Key Concepts in Mathematics 1

Types of Numbers:
- Natural numbers: 1, 2, 3, ...
- Whole numbers: 0, 1, 2, 3, ...
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational numbers: Fractions and decimals (e.g., 1/2, 0.75)
- Irrational numbers: Non-repeating, non-terminating decimals (e.g., √2, π)
Basic Operations:
- Addition (+)
- Subtraction (−)
- Multiplication (×)
- Division (÷)
- Order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right) (PEMDAS/BODMAS)

Variables and Expressions:
- Variables: Symbols representing numbers (e.g., x, y)
- Expressions: Combinations of numbers and variables (e.g., 2x + 3)
Equations:
- Definition: Mathematical statements that two expressions are equal (e.g., 2x + 3 = 7)
- Solving equations: Isolating the variable to find its value.

Basic Shapes:
- Triangle: 3 sides, sum of angles = 180°
- Square: 4 equal sides, angles = 90°
- Circle: Defined by radius and diameter.
Perimeter and Area:
- Perimeter: Sum of the sides of a shape.
- Area:
  - Rectangle: A = length × width
  - Triangle: A = (base × height) / 2
  - Circle: A = πr² (r = radius)

Data Collection:
- Types of data: Qualitative (categorical) and quantitative (numerical).
Measures of Central Tendency:
- Mean: Average of a set of numbers.
- Median: Middle value when numbers are arranged in order.
- Mode: Most frequently occurring number.

Basic Concepts:
- Experiment: An action or process that results in one or more outcomes.
- Probability: Measure of the likelihood of an event occurring, calculated as P(Event) = (Number of favorable outcomes) / (Total number of outcomes).

Definition: A relation that assigns exactly one output for each input (e.g., f(x) = 2x + 3).
Types:
- Linear functions: Graph forms a straight line.
- Quadratic functions: Graph forms a parabola.

Strategies:
- Understand the problem.
- Devise a plan.
- Carry out the plan.
- Review/extend: Check results and explore further implications.

These key concepts form the foundation of Mathematics 1 and are essential for further studies in higher mathematics.

Types of Numbers:
- Natural numbers start from 1 and increase incrementally (1, 2, 3,...).
- Whole numbers include all natural numbers plus zero (0, 1, 2, 3,...).
- Integers encompass all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...).
- Rational numbers consist of fractions and decimals, such as 1/2 and 0.75.
- Irrational numbers are represented by non-repeating, non-terminating decimals, including numbers like √2 and π.
Basic Operations:
- Four fundamental operations: Addition (+), Subtraction (−), Multiplication (×), and Division (÷).
- The order of operations is crucial for solving expressions, following PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Variables and Expressions:
- Variables are symbols that denote unknown quantities (e.g., x, y).
- Expressions are formed by combining numbers and variables (e.g., 2x + 3).
Equations:
- Equations are mathematical statements asserting the equality of two expressions, for instance, 2x + 3 = 7.
- Solving equations involves isolating the variable to determine its value.

Basic Shapes:
- Triangles have 3 sides, with the sum of their angles always equaling 180°.
- Squares consist of four equal sides, with all angles measuring 90°.
- Circles are defined by their radius and diameter.
Perimeter and Area:
- Perimeter is calculated as the total length of all sides of a shape.
- Area formulas vary by shape:
  - Rectangle: Area = length × width.
  - Triangle: Area = (base × height) / 2.
  - Circle: Area = πr², where r is the radius.

Data Collection:
- Data is categorized into qualitative (categorical) and quantitative (numerical) types.
Measures of Central Tendency:
- Mean is calculated as the average of a data set.
- Median represents the middle value when data is ordered.
- Mode indicates the number that appears most frequently in a data set.

Basic Concepts:
- An experiment is defined as an action or process yielding one or more outcomes.
- Probability quantifies the likelihood of an event, determined by the formula P(Event) = (Number of favorable outcomes) / (Total number of outcomes).

Definition: A function describes a relationship where each input corresponds to exactly one output, exemplified by f(x) = 2x + 3.
Types of Functions:
- Linear functions produce a straight-line graph.
- Quadratic functions yield a parabolic graph.

Strategies:
- Thoroughly understand the problem before attempting a solution.
- Devise a plan to tackle the problem effectively.
- Execute the plan to reach a solution.
- Review and extend: Analyze results for accuracy and consider broader implications.