as the denominator should be entered as
    z x/y
    . For example, enter "one and two thirds" as
    1 2/3
  • Enter "the square root of x" as
  • Enter powers with x as the base and y as the exponent as
    . For example, enter "n to the 7th power" as
    Make sure to include any necessary grouping symbols. For example,
    is different from
  • Enter coordinate pairs as
    . For example, enter the pair "x=2 and y=8" as
  • Write coefficients of variables and square roots without the multiplication sign. For example, enter
    instead of
    instead of
    . The only exception is when you are asked to entering scientific notation, such as
  • Enter polynomials in decreasing degree order. For example, enter
    instead of
  • Enter expressions in alphabetical order when using multiple variables. For example, enter
    instead of
  • Enter the pi symbol as
    . Do not copy-paste the symbol from another program—the computer won't be able to read it!
  • For problems dealing with interval notation, carefully follow the instructions given by the problem.
  • Only round if the problem asks you to round, and only do so at the end of the calculation process.