10th Class

 Areas Related to Circles      

• A circle is a closed curve in a plane drawn in such a way that every point on this curve is at a constant distance (r units) from a fixed point O inside it.

The fixed point O is called the centre of the circle and the constant distance r is called the length of radius of the circle.  

• Circumference of a circle:

The perimeter of a circle is called its circumference. The length of the thread that winds tightly around the circle exactly once gives the circumference of the circle. Circumference\[=2\pi r=\pi d\], where r = radius and d = diameter. Here \[\pi \] (Pi) is a constant.   Note: The approximate value of n is more...

  Surface Area and Volume      

• A right circular cylinder is a solid generated by the revolution of a rectangle about one of its sides.

(i) Volume\[(V)=\pi {{r}^{2}}h\]     (ii) Curved surface area (C.S.A.) \[=2\pi \,rh\]          (iii) Base area\[=\pi \,{{r}^{2}}\]        (iv) Total surface area (T.S.A.) \[=2\pi \,r(h+r)\]

• Hollow cylinders:  

                                            (i) Volume of material \[=\pi h({{R}^{2}}-r)\]                        (ii) Curved surface area \[=2\pi h(R+r)\]                                              (iii) Total surface area \[=2\pi (R+r)(h+R-r)\]

• Right circular cone: If a right angled triangle is revolved about one of the sides containing the right angle, the more...

 Statistics      

• Statistics: The science of collection, organization, presentation, analysis and interpretation of numerical data is called statistics.

 

• Raw data: The collection of actual information used to make logical inferences is called raw data.

 

• Frequency table: The table in which raw data is condensed and presented is called the frequency table.

 

• Measure of central tendency: the tendency in the data to be concentrated around a certain single value that represents the whole set of data is called a measure of central tendency or average.

 

• Series: While 'preparing a frequency distribution table, classes can be considered in two ways- (i) inclusive or discrete series and (ii) Exclusive or 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, more...

 Light Reflection and Refraction  

• Light: It is a form of energy which when reflected by objects falls on the eyes and enables us to see the objects. Light propagates as electromagnetic waves. It does not require a medium for its propagation.

 

• The speed of light in free space or vacuum is\[3\times {{10}^{8}}\,m\,{{s}^{-1}}\].All colours of light travel with different speeds. The speed of light in a medium is less than that in vacuum.

 

• Reflection: The bouncing back of light rays incident on a surface in the opposite direction in the same medium is called reflection of light.

 

• Reversibility of light: If a ray of light is reversed, it always retraces its previous path. Object and image positions are more...

  The Human Eye and the colourful World    

• The Human Eye

 

• The human eye is made of structures like cornea, iris, lens and retina, which allow refraction to take place and form images. Because of the presence of two eyes we have a binocular (3-D) vision..

 

• Persistence of vision It is a phenomenon where the brain continues to sense the image, even after the object has been removed. This illusion continues for a very short time (appr. 1/16th of a second).

 

• Power of accommodation of the eye

 

• The ability of an eye to focus the distant and more...

  Electricity    

• Every atom as a whole is electrically neutral. Its total positive charge is equal to its total negative charge. Charges are produced by loss or gain of electrons.

 

• Charges in motion and current: Charges in motion constitutes current electricity. An electric current is the rate of flow of electric charge through a given cross section of a conductor. Charge flows from higher potential to lower potential. By convention the flow of charges is taken as the flow of positive charges. Negative charges flows from lower potential to higher potential.

 

• Electric potential: at a point in a field more...

 Magnetic Effects of Electric Current  

• Magnetic field and field lines: The space surrounding a magnet in which magnetic force is exerted is called a magnetic field. The magnetic field lines are the lines drawn in a magnetic field along which a north magnetic pole would move. The magnetic field lines always begin from the N-pole of a magnet and end on the S-pole of the magnet. The strength of magnetic field is indicated by the degree of closeness of the field lines. If the field lines are closer together, the magnetic field is the strongest.

 

• Magnetic field due to a current carrying conductor: The patterns of various magnetic fields or shapes of field lines produced by a current carrying conductor like straight more...

 Sources of Energy    

• Sources of energy

A source of energy is the one which can provide adequate amount of energy in a convenient form over a long period of time.  

• Renewable sources of energy

Sources of energy which are being produced continuously in nature and are inexhaustible are called renewable sources of energy. The renewable sources of energy are: solar energy, wind energy, hydro energy, bio fuels (wood, biogas), hydrogen, energy from oceans and geothermal energy.  

• Non-renewable sources of energy

Sources of energy which have been accumulated in nature over a very, very long period of time and cannot be quickly replaced when exhausted more...

 Chemical Reactions and Equations    

• Chemical reactions

  A chemical reaction is a process in which substances undergo change to produce new substances with new properties. The substances which take part in a chemical reaction are known as reactants. The new substances formed during a chemical reaction are known as products.  

• The important characteristics of chemical reactions are: evolution of a gas, formation of a precipitate, change in colour, change in temperature, and change in state.

 

• Chemical equations

A chemical equation is a short hand representation of a chemical reaction using symbols and formulae of the substances involved in the reaction.  

• A balanced more...