Math Fundamentals

Numbers and Operations

• Number Systems:
  • Natural numbers (1, 2, 3, ...)
  • Whole numbers (0, 1, 2, 3, ...)
  • Integers (...,-3, -2, -1, 0, 1, 2, 3, ...)
  • Rational numbers (fractions, e.g. 3/4, 22/7)
  • Real numbers (includes rational and irrational numbers, e.g. π, e)
• Operations:
  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
  • Exponentiation (^)
  • Root extraction (√)

Algebra

• Equations and Inequalities:
  • Linear equations (e.g. 2x + 3 = 5)
  • Quadratic equations (e.g. x^2 + 4x + 4 = 0)
  • Inequalities (e.g. 2x - 3 > 5)
• Functions:
  • Domain and range
  • Graphs of functions
  • Composition of functions

Geometry

• Points, Lines, and Planes:
  • Midpoint and distance formulas
  • Slope and intercept of a line
  • Angle properties (e.g. complementary, supplementary, adjacent)
• Shapes:
  • Properties of triangles (e.g. congruent, similar, right)
  • Properties of quadrilaterals (e.g. rectangles, squares, trapezoids)
  • Properties of circles (e.g. center, radius, circumference)

Calculus

• Limits:
  • One-sided and two-sided limits
  • Infinite limits
• Derivatives:
  • Rules of differentiation (e.g. power rule, product rule, chain rule)
  • Geometric interpretation of derivatives
• Integrals:
  • Definite and indefinite integrals
  • Rules of integration (e.g. substitution, integration by parts)

Statistics and Probability

• Data Analysis:
  • Types of data (e.g. quantitative, categorical)
  • Measures of central tendency (e.g. mean, median, mode)
  • Measures of variability (e.g. range, variance, standard deviation)
• Probability:
  • Basic concepts (e.g. experiment, outcome, sample space)
  • Rules of probability (e.g. addition, multiplication)
  • Conditional probability and independence