Math Fundamentals Quiz

Numbers and Operations

• Types of Numbers:
  • Natural Numbers: 1, 2, 3,...
  • Whole Numbers: 0, 1, 2, 3,...
  • Integers:..., -3, -2, -1, 0, 1, 2, 3,...
  • Rational Numbers: fractions, decimals, and percents
  • Irrational Numbers: non-repeating, non-terminating decimals (e.g., π, e)
  • Real Numbers: all rational and irrational numbers
• Number Operations:
  • Addition: combining two or more numbers to get a total or sum
  • Subtraction: finding the difference between two numbers
  • Multiplication: repeated addition of a number
  • Division: sharing a number into equal parts or groups
  • Exponents: raising a number to a power (e.g., 2^3 = 2 × 2 × 2)
  • Roots: finding a value that, when multiplied by itself, gives a specified number (e.g., √16 = 4)

Algebra

• Variables and Expressions:
  • Variables: letters or symbols representing unknown values
  • Expressions: combinations of variables, numbers, and operations
  • Simplifying Expressions: combining like terms and removing parentheses
• Equations and Inequalities:
  • Equations: statements with equal values (e.g., 2x + 3 = 5)
  • Inequalities: statements with unequal values (e.g., 2x + 3 > 5)
  • Solving Equations: finding the value of the variable that makes the equation true
  • Solving Inequalities: finding the range of values that make the inequality true

Geometry

• Points, Lines, and Planes:
  • Points: locations in space, represented by coordinates (x, y)
  • Lines: sets of points extending infinitely in two directions
  • Planes: flat surfaces extending infinitely in all directions
• Angles and Measurements:
  • Angle: formed by two rays sharing a common endpoint (vertex)
  • Types of Angles: acute, right, obtuse, straight, and reflex
  • Measurement Units: degrees, radians, and metric units (e.g., inches, centimeters)

Data Analysis and Statistics

• Data Types:
  • Qualitative Data: categorical, non-numerical data (e.g., colors, names)
  • Quantitative Data: numerical data (e.g., heights, temperatures)
• Data Visualization:
  • Charts: bar, pie, and Pareto charts
  • Graphs: line, scatter, and histogram graphs
  • Plots: box and whisker plots
• Measures of Central Tendency:
  • Mean: average value
  • Median: middle value
  • Mode: most frequent value

Calculus

• Limits:
  • Concept of a limit: approaching a value as the input changes
  • Notation: lim x→a f(x) = L
• Derivatives:
  • Rate of Change: measuring how a function changes as the input changes
  • Notation: f'(x) or (d/dx)f(x)
• Integrals:
  • Accumulation of a Function: finding the total amount of change
  • Notation: ∫f(x)dx or ∫[a, b] f(x)dx