Alcumus

Alcumus is a game that is designed to help students focus on a variety of subjects, prealgebra, algebra, number theory, counting and probability, geometry, and precalculus.

Alcumus is free; however, you must have an AoPS account to play. For instructions on how to get one, visit the page Creating An Account. Users are able to earn achievements for their accounts. They are also able to receive quests, and complete them.

There are six sections on Alcumus, along with many topics. Here they are!

## Topics

### Pre-Algebra

* Arithmetic - Addition
* Arithmetic - Multiplication
* Arithmetic - Negatives
* Arithmetic - Subtraction
* Arithmetic - Reciprocals
* Arithmetic - Division
* Squares
* General Positive Exponents
* Order of Operations
* Negative and Zero Exponents
* Multiples
* Divisibility
* Primes and Composite Basics
* Prime Factorization
* Least Common Multiple
* Divisors
* Greatest Common Divisor
* Fraction Multiplication
* Fraction Division
* Fractions And Exponents
* Simplifying Fractions
* Fraction Addition And Subtraction
* Mixed Numbers
* Expressions
* Basic Linear Equations
* Advanced Linear Equations
* Word Problems
* Inequalities
* Decimal Arithmetic
* Rounding Decimals
* Decimals and Fractions
* Repeating Decimals
* Ratio Basics
* Proportions
* Unit Conversions
* Speed and Other Rates
* Simple Percents
* Combining Percents
* Integer Square Roots
* Non-integer Square Roots
* Angle Basics
* Parallel Lines and Triangles
* Angles In a Polygon
* Length and Perimeter
* Area
* Circles
* The Pythagorean Theorem
* Special Right Triangles
* Quadrilaterals
* Basic Statistics
* Statistics - Reading Tables or Charts
* Counting Lists
* Venn Diagrams
* The Multiplication Principle in Counting
* Permutations
* Casework Counting
* Counting Pairs
* Basic Probability
* All Topics in Prealgebra

### Algebra

* Prerequisites - Arithmetic Review
* Prerequisites - Exponent Laws
* Prerequisites - Square Roots
* Prerequisites - Fractional Exponents
* Evaluating Expressions
* Simplifying One-Variable Expressions
* One-Variable Distribution
* One-Variable Linear Equations
* Word Problems in One Variable
* Linear Equations in Disguise
* Solving Two-Variable Systems
* Two-Variable Word Problems
* Advanced Systems
* Advanced Systems of Equations
* Ratios
* Unit Conversions
* Percents
* Direct Proportion
* Inverse Proportion
* Rate Problems
* Distance in the Plane
* Midpoint of a Segment
* Graphing Lines
* Graphing Multiple Lines
* Solving Linear Inequalities
* Multiplying Binomials
* Factoring Monic Quadratics
* Factoring General Quadratics
* Sum and Products of Roots
* Sum and Products of Roots
* Square of a Binomial
* Difference-of-Squares
* Rationalizing Denominators
* Simon's Favorite Factoring Trick
* Complex Number Arithmetic
* Quadratic Formula/Discriminant
* Completing the Square
* Quadratic Optimization
* Complex Quadratics
* Graphing Quadratics
* Graphing Circles
* Quadratic Inequalities
* Evaluating Functions
* Domain and Range
* Function Composition
* Inverse Functions
* Functional Operations
* Graphing Functions
* Polynomial Basics
* Polynomial Multiplication
* Exponential and Logarithm Basics
* Interest Rates
* Logarithm Basics
* Radical Expressions and Functions
* Absolute Value
* Floor and Ceiling
* Rational Expressions of Polynomials
* Piecewise-Defined Functions
* Arithmetic Sequences
* Arithmetic Series
* Geometric Sequences
* Geometric Series
* Clever Algebraic Manipulations
* All Topics in Algebra

### Number Theory

* Multiples

* Divisors
* Primes and Composites Basics
* Remainders
* Prime Factorization
* Least Common Multiple
* Greatest Common Divisor
	+ This is sometimes known as Greatest Common Factor as well.
* The Euclidean Algorithm
* LCM/GCD Problem Solving
* Counting Divisors
* Divisor Arithmetic
* Converting from Base 10
* Converting to Base 10
* Base Number Problem-Solving
* Base Number Arithmetic
* The Last Digit (Base 10)
* Terminating Decimals
* Repeating Decimals
* Congruence and Residues
* Modular Arithmetic Sums
* Modular Arithmetic
* Patterns in Modular Arithmetic
* Divisibility Rules
* Divisibility Problem-Solving
* Modular Arithmetic Inverses
* Modular Arithmetic Congruences
* Modular Arithmetic Systems
* Perfect Powers
* Digits
* All Topics in Number Theory

### Counting & Probability

* Counting Numbers in Lists
* Venn Diagrams
* Counting Independent Events
* Factorials
* Permutations
* Casework Counting
* Complementary Counting
* Constructive Counting
* Counting with Restrictions
* Counting with Systems
* Correcting for Overcounting with Division
* Basic Combinations
* Computing Combinations
* Combinations with Restrictions
* Distinguishability
* Basic Probability as Counting
* Basic Probability with Combinations
* Probability with Casework
* Complementary Probability
* Binomial Probability
* Multiplying Probabilities
* Advanced Probability with Combinations
* Probability - Think About It!
* Using Geometry in Probability
* Expected Value
* Pascal's Triangle
* Binomial Theorem
* All Topics in Counting & Probability