Math Basics: Numbers and Algebra

Numbers

• Natural Numbers: 1, 2, 3, ... (positive integers)
• Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (all whole numbers and their negatives)
• Rational Numbers: fractions, e.g., 3/4, 22/7 (can be expressed as a finite decimal)
• Irrational Numbers: cannot be expressed as a finite decimal, e.g., π, e
• Real Numbers: all rational and irrational numbers

Algebra

• Variables: letters or symbols representing unknown values
• Constants: numbers, e.g., 2, 5, 10
• Expressions: combinations of variables, constants, and mathematical operations
• Equations: statements asserting the equality of two expressions, e.g., 2x + 3 = 5

Geometry

• Points: locations in space, represented by coordinates (x, y)
• Lines: sets of points extending infinitely in two directions
• Rays: lines extending from a single point (endpoint) to infinity
• Angles: formed by two rays sharing a common endpoint (vertex)

Trigonometry

• Triangles: three-sided shapes with three vertices and three sides
• Angles in Triangles:
  • Acute: less than 90°
  • Right: exactly 90°
  • Obtuse: greater than 90°
  • Straight: exactly 180°
• Trigonometric Ratios:
  • Sine (sin): opposite side / hypotenuse
  • Cosine (cos): adjacent side / hypotenuse
  • Tangent (tan): opposite side / adjacent side

Numbers

• Natural Numbers are positive integers, starting from 1.
• Whole Numbers are non-negative integers, including 0.
• Integers include all whole numbers and their negatives.
• Rational Numbers are fractions that can be expressed as a finite decimal.
• Irrational Numbers cannot be expressed as a finite decimal, such as π and e.
• Real Numbers encompass all rational and irrational numbers.

Algebra

• Variables are letters or symbols representing unknown values.
• Constants are numbers, such as 2, 5, or 10.
• Expressions are combinations of variables, constants, and mathematical operations.
• Equations are statements asserting the equality of two expressions, such as 2x + 3 = 5.

Geometry

• Points are locations in space, represented by coordinates (x, y).
• Lines are sets of points extending infinitely in two directions.
• Rays are lines extending from a single point (endpoint) to infinity.
• Angles are formed by two rays sharing a common endpoint (vertex).

Trigonometry

• Triangles are three-sided shapes with three vertices and three sides.
• Angles in Triangles can be:
  • Acute: less than 90°
  • Right: exactly 90°
  • Obtuse: greater than 90°
  • Straight: exactly 180°
• Trigonometric Ratios are:
  • Sine (sin): opposite side / hypotenuse
  • Cosine (cos): adjacent side / hypotenuse
  • Tangent (tan): opposite side / adjacent side