Basic Arithmetic and Number Systems

Basic Arithmetic Operations

• Addition: Combining two or more numbers to find a total. The sum is the result.
• Subtraction: Finding the difference between two numbers. The difference is the result.
• Multiplication: Repeated addition of the same number. The product is the result.
• Division: Finding how many times one number goes into another. The quotient is the result.

Number Systems

• Natural numbers (or counting numbers): 1, 2, 3,... Used for counting.
• Whole numbers: 0, 1, 2, 3,... Include zero and counting numbers.
• Integers:..., -3, -2, -1, 0, 1, 2, 3,... Include negative and positive whole numbers.
• Rational numbers: Numbers expressible as a fraction p/q, where p and q are integers, and q ≠ 0. Examples: 1/2, 3/4, -2/5.
• Irrational numbers: Numbers not expressible as a fraction of two integers. Examples: π (pi) and √2.
• Real numbers: The set of all rational and irrational numbers. Represented on a number line.
• Imaginary numbers: Numbers involving the square root of -1, denoted as "i". Complex numbers combine real and imaginary numbers.

Algebra

• Variables: Symbols (e.g., x, y, z) representing unknown values.
• Expressions: Combinations of variables, numbers, and operators (e.g., 2x + 3y - 5).
• Equations: Statements showing the equality of two expressions (e.g., 2x + 5 = 11).
• Solving equations: Finding the value(s) of the variable(s) making the equation true.
• Inequalities: Statements showing one expression is greater than or less than another (e.g., x > 5).

Geometry

• Points: Basic geometric elements with no size.
• Lines: Straight paths extending infinitely in both directions.
• Angles: Formed by two rays meeting at a common endpoint. Measured in degrees or radians.
• Polygons: Two-dimensional shapes with straight sides. Examples: triangles, quadrilaterals, pentagons.
• Circles: Two-dimensional shapes with all points equidistant from a central point (the center).
• Solids: Three-dimensional shapes. Examples: cubes, spheres, cones, and cylinders.

Functions and Graphs

• Functions: Relationships between inputs (domain) and outputs (range), where each input maps to exactly one output.
• Graphs: Visual representations of functions or data using coordinates in a Cartesian plane (x and y axes).
• Linear functions: Functions whose graphs are straight lines. Expressed as y = mx + b, where m is the slope and b is the y-intercept.
• Quadratic functions: Functions involving a squared variable (e.g., y = ax² + bx + c). Their graphs are parabolas.
• Exponential functions: Functions where the variable is an exponent (e.g., y = ab^x).
• Logarithmic functions: Inverse functions of exponential functions. Logarithms represent the exponent to which a base must be raised to produce a given number.

Basic Statistics

• Data: Sets of facts or figures.
• Measures of central tendency: Values describing the center of a data set. Mean (average), Median (middle value), Mode (most frequent value).
• Measures of dispersion: Values describing the spread of data. Standard deviation, variance.

Trigonometry

• Right-angled triangles: Triangles with a 90-degree angle.
• Trigonometric functions (sine, cosine, tangent, etc.): Relationships between the angles and sides of a right-angled triangle.
• Applications of trigonometry: Solving triangles, calculating heights, distances, and other real-world problems.

Calculus

• Limits: Describing the behavior of a function as its input approaches a certain value.
• Derivatives: Measuring the rate of change of a function.
• Integrals: Calculating the area under a curve or accumulating a rate of change.
• Applications of calculus: Optimization problems, motion problems, and advanced scientific and engineering applications.

Test your knowledge on basic arithmetic operations such as addition, subtraction, multiplication, and division. Additionally, explore various number systems including natural numbers, whole numbers, integers, rational, irrational, and real numbers. Challenge yourself to understand these foundational concepts in mathematics.