Theme 01: Rational and irrational number.

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Theme 02: Compound interest

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Theme 03: Expansions

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Theme 04: Factorisation

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Theme 05: Simultaneous linear equation

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Theme 06: Problems on simultaneous linear equations

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Theme 07: Quadratic Equations

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Theme 08: Indices

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Theme 09: Logarithms

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Theme 10: Triangles

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Theme 11: Mid-point Theorems

The Midpoint Theorem is a fundamental concept in geometry that relates to the properties of line segments. In the ICSE Class 9 Mathematics curriculum, the Midpoint Theorem is typically covered as part of the chapter on Lines and Angles or Triangles. Here's a summary of the Midpoint Theorem:
**Midpoint Theorem**: In a given line segment, the line segment joining the midpoints of the two sides is parallel to the third side and is half of its length.
**Statement of the Theorem**: Let (AB) be a line segment and (M) be the midpoint of (AB). If (P) is any point on the line segment (AB), then (2 times PM = AB).
**Proof of the Theorem**: The proof involves constructing a parallel line through (P) to (AB), intersecting (AM) and (BM) at points (N) and (O), respectively. Using the properties of parallel lines, it can be shown that (2 times PM = AB).
**Application of the Theorem**: The Midpoint Theorem is used in various geometric proofs and constructions. It helps in understanding the relationship between the sides and diagonals of a triangle and is often used to prove other theorems related to triangles and quadrilaterals.
**Example**: In a triangle (ABC), (D) is the midpoint of (BC). If (AD) is extended to (E) such that (DE = AD), prove that (AB = 2 times DE).
**Conclusion**: The Midpoint Theorem is a fundamental concept in geometry that helps in understanding the properties of line segments and their relationships in geometric figures. It is a key theorem that forms the basis for many other theorems in geometry.

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Theme 12: Pythagoras Theorems

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Theme 13: Rectilinear figures

In the ICSE Class 9 Mathematics syllabus, the topic of "Rectilinear Figures" typically covers various polygons and their properties. Here's a summary of the key concepts usually included in this topic:
1. **Polygon**: A polygon is a closed figure formed by three or more line segments. It is classified based on the number of sides it has. Examples include triangles, quadrilaterals, pentagons, etc.
2. **Types of Polygons**:
- **Triangle**: A polygon with three sides. Classified based on angles as acute, obtuse, or right-angled triangles.
- **Quadrilateral**: A polygon with four sides. Examples include square, rectangle, parallelogram, rhombus, trapezium, etc.
- **Pentagon, Hexagon, etc.**: Polygons with five, six, or more sides, respectively.
3. **Properties of Rectilinear Figures**:
- **Interior Angles**: The sum of interior angles of an n-sided polygon is (n-2) * 180 degrees.
- **Exterior Angles**: The exterior angle of a polygon is equal to 360 degrees divided by the number of sides.
- **Diagonals**: The number of diagonals in a polygon can be calculated using the formula: n(n-3)/2, where n is the number of sides.
4. **Special Types of Quadrilaterals**:
- **Square**: A quadrilateral with all sides equal and all angles right angles.
- **Rectangle**: A quadrilateral with opposite sides equal and all angles right angles.
- **Parallelogram**: A quadrilateral with opposite sides parallel and equal.
- **Rhombus**: A quadrilateral with all sides equal but not necessarily right angles.
- **Trapezium**: A quadrilateral with one pair of parallel sides.
5. **Area and Perimeter**:
- **Area**: The area of a polygon can be calculated using different formulas based on the type of polygon.
- **Perimeter**: The perimeter is the sum of all the sides of the polygon.
6. **Application Problems**: Real-life problems involving the calculation of areas and perimeters of rectilinear figures.
This summary provides a general overview of the topic "Rectilinear Figures" in the ICSE Class 9 Mathematics syllabus. Students are advised to refer to their textbooks and practice solving problems to master these concepts.

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Theme 14: Theorems on area

In the ICSE Class 9 Mathematics curriculum, the topic of theorems on area typically covers various theorems and concepts related to the calculation of area in different geometric shapes. Here's a summary of the key theorems and concepts:
1. **Area of a Triangle**: The area of a triangle can be calculated using the formula A = 1/2 * base * height, where the base is the length of the triangle's base and the height is the perpendicular distance from the base to the opposite vertex.
2. **Area of a Parallelogram**: The area of a parallelogram is equal to the product of its base and height, i.e., A = base * height.
3. **Area of a Trapezium**: The area of a trapezium is equal to half the sum of the lengths of its parallel sides multiplied by the height, i.e., A = 1/2 * (a + b) * h, where 'a' and 'b' are the lengths of the parallel sides and 'h' is the height.
4. **Area of a Rhombus**: The area of a rhombus can be calculated as half the product of its diagonals, i.e., A = 1/2 * d1 * d2, where 'd1' and 'd2' are the lengths of the diagonals.
5. **Area of a Circle**: The area of a circle is given by the formula A = π * r^2, where 'r' is the radius of the circle and π (pi) is a constant approximately equal to 3.14159.
6. **Pythagoras Theorem**: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where 'a' and 'b' are the lengths of the two shorter sides (legs) and 'c' is the length of the hypotenuse.
These theorems and formulas are essential for calculating the areas of different geometric shapes and are foundational concepts in geometry and mathematics.

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Theme 15: Circle

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Theme 16: Mensuration

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Theme 17: Trigonometrical Ratios

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Theme 18: Trigonometrical ratios of standard angles

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Theme 19: Coordinate Geometry

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Theme 20: Statistics.

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