Basic Arithmetic and Number Systems

Study Notes

Basic Arithmetic Operations

Addition involves combining two or more numbers to find their sum.
Subtraction involves finding the difference between two numbers.
Multiplication involves repeated addition of a number.
Division involves distributing a number into equal groups.

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: 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 of two integers, such as pi (π) and the square root of 2 (√2).
Real numbers: the set of all rational and irrational numbers.
Complex numbers: numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).

Algebraic Expressions

Variables: symbols that represent unknown values.
Constants: fixed values.
Terms: parts of an expression separated by addition or subtraction signs.
Coefficients: numerical factors of variables in terms.
Polynomials: algebraic expressions consisting of variables and coefficients, combined by addition, subtraction, and multiplication.

Equations and Inequalities

Equations: statements that show the equality of two expressions.
Solving equations: finding the values of variables that make the equation true.
Inequalities: statements that show relationships of less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥) between two expressions.
Solving inequalities: finding the values of variables that make the inequality true.

Geometry

Points, lines, and planes: fundamental building blocks for geometric shapes.
Angles: formed by two rays sharing a common endpoint.
Triangles: polygons with three sides and three angles.
Quadrilaterals: polygons with four sides and four angles.
Circles: shapes with all points equidistant from a central point.
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.

Basic Geometry Theorems

Pythagorean Theorem: for a right-angled triangle, the square of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the other two sides.

Measurement

Units of measurement: standard units for length, weight, volume, etc.
Converting units involve using conversion factors to change values from one unit to another.

Functions

Functions: relationships between input and output values
Domain: all possible input values.
Range: all possible output values.
Graphing functions: visually representing the relationship between inputs and outputs.

Statistics

Data collection: gathering information about variables or quantities.
Measures of central tendency: mean, median, and mode; representing the center of a data set.
Measures of dispersion: standard deviation and variance; showing data spread.
Probability: the numerical measure of the likelihood of an event occurring.

Sets and Logic

Sets: collections of objects, which may be finite or infinite.
Logic: a systematic way to evaluate statements or arguments; using terms like 'and,' 'or,' 'if-then.'
Venn diagrams: visual representations of relationships between sets.

Description

This quiz covers foundational concepts in arithmetic operations, including addition, subtraction, multiplication, and division. It also explores various number systems such as natural, whole, integers, and more, alongside the basics of algebraic expressions. Test your understanding of these essential mathematical principles!