9th Class

Heron's Formula  

• Area of a triangle \[=\frac{1}{2}\times \operatorname{base}\,\times \,height\]

       

• Area of a right angled isosceles triangle with perpendicular sides each equal to 'a' units\[=\frac{1}{2}{{a}^{2}}\] sq. Units.

   

• Heron's formula:

            Area of a triangle \[=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}\]where a, b, c more...

Surface Areas and Volumes  

• Cuboid: Let be the length, V the breadth and 'h' the height of a cuboid, then

            (i) Sum of the lengths of the 12 edges of a cuboid                                                             (ii) Lateral surface area \[=2\left( l+b \right)\times h\]             (iii) Total surface area \[=2\left( lb\text{  }bh\text{ }+\text{ }hl \right)\]                 (iv) Diagonal  \[=\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\]                                     (v) Volume                          

• Cube: If 'a' is the edge of a cube, then

            (i) Sum of the lengths of the 12 edges of a cube = 12a                            more...

Statistics  

• Statistics, a branch of mathematics is useful in the collection, classification and interpretation of data.

 

• The word statistics is used in two different senses:

            (i) In plural sense, statistics means data.             (ii) In singular sense, statistics is the science which deals with the collection, presentation, analysis and interpretation of some numerical data.  

• Data: The word data means information in the form of numerical figures or a set of given facts.

 

• A statistical data is collected by a single person or by a group of persons having uniform approach.

            Someone who carries out the job of collection of data is called an investigator.  

• Primary data: The data collected for more...

Probability  

• Random experiment:

            An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance is called a random experiment.             e.g. (1) Tossing a coin.    (2) Rolling an unbiased die.  

• Sample space:

            The set S of all possible outcomes of a random experiment is called the sample space.             e.g., (1) In tossing a coin, sample space (S) = {H, T}             (2) In rolling a die, sample space (S) = {1,2,3,4,5,6}  

• Probability:

            Probability is a concept which numerically measures the degree of certainty of the occurrence of events.  

• Definition of probability:

            In a random experiment, let S be the sample space and let E more...

  Motion   Synopsis  

• Rest and motion: If the object's position does not change with respect to time and surroundings, it is said to be at rest. If the position of an object changes with time and surroundings, it is said to be in motion.

 

• Displacement: The change in the position of a particle during a time interval is called its displacement in that time interval.

 

• Scalar quantity: A quantity that has only magnitude but no direction is called a scalar quantity, e.g., distance, speed, etc.

 

• Vector quantity: A quantity that has both magnitude and direction is called a vector quantity, e.g., displacement, velocity, etc.

 

• Speed: The speed of an object more...

  Force and Laws of Motion   Synopsis  

• Force

Force is that cause which produces an acceleration in the body on which it acts. A force or a set of forces can change the speed of body, change the direction of the motion of the body and change the shape of the body.  

• Balanced and unbalanced forces

If a set of forces acting on a body produces no acceleration in it/then the forces are called balanced forces. If the set of forces produces an acceleration, they are said to be unbalanced forces.  

• Types of forces Contact force.     2. Non-contact force.

 

• Newton's first Law of Motion

A particle remains at rest or moves in a straight more...

  Gravitation and Pressure   Synopsis  

• Gravitation: The gravitational force of the earth is responsible for holding the atmosphere above the earth and it also keeps us firmly on the ground.

 

• Universal Law of Gravitation: Everybody in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction offeree is along the line joining the centres of the two bodies.

 

• Free Fall: The falling of a body from a height towards the earth under the gravitational force of earth (with no other forces acting on it) is called a free fall.

  Motion of bodies under the influence of gravitational more...

  Work, Energy and Power   Synopsis  

• Work

Work is said to be done only when a force displaces an object. The amount of work done by a body is measured as the product of magnitude of the force applied and the distance moved by the body in the direction of the force. Work is a scalar quantity.   Work = force \[\times \] displacement of the body, W = F \[\times \] S W = FS \[Cos\,\,\theta \] Where 'S' is the displacement of the object and \[\,\theta \] is the angle between the force and displacement. W = FS if the displacement is along the force then \[\,\theta =0\,\,and\,\,cos\,\,\theta =1\] W = -FS if the displacement is opposite to the force then \[\theta ={{180}^{{}^\circ }}\]and \[Cos\,\theta =-1\]. If more...

  Sound   Synopsis  

• Sound:

Sound is a form of energy that produced due to vibration s of different object  

• Sound is a wave motion produced by a vibrating source. A medium is necessary for its propagation as it is a mechanical wave. Sound cannot travel in Vacuum. The vibration source produces compression and refraction pulses which travel one after the other in the medium. Sound wave are longitudinal waves.

 

• The speed (v), frequency (f) and the wavelength \[(\lambda )\]of a sound wave are related by the equation:

\[V=f\lambda \]  

• Characteristics of sound:

Pitch - Depends on the frequency. Higher the frequency, higher is the pitch Loudness - Depends on amplitude, More the more...

  Matter in our Surroundings   Synopsis  

• Matter exists in three states, namely, in the solid, liquid and gaseous states.

 

• The physical properties of solids are density, specific gravity, hardness, odour, colour, point/freezing point, viscosity, solubility and heat conduction.

Particles are arranged in a regular pattern. They are closely packed and have fixed positions. They do not move freely but only vibrate and spin around their fixed positions. They are held together by strong attractive forces and have the least amount of energy.  

• The properties of liquids are surface tension, adhesion, cohesion, viscosity, buoyancy and

Vaporisation Particles are not arranged in a regular pattern. They are further apart and do not have fixed positions. They move freely and around one more...