Topics
Basic Concepts in Geometry
Angles
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
- Introduction to Practical Geometry
- Constructing a Bisector of an Angle
- Constructing a Bisector of an Angle
- Constructing a Copy of an Angle of Unknown Measure
- Angles of Special Measures - 30°, 45°, 60°, 90°, and 120°
Integers
Operations on Fractions
- Concept of Fractions
- Fraction on the Number Line
- Types of Fraction
- Concept of Proper Fractions.
- Improper Fraction and Mixed Fraction
- Concept for Equivalent Fractions
- Like and Unlike Fraction
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Fraction
- Concept for Reciprocal of a Fraction
- Division of Fractions
Decimal Fractions
- Concept of Decimal Numbers
- Place Value in the Context of Decimal Fraction.
- Concept of Tenths, Hundredths and Thousandths in Decimal
- Interconversion of Fraction and Decimal
- Representing Decimals on the Number Line
- Addition of Decimal Numbers
- Subtraction of Decimals Fraction
- Multiplication of Decimal Numbers
- Division of a Decimal Number by a Whole Number
- Division of a Decimal Number by Another Decimal Number
Bar Graphs
Symmetry
Divisibility
HCF-LCM
Equations
Ratio and Proportion
Percentage
Profit –Loss
Banks and Simple Interest
Triangles and Their Properties
Quadrilaterals
Geometrical Constructions
Three Dimensional Shapes
notes
Cone:
A cone is a three-dimension solid object that has a circular base joined to point by a curved side and one vertex.
Type of Cone:
There are two types of cone:
1. Right Circular Cone:
A right circular cone is a cone whose base is a circle and whose axis is perpendicular to the base.
This is called a right circular cone.
In Fig, point A is called the vertex, AB is called the height, BC is called the radius, and AC is called the slant height of the cone. Here B will be the center of the circular base of the cone. The height, radius, and slant height of the cone are usually denoted by h, r, and l respectively.
2. Oblique Cone:
A cone which has a circular base but the axis of the cone is not perpendicular with the base, is called an Oblique cone.
Properties of Right Circular Cone:
- All elements of a right circular cone are equal.
- A section of a right circular cone that contains the vertex and two points of the base is an isosceles triangle.
- A right circular cone is a circular cone whose axis is perpendicular to its base.
- A cone has only one face, which is the circular base but no edges or vertices.
- A cone has only a vertex point.
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