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  • Carbon and its Compounds | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Two or more elements combine to form compounds. There are two types of compounds- Organic Compound and Inorganic Compounds. Organic compounds are the one which are made up of carbon and hydrogen. (Scroll down till the end…) Study Tools Audio, Visual & Digital Content Revision Notes… readmore

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    Two or more elements combine to form compounds. There are two types of compounds- Organic Compound and Inorganic Compounds. Organic compounds are the one which are made up of carbon and hydrogen. (Scroll down till the end…)

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  • CIRCLES | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Introduction to Circles There are many objects in our life which are round in shape. A few examples are the clock, dart board, cartwheel, ring, Vehicle wheel, Coins, etc. (Scroll down to continue …)(Scroll down till end of the page) Study Tools Audio, Visual & Digital… readmore

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    Introduction to Circles

    There are many objects in our life which are round in shape. A few examples are the clock, dart board, cartwheel, ring, Vehicle wheel, Coins, etc. (Scroll down to continue …)(Scroll down till end of the page)

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    Circles

    Circles

    • Any closed shape with all points connected at equidistant from the centre forms a Circle.
    • Any point which is equidistant from anywhere from its boundary is known as the Centre of the Circle.
    • Circles
    • Radius is a Latin word which means ‘ray’ but in the circle it is the line segment from the centre of the circle to its edge. So any line starting or ending at the centre of the circle and joining anywhere on the border of the circle is known as the Radius of Circle.

    Interior and Exterior of a Circle

    Interior and Exterior of a Circle

    In a flat surface, the interior of a circle is the line whose distance from the centre is less than the radius. 

    The exterior of a circle is the line in the plane whose distance from the centre is larger than the radius.

    Terms related to circle

    Arc

    • Chord: Any straight line segment that’s both endpoints falls on the boundary of the circle is known as Chord. In Latin, it means ‘bowstring’.
    • Diameter: Any straight line segment or Chord which passes through the centre of the Circle and its endpoints connects on the boundary of the Circle is known as the Diameter of Circle. So in a circle Diameter is the longest chord possible in a circle.
    • Arc: Any smooth curve joining two points is known as Arc. So in Circle, we can have two possible Arcs, the bigger one is known as Major Arc and the smaller one is known as Minor Arc.
    • Circumference: It is the length of the circle if we open and straighten it out to make a line segment.

    Segment and Sector of the Circle

    Segment and Sector of the Circle

    A segment of the circle is the region between either of its arcs and a chord. It could be a major or minor segment.

    Sector of the circle is the area covered by an arc and two radii joining the centre of the circle. It could be the major or minor sector.

    Angle Subtended by a Chord at a Point

    Angle Subtended by a Chord at a Point

    If in a circle AB is the chord and is making ∠ACB at any point of the circle then this is the angle subtended by the chord AB at a point C.

     Likewise, ∠AOB is the angle subtended by chord AB at point O i.e. at the centre and ∠ADB is also the angle subtended by AB at point D on the circle.

    Theorem 1: Any two equal chords of a circle subtend equal angles at the centre.

    Any two equal chords of a circle subtend equal angles at the centre

    Here in the circle, the two chords are given and PQ = RS with centre O.

    So OP = OS = OQ = OR (all are radii of the circle)

    ∆POQ ≅ ∆SOR

    ∠POQ = ∠SOR  

    This shows that the angles subtended by equal chords to the centre are also equal.

    Theorem 2: If the angles made by the chords of a circle at the centre are equal, then the chords must be equal.

    A perpendicular from the centre of a circle to any chord then it bisects the chord.

    This theorem is the reverse of the above Theorem 1.

    Perpendicular from the Centre to a Chord

    Theorem 3: If we draw a perpendicular from the centre of a circle to any chord then it bisects the chord.

    If we draw a perpendicular from the centre to the chord of the circle then it will bisect the chord. And the bisector will make a 90° angle to the chord.

    Theorem 4: The line which is drawn from the centre of a circle to bisect a chord must be perpendicular to the chord.

    The centre of a circle to bisect a chord must be perpendicular to the chord.

    If we draw a line OB from the centre of the circle O to the midpoint of the chord AC i.e. B, then OB is the perpendicular to the chord AB.

    If we join OA and OC, then

    In ∆OBA and ∆OBC,

    AB = BC (B is the midpoint of AC)

    OA = OC (Both are the radii of the same circle)

    OB = OB (same side)

    Hence, ΔOBA ≅ ΔOBC (both are congruent by SSS congruence rule)

    ⇒ ∠OBA = ∠OBC (respective angles of congruent triangles)

    ∠OBA + ∠OBC = ∠ABC = 180° [Linear pair]

    ∠OBC + ∠OBC = 180° [Since ∠OBA = ∠OBC]

    2 x ∠OBC = 180°

    ∠OBC = 90o

    ∠OBC = ∠OBA = 90°

    ∴ OB ⊥ AC

    Circle through Three Points

    Theorem 5: There is one and only one circle passing through three given non-collinear points.

     one and only one circle passing through three given non-collinear points.

    In this figure, we have three non-collinear points A, B and C. Let us join AB and BC and then make the perpendicular bisector of both so that RS and PQ the perpendicular bisector of AB and BC respectively meet each other at Point O.

    Now take the O as centre and OA as the radius to draw the circle which passes through the three points A, B and C.

    This circle is known as Circumcircle. Its centre and radius are known as the Circumcenter and Circumradius.

    Equal Chords and Their Distances from the Centre

    Theorem 6: Two equal chords of a circle are at equal distance from the centre.

    Two equal chords of a circle are at equal distance from the centre.

    AB and CD are the two equal chords in the circle. If we draw the perpendicular bisector of these chords then the line segment from the centre to the chord is the distance of the chord from the centre.

    If the chords are of equal size then their distance from the centre will also be equal.

    Theorem 7: Chords at equal distance from the centre of a circle are also equal in length. This is the reverse of the above theorem which says that if the distance between the centre and the chords are equal then they must be of equal length.

    Angle Subtended by an Arc of a Circle

    Angle Subtended by an Arc of a Circle

    The angle made by two different equal arcs to the centre of the circle will also be equal.

    There are two arcs in the circle AB and CD which are equal in length.

    So ∠AOB = ∠COD.

    Theorem 8: The angle subtended by an arc at the centre is twice the angle subtended by the same arc at some other point on the remaining part of the circle.

     The angle subtended by an arc at the centre is twice the angle subtended by the same arc

    In the above figure ∠POQ = 2∠PRQ.

    Theorem 9: Angles from a common chord which are on the same segment of a circle are always equal.

    Angles from a common chord which are on the same segment of a circle are always equal.

    If there are two angles subtended from a chord to any point on the circle which are on the same segment of the circle then they will be equal.

    ∠a = (1/2) ∠c (By theorem 8)

    ∠b = (1/2) ∠c

    ∠a = ∠b

    Cyclic Quadrilaterals

    If all the vertices of the quadrilateral come in a circle then it is said to be a cyclic quadrilateral.

    Theorem 10: Any pair of opposite angles of a cyclic quadrilateral has the sum of 180º.

    Cyclic Quadrilaterals

    ∠A + ∠B + ∠C + ∠D = 360º (angle sum property of a quadrilateral)

    ∠A + ∠C = 180°

    ∠B + ∠D = 180º

    Theorem 11: If the pair of opposite angles of a quadrilateral has a sum of 180º, then the quadrilateral will be cyclic.

    This is the reverse of the above theorem.

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  • COMBUSTION AND FLAME | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Combustion: The process of burning a substance in the presence of air (oxygen) andundergoes a chemical reaction to produce heat and light. The substances which burn in air are called combustible. Oxygen (in air) is essential for combustion. During the process of combustion, heat and light… readmore

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    Combustion: The process of burning a substance in the presence of air (oxygen) andundergoes a chemical reaction to produce heat and light. The substances which burn in air are called combustible.

    Oxygen (in air) is essential for combustion. During the process of combustion, heat and light are given out. Ignition temperature is the lowest temperature at which a combustible substancecatches fire.

    Types of combustion: The type of combustion differs depending on the type of fuel. (Scroll down till end of the page)

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    Based on nature and intensity combustions are classified into three types. They are:
    (i) Rapid combustion
    (ii) Spontaneous combustion
    (iii) Explosion

    Flame: It is a zone or burning vapour. The substances which vaporise during
    burning give flames.

    Example: Kerosene oil and molten wax. Inflammable substances have very low ignition temperature. Fire can be controlled by removing one or more requirements essential for producing fire. Water is commonly used to control fires. Water cannot be used to control fires involving electrical equipments or oils.

    There are three different zones of a flame – dark zone, luminous zone and non-luminous zone.

    Fuel is any material that is burned to obtain energy that can be used to heat or
    A good fuel must:

    Oxides of sulphur and nitrogen produced by the burning of coal, diesel and
    petrol cause Acid rain which is harmful for crops, buildings and soil.

    Be readily
    available. Be cheap. Burn easily at a moderate rate.

    Produce a large amount of heat. • Not leave behind any undesirable
    Fuels differ in their efficiency and cost. Fuel efficiency is expressed in terms of its calorific value which is expressed in
    units of kilo joule per kg.

    Types of Fuels:
    (i) Solid Fuels: Combustible substances which are solid at room
    temperature.Example: coal, coke, wood, charcoal, etc. (ii) Liquid fuels: Volatile liquids which produce combustible vapour. Example:
    Petrol,kerosene, alcohol, diesel, etc. (iii) Gaseous fuels: Combustible gases or mixture of combustible gases. Example:
    Effects of Burning of Fuels:
    (i) Carbon fuels like wood, coal petroleum release un burnt carbon particles. Theseare dangerous pollutants causing respiratory diseases, such as asthma.

    (ii) Incomplete combustion of carbon fuels gives carbon monoxide which
    is apoisonous gas.

    (iii) Increased concentration of carbon dioxide in the air is believed to cause
    globalwarming.

    (iv) Oxides of Sulphur and nitrogen dissolve in rain water and form acids. Such
    rain is Un burnt carbon particles in air are dangerous pollutants causing respiratoryproblems.

    Incomplete combustion of a fuel gives poisonous carbon monoxide gas. Increased percentage of carbon dioxide in air has been linked to global warming.

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  • Lines and Angles | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Point: Point is an exact position in space with no dimensions, represented by a dot. Ray: Ray is a part of a line that starts at an endpoint and extends infinitely away from the end point in single direction. Line or Straight line: A line or… readmore

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    Point: Point is an exact position in space with no dimensions, represented by a dot.

    Ray: Ray is a part of a line that starts at an endpoint and extends infinitely away from the end point in single direction.

    Line or Straight line: A line or straight line is perfectly straight and extends forever in both direction.

    Line segment: A line segment is the part of a line between two points. (Scroll down till end of the page)

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    Intersecting lines: Two or more lines that have one and only one point in common.

    Point of intersection: Point of intersection is a common point at which the intersecting lines meet.

    Transversal: Transversal is a line that intersects two or more lines which lie in the same plane at distinct points.

    Parallel lines: Parallel lines are the lines on a plane which never meet. They are at a distance apart.

    Complementary Angles: Complementary angles are the angles whose total is equal to 90o .

    Supplementary Angles: Suplementary angles are the angles whose total is equal to 180o

    Adjacent Angles: Adjacent Angles are the angles which have a common vertex and a common interior points.

    Linear Pair of Angles: Linear pair of angles is a pair of adjacent angles whose non-common sides are opposite rays.

    Vertically Opposite Angles: Vertically opposite angles are the angles formed by two intersecting lines which have the have common arms.

    Angles made by Transversal:

    When two lines are intersecting by a transversal, eight angles are formed.

    Transversal of Parallel Lines: If two parallel lines are intersected by a transversal, each pair of:

    • Corresponding angles are congruent.
    • Alternateinterior angles are congruent.
    • Alternate exterior angles are congruent.

    If the transversal is perpendicular to the parallellines, all of the angles formed are congruent to 90o angles.

    1. A line which intersects two or more given lines at distinct points is called a transversal to the given lines.
    2. Lines in a plane are parallel if they do not intersect when produced indefinitely in either direction.
    3. The distance between two intersecting lines is zero.
    4. The distance between two parallel lines is the same everywhere and is equal to the perpendicular distance between them.

    If two parallel lines are intersected by a transversal then:

    • pairs of alternate (interior orexterior) angles are equal.
    • pairs of corresponding angles are equal.
    • interior angles onthe same sideof the transversal are supplementary.

    6. If two non-parallel lines are intersected by transversal then none of (i), (ii) and (iii) hold true in 5. 7.

    If two lines are intersected by a transversal, then they are parallel if any one of the following is true:

    • The angles of a pair of corresponding angles are equal.
    • The angles of a pairof alternate interior angles are equal.
    • The angles of a pairof interior angles on the sameside of the transversal are supplementary.
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  • Lines and Angles | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore

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  • Physical and Chemical Changes | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Changes can be of two types, physical and chemical. Physical changes are changes in the physical properties of substances. Due to physical chages new substances are not formed. Physical changes may be reversible. Examples: crushing a can, glowing of an electric bulb, tearing of paper, mixing… readmore

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    Changes can be of two types, physical and chemical.

    Physical changes are changes in the physical properties of substances.

    Due to physical chages new substances are not formed.

    Physical changes may be reversible.

    Examples: crushing a can, glowing of an electric bulb, tearing of paper, mixing of sand and water. (Scroll down till end of the page)

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    Chemical Changes are changes in which the composition and chemical properties of the substance get changed.

    In chemical changes new substances are produced. The most of the chemical changes are irreversible and permanent.

    Note: Some chemical changes are reversible, known as reversible chemical changes.

    Example: burning of a candle, formation of curd from milk, ripening of fruits.

    Some Chemical Reactions in daily life:

    Rusting of Iron: Rusting is the process in which iron turns into iron oxide.

    It happens when iron comes into contact with water and oxygen. The process is a type of corrosion that occurs easily under natural conditions.

    Prevention of Rusting:

    1. By Painting
    2. By Oiling and greasing
    3. By Chromium plating
    4. By Galvanizing
    5. By Alloying

    Cooking of food: Cooking causes breakdown of complex molecules of carbohydrates, fats and proteins into smaller molecules.

    It is regarded as a decomposition reaction.

    Cooked food is easier to digest than uncooked food.

    3. Decay of Organic Substances: Microorganisms like fungi and bacteria produce enzymes which break down complex organic compounds into smaller substances.

    It is also regarded as a decomposition reaction.

    Some substances can be obtained in pure state from their solutions by crystallization.

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  • Squares and Square Roots | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4). If a natural number m can be expressed as n2, where n is also a natural number, then… readmore

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    Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4).

    If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. (Scroll down till end of the page)

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    All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place. Square numbers can only have even number of zeros at the end. Square root is the inverse operation of square.

    There are two integral square roots of a perfect square number.

    Positive square root of a number is denoted by the symbol For example, 32=9 gives

    Perfect Square or Square number: It is the square of some natural number. If m=n2, then m is a perfect square number where m and n are natural numbers. Example: 1=1 x 1=12, 4=2 x 2=22.

    Properties of Square number:

    1. A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
    2. A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
    3. Square of even numbers are even. Example: 22 = 4, 42=16 etc.
    4. Square of odd numbers are odd. Example: 52 = 25, 92 = 81, etc.
    5. A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
    6. The difference of squares of two consecutive natural number is equal to their sum. (n + 1)2– n2 = n+1+n. Example: 42 – 32 =4 + 3=7. 122– 112 =12+11 =23, etc.
    7. A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean

    triplet, if m2 + n2 = p2: 32 + 42 = 25 = 52

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  • The Wonderful World of Science | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore

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  • Acids, Bases and Salts | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage There are three types of Substances: Acids, Bases and Salts Acids: Acids are sour in taste. They are corrosive in nature. A concentrated acid cuts through clothes and eats away the wool. If it falls on the skin, it can cause burns. They are good conductors… readmore

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    There are three types of Substances: Acids, Bases and Salts

    Acids: Acids are sour in taste. They are corrosive in nature.

    A concentrated acid cuts through clothes and eats away the wool.

    If it falls on the skin, it can cause burns.

    They are good conductors of electricity, as they allow the passage of electric current through them. (Scroll down till end of the page)

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    Types of Acids:

    (i) Mineral Acids: These are acids prepared from minerals present in the earth’s crust.

    (ii) Organic Acids: These are acids produced by plants and animals (except hydrochloric acid).

    1. Weak Acids: These do not dissociate completely in solution.
    2. Examples: tartaric acid, lactic acid.
    3. Strong Acids: These dissociate completely in solution. Example: nitric acid, sulphuric acid.

    Neutralization: It is the reaction between an acid and a base which results in formation of salt and water.

    Acid + Base ———-> Salt + Water

    Example: HCl + NaOH ———-> NaCl + H2O

    Neutralisation in Everyday Life:

    Indigestion: Too much acid in stomach causes indigestion. It is neutralized by taking an antacid like milk of magnesia.

    Ant sting: When an ant bites, it injects formic acid into the skin. The effect is neutralized by rubbing moist baking soda (sodium hydrogen carbonate) or calamine (containing zinc carbonate).

    (iii) Soil treatment: When the soil is too acidic, it is neutralized by treating with

    quicklime (calcium oxide) or slaked lime (calcium hydroxide).

    Bases: Bases are bitter in taste and soapy to touch.

    Types of Bases:

    1. Weak Bases: These naturally produce less hydroxide ions in solution. Example: magnesium hydroxide, ammonium hydroxide.
    2. Strong Bases: These produce more number of hydroxide ions on dissolving in water. Example: Sodium hydroxide(NaOH), Potassium hydroxide (KOH)

    Substances which are neither acidic nor basic are called neutral.

    An acid and a base neutralise each other and form a salt. A salt may be acidic, basic or neutral in nature.

    Solutions of substances that show different colour in acidic, basic and neutral solutions are called indicators.

    Indicators: It is special chemical that changes its colour to indicate the presence of a chemical substance.

    It is used to confirm the presence of an acid, a base or a neutral solution.

    Classification of Indicators:

    Natural Indicators:

    1. Litmus: It is extracted from lichens. It is available in the form of strips of paper or in the form of a solution.· Acid turns blue litmus red. Bases turn red litmus blue.
    2. Turmeric: It remains yellow in neutral and acidic solutions but turns red in alkaline solutions.
    3. China rose: It turns acidic solutions to dark pink (magenta) and basic solution to green.
    4. Red cabbage: It turns acidic solutions to red and basic solutions to blue.

    Other Indicators:

    1. Methyl Orange: It gives pinkish red colour with acidic solutions and yellow colour with bases.
    2. Phenolphthalein: It is an acid-base indicator. It is colourless in acidic solutions but turns pink in alkali solutions.
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