Basic Arithmetic Operations and Number Systems

Study Notes

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 by taking one away from the other. The difference is the result.
Multiplication: Repeated addition of the same number. The product is the result.
Division: Separating a number into equal groups. The quotient is the result.
Order of operations (PEMDAS/BODMAS): A set of rules for evaluating expressions. Parentheses/Brackets first, then Exponents/Orders, Multiplication and Division (left to right), and finally Addition and Subtraction (left to right).

Number Systems

Natural Numbers: Counting numbers (1, 2, 3,...).
Whole Numbers: Natural numbers plus zero (0, 1, 2, 3,...).
Integers: Whole numbers and their opposites (-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 is not zero.
Irrational Numbers: Numbers that cannot be expressed as a fraction, and their decimal representations are non-repeating and non-terminating (e.g., π, √2).
Real Numbers: The set of all rational and irrational numbers.
Complex Numbers: Numbers of the form a + bi, where a and b are real numbers, and i is the imaginary unit (i² = -1).

Algebra

Variables: Symbols (letters) that represent unknown values.
Expressions: Combinations of numbers, variables, and operations.
Equations: Statements that show two expressions are equal. Solving equations involves finding the value of the unknown variable.
Inequalities: Statements that compare two expressions using symbols like <, >, ≤, ≥.
Linear Equations: Equations that form a straight line when graphed. They typically have the form y = mx + b.
Polynomials: Expressions involving variables and coefficients, such as x² + 2x + 1.

Geometry

Points, lines, and planes: Fundamental geometric objects.
Angles: Formed by two rays sharing a common endpoint.
Triangles: Polygons with three sides.
Quadrilaterals: Polygons with four sides.
Circles: Sets of points equidistant from a central point (the center).
Perimeter: The distance around a two-dimensional shape.
Area: The amount of space enclosed by a two-dimensional shape.
Volume: The amount of space occupied by a three-dimensional shape.
Pythagorean Theorem: In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a² + b² = c²).

Data Analysis and Probability

Data collection: Gathering information about a specific topic.
Data representation: Showing data (ex: charts, graphs, tables).
Measures of central tendency: Mean, median, and mode describe the center of a set of data.
Measures of dispersion: Range, standard deviation, and variance describe the spread or variation in a set of data.
Probability: The chance of an event occurring.

Trigonometry

Trigonometric functions: Sine, cosine, and tangent relate angles and sides of right triangles.
Unit circle: A circle with a radius of 1, used to define trigonometric ratios.
Applications of trigonometry: Used in various fields like engineering, astronomy, and navigation.

Description

Test your knowledge on basic arithmetic operations including addition, subtraction, multiplication, and division. Additionally, explore different number systems such as natural numbers, integers, and rational numbers. This quiz will help you understand how to apply these concepts effectively.