Course Content
Theme 01: Rational and irrational number.
Theme 02: Compound interest
Theme 03: Expansions
Theme 04: Factorisation
Theme 05: Simultaneous linear equation
Theme 08: Indices
Theme 09: Logarithms
Theme 10: Triangles
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.
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.
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.
Theme 15: Circle
Theme 19: Coordinate Geometry
Mathematics – 9
About Lesson

In ICSE Class 9 Mathematics, the topic of mensuration covers various concepts related to the measurement of geometric figures. Here’s a summary of the key concepts typically included in this chapter:

1. **Area and Perimeter**:
– Formulas for finding the area and perimeter of basic shapes such as rectangles, squares, triangles, and circles.
– Understanding the difference between perimeter (the total length of the boundary) and area (the space enclosed by the boundary).

2. **Surface Area and Volume**:
– Formulas for finding the surface area and volume of basic 3D shapes such as cubes, cuboids, cylinders, cones, and spheres.
– Understanding the concept of surface area (the total area of all the surfaces of a 3D shape) and volume (the space occupied by a 3D shape).

3. **Composite Figures**:
– Calculating the area and perimeter of composite figures, which are made up of two or more simpler shapes.
– Applying the concept of breaking down complex shapes into simpler ones to calculate their area and perimeter.

4. **Applications of Mensuration**:
– Solving real-life problems involving area, perimeter, surface area, and volume.
– Examples include calculating the amount of paint needed to cover a wall, determining the cost of fencing a garden, or finding the volume of a container.

5. **Units of Measurement**:
– Understanding different units of measurement for length, area, and volume (e.g., centimeters, square meters, cubic centimeters).

6. **Practical Geometry**:
– Applying mensuration concepts in practical geometry, such as constructing shapes with given measurements or dimensions.

7. **Word Problems**:
– Solving word problems that require the application of mensuration formulas to find unknown quantities.

Overall, the mensuration chapter in ICSE Class 9 Mathematics focuses on developing students’ ability to calculate the measurements of various geometric figures and apply these concepts to solve real-world problems.