Algebra Basics

Equations and Inequalities:
- Linear equations: ax + by = c, where a, b, and c are constants
- Quadratic equations: ax^2 + bx + c = 0, where a, b, and c are constants
- Systems of linear equations: solving multiple equations simultaneously
Functions:
- Domain and range: input and output values of a function
- Composition of functions: combining two or more functions
- Inverse functions: reversing the input and output values
Graphing:
- Cartesian coordinates: plotting points on a grid
- Graphing linear and quadratic functions

Points, Lines, and Planes:
- Midpoint and distance formulas
- Slope and intercept of a line
- Angle relationships: complementary, supplementary, and corresponding angles
Triangles:
- Angle sum property: sum of interior angles is 180°
- Pythagorean theorem: a^2 + b^2 = c^2 for right triangles
- Congruent and similar triangles
Polygons and Circles:
- Properties of regular polygons: number of sides, interior and exterior angles
- Circumference and area of circles

Divisibility:
- Factors and multiples: prime and composite numbers
- Greatest common divisor (GCD) and least common multiple (LCM)
- Divisibility rules: testing for divisibility by 2, 3, 4, etc.
Prime Numbers:
- Properties of prime numbers: uniqueness, distribution, and testing
- Prime factorization: expressing a number as a product of prime factors
Modular Arithmetic:
- Congruences: equivalence relations modulo n
- Properties of modular arithmetic: addition, multiplication, and inverses

Counting Principles:
- Fundamental counting principle: product rule for counting
- Permutations: arranging objects in a specific order
- Combinations: selecting objects without regard to order
Recurrence Relations:
- Defining and solving recurrence relations
- Applications to counting and probability
Generating Functions:
- Defining and applying generating functions
- Extracting coefficients and solving recurrence relations

Operations:
- Vector addition and scalar multiplication
- Dot product and cross product
Properties:
- Magnitude and direction of vectors
- Unit vectors and normalization
Applications:
- Vector projections and decompositions
- Work and energy: force and displacement vectors

Equations and Inequalities:
- Linear equations have the form ax + by = c, where a, b, and c are constants.
- Quadratic equations have the form ax^2 + bx + c = 0, where a, b, and c are constants.
- Systems of linear equations involve solving multiple equations simultaneously.
Functions:
- Domain and range refer to the input and output values of a function.
- Composition of functions involves combining two or more functions.
- Inverse functions reverse the input and output values.

Points, Lines, and Planes:
- Midpoint formula calculates the midpoint of a line segment.
- Distance formula calculates the distance between two points.
- Slope and intercept of a line can be used to graph it.
- Angle relationships include complementary, supplementary, and corresponding angles.
Triangles:
- Angle sum property states that the sum of interior angles is 180°.
- Pythagorean theorem states that a^2 + b^2 = c^2 for right triangles.
- Congruent triangles have equal sides and angles, while similar triangles have proportional sides.
Polygons and Circles:
- Regular polygons have a fixed number of sides and interior and exterior angles.
- Circumference and area of circles can be calculated using formulas.

Divisibility:
- Factors and multiples are prime or composite numbers.
- Greatest common divisor (GCD) and least common multiple (LCM) can be calculated.
- Divisibility rules test for divisibility by 2, 3, 4, etc.
Prime Numbers:
- Prime numbers have unique properties, such as distribution and testing.
- Prime factorization expresses a number as a product of prime factors.
Modular Arithmetic:
- Congruences are equivalence relations modulo n.
- Modular arithmetic has properties, such as addition, multiplication, and inverses.

Counting Principles:
- Fundamental counting principle uses the product rule for counting.
- Permutations arrange objects in a specific order.
- Combinations select objects without regard to order.
Recurrence Relations:
- Defining and solving recurrence relations is used in counting and probability.
- Applications include counting and probability.
Generating Functions:
- Defining and applying generating functions is used in counting and probability.
- Extracting coefficients and solving recurrence relations is possible.

Operations:
- Vector addition and scalar multiplication are used to combine vectors.
- Dot product and cross product are used to calculate vector quantities.
Properties:
- Magnitude and direction of vectors are important properties.
- Unit vectors and normalization are used to simplify vectors.
Applications:
- Vector projections and decompositions are used in physics and engineering.
- Work and energy involve force and displacement vectors.