#### 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

**Sphere:**

A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere.

**Properties of Sphere:**

- The opposite sides of a rectangle are parallel.
- A sphere is perfectly symmetrical.
- It is not a polyhedron.
- All points on the surface are the same distance “r” from the center.
- It has no side or corner.
- It has constant mean curvature.
- It has a constant width and circumference.
- The sphere has just one curved face.
- It does not have any vertices or edges.

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