Basic Arithmetic and Number Systems

Study Notes

Basic Arithmetic Operations

Addition combines two or more numbers to find their total. Example: 2 + 3 = 5.
Subtraction finds the difference between two numbers. Example: 5 - 2 = 3.
Multiplication is repeated addition. Example: 3 x 4 = 12 (3 added 4 times).
Division separates a number into equal groups. Example: 12 ÷ 3 = 4 (12 divided into 3 equal groups).
Order of operations (PEMDAS/BODMAS) dictates the sequence for evaluating expressions: 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,... (includes zero)
Integers: ..., -3, -2, -1, 0, 1, 2, 3,... (includes negative whole numbers)
Rational numbers: numbers expressed as p/q, where p and q are integers and q ≠ 0. Examples: 1/2, 3, -2/5.
Irrational numbers: numbers not expressible as a fraction of two integers. Examples: π, √2.
Real numbers: all rational and irrational numbers.

Algebra

Variables represent unknown quantities. Example: In x + 2 = 5, 'x' is a variable.
Equations state that two expressions are equal. Example: x + 2 = 5.
Inequalities show a relationship of greater than or less than. Example: x > 2 or x < 5.
Solving equations involves isolating the variable to find its value.
Linear equations represent a straight line on a graph. Common form: y = mx + b.
Polynomials are expressions with variables and coefficients. Example: 2x² + 3x - 1.

Geometry

Points in a two-dimensional space are defined by their x and y coordinates.
Shapes in a two-dimensional space, like triangles, rectangles, and circles, have properties concerning sides, angles, and areas.
Three-dimensional shapes, like cubes and spheres, have properties such as volume, surface area, and their dimensions.
The Pythagorean Theorem relates the sides of a right-angled triangle: a² + b² = c².

Data Analysis

Data collection, organization, and analysis are key mathematical aspects.
Data visualization (charts and graphs) helps interpret data concisely.
Statistics involves collecting, organizing, analyzing, and interpreting data. Mean, median, mode, and range are common statistical measures.

Functions

A function maps inputs to outputs. Each input has exactly one output.
Functions are often represented with equations or graphs.
Common functions include linear, quadratic, and exponential functions.
Understanding domain (possible inputs) and range (possible outputs) is crucial for analyzing functions.

Trigonometry

Trigonometry deals with relationships between angles and sides of triangles, especially right-angled triangles.
Trigonometric ratios (sine, cosine, tangent) relate angles to ratios of sides.
Trigonometry has applications in fields such as engineering and physics.

Calculus

Calculus deals with continuous change.
Differentiation calculates a function's instantaneous rate of change.
Integration calculates the accumulation of change over an interval.

Probability and Statistics

Probability determines the likelihood of events.
Statistics involves collecting, organizing, and interpreting data.
Probability and statistics are used for prediction and inference.

Description

This quiz covers fundamental arithmetic operations such as addition, subtraction, multiplication, and division, along with the order of operations. It also explores different number systems including natural numbers, whole numbers, integers, and rational numbers. Test your understanding of these basic mathematical concepts!