Arithmetic Operations and Number Systems

Study Notes

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.
Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Commutative Property: Changing the order of numbers in addition or multiplication does not change the result.
Associative Property: Changing the grouping of numbers in addition or multiplication does not change the result.
Distributive Property: Multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.

Number Systems

Natural Numbers (counting numbers): 1, 2, 3,...
Whole Numbers: 0, 1, 2, 3,... Combining natural numbers and zero.
Integers:... -3, -2, -1, 0, 1, 2, 3,... Including negative whole numbers.
Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Examples include fractions, terminating decimals, and repeating decimals.
Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers. Their decimal representations are non-terminating and non-repeating. Examples include √2, π.
Real Numbers: The combination of rational and irrational numbers.

Algebra

Variables: Symbols (like x, y, z) that represent unknown values.
Expressions: Combinations of variables and numbers using mathematical operations.
Equations: Statements that show two expressions are equal. They can be solved to find the value of the variable.
Inequalities: Statements that show the relationship between two expressions using symbols such as <, >, ≤, ≥.
Linear Equations: Equations that form a straight line when graphed. Usually involve a variable to the first power only.
Quadratic Equations: Equations that form a parabola when graphed. Usually involve a variable to the second power.
Polynomials: Expressions that combine variables and constants using addition, subtraction, and multiplication.

Geometry

Points, lines, planes: fundamental building blocks of geometry.
Angles: Formed by two rays sharing a common endpoint.
Polygons: Closed figures formed by line segments.
Triangles: Polygons with three sides.
Quadrilaterals: Polygons with four sides.
Circles: A set of all points equidistant from a central point (the radius).
Area: The amount of space inside a two-dimensional figure.
Perimeter: The distance around the outside of a two-dimensional figure.
Volume: The amount of space occupied by a three-dimensional figure.
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.
Similar and Congruent Figures: Similar figures have the same shape but not necessarily the same size; congruent figures have the same size and shape.

Data Analysis

Data: A collection of values or observations.
Statistics: The study of collecting, organizing, analyzing, interpreting, and presenting data.
Measures of Central Tendency: Mean, median, and mode - describing the centre of a data set.
Measures of Dispersion: Range, variance, and standard deviation - describing the spread of data.

Other Important Concepts

Sets: Collections of objects.
Functions: Relationship between input and output values.
Counting Principles: Fundamental counting principle, permutations, and combinations.
Logic: Statements, reasoning, and arguments.
Probability: The likelihood of an event occurring.

Description

This quiz covers the fundamental concepts of arithmetic operations including addition, subtraction, multiplication, and division. It also explores number systems like natural numbers, whole numbers, and integers, along with important properties such as commutative, associative, and distributive properties. Test your knowledge and understanding of these essential mathematical concepts.