Math Basics: Algebra, Geometry, and Number Properties

Algebra

• Study of variables and their relationships, often expressed through the use of symbols, equations, and functions.
• Involves the solution of equations and the manipulation of expressions to solve problems.
• Key concepts:
  • Variables and constants
  • Algebraic expressions and equations
  • Linear equations and inequalities
  • Quadratic equations and formulas
  • Functions and graphing

Geometry

• Branch of mathematics that deals with the study of shapes, sizes, and positions of objects.
• Involves the study of points, lines, angles, and planes, and their relationships.
• Key concepts:
  • Points, lines, and planes
  • Angles and angle properties
  • Properties of congruent and similar figures
  • Perimeter, area, and volume of various shapes
  • Coordinate geometry and trigonometry

Integers

• Whole numbers, either positive, negative, or zero, without a fractional part.
• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
• Key concepts:
  • Adding and subtracting integers
  • Multiplying and dividing integers
  • Order of operations with integers
  • Properties of integer operations (commutative, associative, distributive)

Law of Indices

• A set of rules for manipulating expressions involving indices (exponents).
• Key concepts:
  • Product of powers: a^m × a^n = a^(m+n)
  • Quotient of powers: a^m ÷ a^n = a^(m-n)
  • Power of a power: (a^m)^n = a^(mn)
  • Zero and negative indices

LCM (Least Common Multiple) and HCF (Highest Common Factor)

• LCM: the smallest positive integer that is a multiple of two or more integers.
• HCF: the largest positive integer that divides two or more integers without a remainder.
• Key concepts:
  • Finding LCM and HCF using prime factorization
  • Applications of LCM and HCF in real-world problems
  • Relationship between LCM and HCF: LCM(a, b) × HCF(a, b) = a × b