Basic Arithmetic and Number Systems

Basic Arithmetic Operations

• Addition: Combining two or more numbers to find their total. Example: 2 + 3 = 5
• Subtraction: Finding the difference between two numbers. Example: 5 - 2 = 3
• Multiplication: Repeated addition of the same number. Example: 2 x 3 = 6
• Division: Separating a number into equal parts. Example: 6 ÷ 2 = 3

Number Systems

• Natural numbers: Counting numbers (1, 2, 3,...).
• Whole numbers: Natural numbers and zero (0, 1, 2, 3,...).
• Integers: Whole numbers and their negative counterparts (-3, -2, -1, 0, 1, 2, 3,...).
• Rational numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Examples: 1/2, 3, -2/5.
• Irrational numbers: Numbers that cannot be expressed as a fraction of two integers. Examples: √2, π.
• Real numbers: The set of all rational and irrational numbers.

Basic Algebra

• Variables: Symbols (usually letters) that represent unknown values.
• Expressions: Combinations of variables, numbers, and operations (e.g., 2x + 3).
• Equations: Statements that show the equality of two expressions (e.g., 2x + 3 = 7).
• Solving equations: Finding the value of the variable that makes the equation true. Example: Solving 2x + 3 = 7 yields x = 2

Geometry

• Points: Basic building blocks of geometry.
• Lines: Straight paths extending infinitely in both directions.
• Angles: Formed by two rays sharing a common endpoint (vertex).
• Polygons: Closed shapes formed by straight line segments.
• Triangles: Polygons with three sides.
• Quadrilaterals: Polygons with four sides.
• Circles: Set of all points equidistant from a center point.
• Area: The amount of space enclosed by a two-dimensional shape.
• Perimeter: The total length of the sides of a two-dimensional shape.
• Volume: The amount of space occupied by a three-dimensional shape.

Measurement

• Length: Measured in units like meters, centimeters, feet, inches.
• Weight/Mass: Measured in units like kilograms, grams, pounds, ounces.
• Volume: Measured in units like cubic meters, liters, gallons.
• Time: Measured in units like seconds, minutes, hours, days, years.

Ratio and Proportion

• Ratio: A comparison of two quantities. Example: 2:3 or 2/3.
• Proportion: An equation that states that two ratios are equal. Example: 2/3 = 4/6.

Data Analysis

• Data: Collection of facts, figures, and observations.
• Statistics: Methods for collecting, organizing, summarizing, and analyzing data.
• Mean: The average of a set of numbers.
• Median: The middle value in a sorted set of numbers.
• Mode: The most frequent value in a set of numbers.

Introduction to Functions

• Function: A relationship between two variables where each input value corresponds to exactly one output value.
• Input (x) : Independent variable
• Output (y) : Dependent variable
• Representing functions: Equations, graphs, tables

Sets

• Set: a collection of distinct objects.
• Notation (e.g. {1,2,3}, {2,4,6,8}).
• Set operations (union (∪), intersection (∩)).

Fundamentals of Counting

• Counting techniques (e.g., permutations, combinations).
• Fundamental counting principle.

Exponents and Radicals

• Exponents: Numbers that show how many times a base is multiplied by itself. Example: 2³ means 2 * 2 * 2
• Radicals: Operations used to express roots. Example: √4=2

This quiz covers fundamental arithmetic operations including addition, subtraction, multiplication, and division. It also explores different number systems such as natural, whole, integer, rational, irrational, and real numbers. Test your understanding of these essential mathematical concepts.