Math for Grade 8
1 Number Systems
1-1 Understanding Integers
1-2 Operations with Integers
1-3 Rational Numbers
1-4 Operations with Rational Numbers
1-5 Real Numbers and Their Properties
2 Algebra
2-1 Solving Linear Equations
2-2 Graphing Linear Equations
2-3 Systems of Linear Equations
2-4 Inequalities and Their Graphs
2-5 Polynomials and Their Operations
3 Geometry
3-1 Basic Geometric Figures
3-2 Angles and Their Measurement
3-3 Triangles and Their Properties
3-4 Quadrilaterals and Their Properties
3-5 Circles and Their Properties
3-6 Area and Perimeter of 2D Shapes
3-7 Volume and Surface Area of 3D Shapes
4 Data Handling
4-1 Collecting and Organizing Data
4-2 Measures of Central Tendency
4-3 Graphical Representation of Data
4-4 Probability and Its Applications
5 Functions and Relations
5-1 Introduction to Functions
5-2 Linear Functions and Their Graphs
5-3 Non-Linear Functions and Their Graphs
5-4 Relations and Their Representations
6 Problem Solving and Reasoning
6-1 Mathematical Reasoning
6-2 Problem-Solving Strategies
6-3 Applications of Mathematics in Real-Life Situations
Basic Geometric Figures

Basic Geometric Figures

1. Point

A point is the most fundamental geometric figure. It has no dimensions, meaning it has no length, width, or height. A point is used to specify a location in space.

Example: In a coordinate plane, a point is represented as (x, y), where x and y are the coordinates. For instance, the point (3, 4) indicates a location 3 units along the x-axis and 4 units along the y-axis.

2. Line

A line is a one-dimensional figure that extends infinitely in both directions. It is made up of an infinite number of points arranged in a straight path. Lines are often represented by equations or by connecting two points.

Example: The line equation \( y = 2x + 3 \) represents a line where for every unit increase in x, y increases by 2 units. This line passes through the point (0, 3) and has a slope of 2.

3. Plane

A plane is a two-dimensional surface that extends infinitely in all directions. It is defined by three non-collinear points (points that do not lie on the same line). Planes are used to represent flat surfaces in geometry.

Example: In three-dimensional space, a plane can be represented by the equation \( ax + by + cz = d \), where \( a, b, c, \) and \( d \) are constants. For instance, the plane \( 2x + 3y + 4z = 12 \) represents a flat surface in space.

Analogies to Understand Basic Geometric Figures

Think of a point as a single dot on a piece of paper, a line as a straight path drawn between two points, and a plane as an infinitely large sheet of paper.

Practical Applications

Understanding basic geometric figures is crucial in various fields such as architecture, engineering, and computer graphics. For example, architects use points and lines to design buildings, while computer graphics rely on planes to render 3D objects.