Mathematics Fundamental Operations and Number Systems

Study Notes

Fundamental Operations

Addition involves combining two or more numbers to find their total.
Subtraction is the process of finding the difference between two numbers.
Multiplication is a shorthand for repeated addition. The product is the result.
Division is determining how many times one number is contained within another. The quotient is the result.

Number Systems

Natural numbers (counting numbers): 1, 2, 3, ...
Whole numbers: 0, 1, 2, 3, ... (includes zero)
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (includes negative numbers)
Rational numbers: numbers that can be expressed as a fraction p/q where p and q are integers and q ≠ 0. Examples include 1/2, 3/4, -2/5.
Irrational numbers: numbers that cannot be expressed as a fraction of two integers. Examples include π (pi) and the square root of 2.
Real numbers: 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 (√-1).

Basic Algebra

Variables: Symbols (like x, y, or z) that represent unknown values.
Equations: Statements that show the equality of two expressions. Examples include 2x + 3 = 7, y = 2x + 1.
Inequalities: Mathematical statements that compare two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
Exponents: Represent repeated multiplication. For example, 2³ means 2 multiplied by itself 3 times (2 * 2 * 2 = 8).

Geometry

Basic shapes: circles, squares, triangles, rectangles, etc.
Area: the space inside a two-dimensional shape.
Perimeter: the total distance around the outside of a two-dimensional shape.
Volume: the amount of space occupied by a three-dimensional object.
Solids: three-dimensional shapes, like cubes, spheres, cones, and cylinders.
Angles: formed by two rays or line segments that share a common endpoint.

Data Analysis

Mean (average): the sum of a set of numbers divided by the count of those numbers.
Median: the middle value in a sorted list of numbers.
Mode: the number that appears most frequently in a set of data.
Range: the difference between the largest and smallest values in a set of data.
Statistical representation (graphs, charts, tables): used to visually represent data and trends.

Functions

Function: a relation between a set of inputs (domain) and a set of possible outputs (range) where each input is related to exactly one output. Shown as f(x).

Sets

Set: a collection of distinct objects or elements.
Set operations: union, intersection, and difference.

Number Theory

Prime numbers: Whole numbers greater than 1 that have only two factors: 1 and themselves.
Divisibility rules: methods for determining if one number is divisible by another.
Factors and multiples: factors are numbers that divide evenly into another number, while multiples are the products of a number and an integer.
Greatest Common Factor (GCF): The largest factor that divides two or more numbers.
Least Common Multiple (LCM): The smallest positive multiple that is a multiple of two or more numbers.

Other Important Concepts

Order of operations (PEMDAS/BODMAS): Rules for evaluating expressions with multiple operations.
Scientific notation: A way of writing very large or very small numbers using powers of 10.
Number lines: used to represent numbers and their relative magnitudes.
Proportions: a comparison of two ratios.
Percentages: a proportion that is expressed as a fraction out of 100.

Description

Explore the basic operations of mathematics including addition, subtraction, multiplication, and division. This quiz will also cover number systems such as natural, whole, integers, and rational versus irrational numbers. Test your understanding of these essential concepts in mathematics.