Basic Arithmetic and Number Systems

Study Notes

Basic Arithmetic Operations

Addition combines two or more numbers to find their sum.
Subtraction finds the difference between two numbers.
Multiplication is repeated addition of a number.
Division distributes a number into equal parts.
Order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

Number Systems

Natural numbers (counting numbers): 1, 2, 3,...
Whole numbers: 0, 1, 2, 3,...
Integers: ..., -3, -2, -1, 0, 1, 2, 3,...
Rational numbers: expressed as a fraction p/q, where p and q are integers, and q ≠ 0.
Irrational numbers: cannot be expressed as a fraction. Examples: π, √2.
Real numbers: all rational and irrational numbers.
Complex numbers: in the form a + bi, where a and b are real numbers, and i is the imaginary unit (√-1).

Algebra

Variables represent unknown quantities.
Equations state that two expressions are equal.
Solving equations isolates the variable.
Inequalities compare expressions using symbols like <, >, ≤, ≥.
Linear equations have a degree of 1 and graph as straight lines.
Quadratic equations have a degree of 2 and graph as parabolas.
Factoring expresses a polynomial as a product of simpler expressions.
Simplifying expressions rewrites an expression more concisely.

Geometry

Points, lines, and planes are fundamental geometric objects.
Angles are formed by two rays sharing a common endpoint.
Polygons are closed figures formed by line segments. Examples: triangles, quadrilaterals, pentagons.
Circles are defined by a center point and radius.
Perimeter is the total distance around a two-dimensional shape.
Area is the space inside a two-dimensional shape.
Volume is the space occupied by a three-dimensional object.
Formulas exist for calculating area, perimeter, and volume of various shapes.

Data Analysis

Collecting, organizing, and interpreting data are key aspects.
Statistics uses data to draw conclusions and make predictions.
Mean, median, and mode measure central tendency.
Range and standard deviation measure data spread.
Graphs and charts visualize data.

Trigonometry

Relates angles and sides of triangles.
Trigonometric functions (sine, cosine, tangent) relate angles to ratios of side lengths.
Applications include navigation, engineering, and physics.

Calculus

Differential calculus deals with rates of change.
Integral calculus deals with accumulation of quantities.
Derivatives measure instantaneous rate of change.
Integrals find accumulated change.
Used in physics, engineering, and finance.

Discrete Mathematics

Focuses on countable objects.
Includes topics like logic, set theory, counting techniques, relations, functions, graphs, and algorithms.

Description

This quiz covers fundamental arithmetic operations including addition, subtraction, multiplication, and division. It also explores various number systems such as natural, whole, integers, rational, irrational, real, and complex numbers, highlighting their definitions and characteristics.