#### 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

**Concept of Cylinder:**

- A cylinder is a three-dimensional shape with two round shapes at either end and two parallel lines connecting the round ends. Bases are always parallel and congruent to each other.
- A closed cylinder has two flat circular faces and one curved face.
- The cylinder has two circular edges and no vertex.

**Type of Cylinder:**

There are two types of cylinder:

**1. Right Circular Cylinder: **

When the two bases of the cylinder are over each other in the exact position and the axis is at the right angle to the base, it is called the cylinder is a right cylinder.

If the bases are circular in shape, then it is called a Right circular cylinder.

If the bases are in an elliptical shape, then it is called an Elliptical Cylinder.

**2. Oblique Cylinder:**

When one of the bases of the cylinder is sideways and the axis is not a right angle to the base, then it is an oblique cylinder.

**Properties of Cylinder:**

- A cylinder has only one curved side.
- A cylinder has two identical flat ends that are circular or elliptical.
- The bases are always congruent and parallel.
- It is similar to the prism since it has the same cross-section everywhere.

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