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  • Data Handling | Study

  • Heat | Assess

  • HERON’S FORMULA | Study

  • Introduction to Graphs | Study

  • IS MATTER AROUND US PURE | Assess

  • Metals and Non-metals | Assess

  • Metals and Non-metals | Study

  • Mindful Eating: A Path to a Healthy Body | Assess

  • Patterns in Mathematics | Assess

  • Data Handling | Study

    Mind Map Overal Idea Content Speed Notes Quick Coverage Data Handling: Deals with the process of collecting data, presenting it and getting result. Data mostly available to us in an unorganised form is called raw data. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Grouped data can be presented readmore

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    Data Handling: Deals with the process of collecting data, presenting it and getting result.

    Data mostly available to us in an unorganised form is called raw data. (Scroll down till end of the page)

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    Grouped data can be presented using histogram. Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.

    In order to draw meaningful inferences from any data, we need to organise the data systematically.

    Frequency gives the number of times that a particular entry occurs.

    Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.

    Statistics: The science which deals with the collection, presentation, analysis and interpretation of numerical data.

    Observation: Each entry (number) in raw data.

    Range: The difference between the lowest and the highest observation in a given data.

    Array: Arranging raw data in ascending or descending order of magnitude. Data can also presented using circle graph or pie chart. A circle graph shows the relationship between a whole and its part.

    There are certain experiments whose outcomes have an equal chance of occurring. A random experiment is one whose outcome cannot be predicted exactly in advance. Outcomes of an experiment are equally likely if each has the same chance of occurring.

    Frequency: The number of times a particular observation occurs in the given data.

    Class Interval: A group in which the raw data is condensed.

    (i) Continuous: The upper limit of a class interval coincides with the lower limit of the next class.

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      • HERON’S FORMULA | Study

        Mind Map Overal Idea Content Speed Notes Quick Coverage Perimeter Perimeter is defined as the outside boundary of any closed shape.  To calculate the perimeter of a given shape we need to add all the sides of the shape. Example: The perimeter of a rectangle is the sum of its all four sides. The unit readmore

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        Perimeter

        Perimeter is defined as the outside boundary of any closed shape. 

        To calculate the perimeter of a given shape we need to add all the sides of the shape.Perimeter

        Example: The perimeter of a rectangle is the sum of its all four sides. The unit of the perimeter is the same as its length.

        Perimeter of the Given rectangle = 3 + 7 + 3 + 7 cm

        Perimeter of rectangle = 20 cm. (Scroll down till end of the page)

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        Area

        Area of any closed figure is the surface enclosed by the perimeter. Unit of Area is the square of the unit of length.

        Area of a triangle

        The general formula to find the area of a triangle, if the height is given, is

        Area of a triangle

        Area of a Right Angled Triangle

        To find the area of a right-angled triangle, we use the formula:

        Area of a triangle

         right-angled triangle, we take the two sides having the right angle, one as the base and one as height.

        Example: Calculate area of a triangle of the Figure.Right angled triangle

        Data: base = 3 cm and height = 4 cm

        Formula: Area of triangle = 1/2 × 3 × 4= 6 cm 2

        Result: Area of a triangle of the Figure is 6 cm 2 .

        Remark: If you take base as 4 cm and height as 3 cm then also the area of the triangle will remain the same.

        Area of Equilateral TriangleEquilateral Triangle

        Equilateral Triangle: Equilateral Triangle is defined as a triangle having three equal sides.

        To calculate the area of the Equilateral Triangle ABC,

        We calculate the height (altitude), AD by making the median of the triangle.

        In the given example, the Height (altitude), AD touches Base of the equilateral triangle at the midpoint of BC, Say point, D. 

        Here the equilateral triangle ABC has three equal sides, such as:

        AB = BC = AC = 10 cm.

        Since, midpoint of BC divides the triangle into two right angle triangles.

        The height, AD, is calculated using Pythagoras theorem. 

        According to Pythagoras theorem, AB2 = AD2 + BD2

        On substituting the values we get, 

        (10)2 = AD2 + (5)2

        AD2 = (10)2 – (5)2

        AD2 = 100 – 25 = 75

        AD = 5√3

        Now we can find the area of the triangle using the formula:

        Area of triangle = 1/2 × base × height

        On substituting the values we get, 

        Area of triangle = 1/2 × 10 × 5√3

         25√3 cm2

        Area of Isosceles TriangleIsosceles Triangle

        In the isosceles triangle also we need to find the height of the triangle then calculate the area of the triangle.

        Here,

        height

        Area of a Triangle — by Heron’s Formula

        The formula of the area of a triangle given by herons is called  Heron’s Formula.

        Heron’s Formula:

        Heron’s Formula

        where a, b and c are the sides of the triangle and s is the semiperimeter 

        semiperimeter

        Generally, this formula is used when the height of the triangle is not possible to find or you can say if the triangle is a scalene triangle.

        Here the sides of triangle areScalene triangle

        AB = 12 cm

        BC = 14 cm

        AC = 6 cm

        triangle

        Application of Heron’s Formula in Finding Areas of Quadrilaterals

        If we know the sides and one diagonal of the quadrilateral then we can find its area by using the Heron’s formula.

        Find the area of the quadrilateral if its sides and the diagonal are given as follows.

        Given, the sides of the quadrilateral

        AB = 9 cmQuadrilaterals

        BC = 40 cm

        DC = 28 cm

        AD = 15 cm

        Diagonal is AC = 41 cm

        Here, ∆ABC is a right angle triangle, so its area will be

        Right angle triangle

        Area of Quadrilateral ABCD = Area of ∆ABC + Area of ∆ADC

        = 180 cm2 + 126 cm2

        = 306 cm2

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        • Introduction to Graphs | Study

          Mind Map Overal Idea Content Speed Notes Quick Coverage Graphical presentation of data is easier to understand. A bar graph is used to show comparison among categories. A pie graph is used to compare parts of a whole. A Histogram is a bar graph that shows data in intervals. (Scroll down till end of the readmore

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          Graphical presentation of data is easier to understand.

          A bar graph is used to show comparison among categories.

          A pie graph is used to compare parts of a whole.

          A Histogram is a bar graph that shows data in intervals. (Scroll down till end of the page)

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          Introduction to Graphs

          A line graph displays data that changes continuously over periods of time. A line graph which is a whole unbroken line is called a linear graph.

          For fixing a point on the graph sheet we need, x-coordinate and y-coordinate.

          The relation between dependent variable and

          through a graph.

          independent variable is shown

          A Bar Graph: A pictorial representation of numerical data in the form of bars (rectangles) of uniform width with equal spacing. The length (or height) of each bar

          represents the given number.

          A Pie Graph: A pie graph is used to compare parts of a whole. The various

          observations or components are represented by the sectors of the circle.

          A Histogram: Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars (rectangles) show the frequency of the class interval, but there is no gap between the bars as there is no gap between the

          class intervals.

          Linear Graph: A line graph in which all the line segments form a part of a single line. Coordinates: A point in Cartesian plane is represented by an ordered pair of numbers.

          Ordered Pair: A pair of numbers written in specified order.

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          • IS MATTER AROUND US PURE | Assess

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            • Metals and Non-metals | Assess

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              • Metals and Non-metals | Study

                Mind Map Overal Idea Content Speed Notes Quick Coverage Elements are classified as metals and non-metals based on different properties. The properties of metals and non-metals are given in the form of table below- Metals Non-metals Metals are lustrous, that is, they have a property to shine. They are not lustrous, that is, they do readmore

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                Elements are classified as metals and non-metals based on different properties. The properties of metals and non-metals are given in the form of table below-

                MetalsNon-metals
                Metals are lustrous, that is, they have a property to shine.They are not lustrous, that is, they do not have shining surface. except, graphite and iodine
                All metals exist as solids except mercury which is liquid at room temperature.They are generally soft, except diamond. 
                They can be drawn into wires, this is known as Ductility.They are non-ductile.
                Metals can be converted into sheets, this is known as Malleability, except mercuryThey are non-malleable 
                They are good conductors of electricity and heat. Except Lead and mercury.They are poor conductors of electricity and heat. Exception-graphite is good conductor of electricity
                They have high density and high melting point. Exception-sodium and potassium have low melting pointsThey have low density compared to metals and low melting point except Diamond which has high melting point

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                Elements are classified as metals and non-metals based on different properties. The properties of metals and non-metals are given in the form of table below-

                MetalsNon-metals
                Metals are lustrous, that is, they have a property to shine.They are not lustrous, that is, they do not have shining surface. except, graphite and iodine
                All metals exist as solids except mercury which is liquid at room temperature.They are generally soft, except diamond. 
                They can be drawn into wires, this is known as Ductility.They are non-ductile.
                Metals can be converted into sheets, this is known as Malleability, except mercuryThey are non-malleable 
                They are good conductors of electricity and heat. Except Lead and mercury.They are poor conductors of electricity and heat. Exception-graphite is good conductor of electricity
                They have high density and high melting point. Exception-sodium and potassium have low melting pointsThey have low density compared to metals and low melting point except Diamond which has high melting point

                Chemical Properties of Metals

                • Metals react with air or oxygen to form metal oxide.

                For Example, Copper reacts with oxygen to form copper oxide.

                Metal + O2 → Metal oxide

                2Cu + O2 → 2CuO

                4Al + 3O­2 → 2Al2O3

                • Oxides of metals can react with both acids and bases to produce salt and water. Such oxides are known as Amphoteric Oxides.

                Al2O3 + 6HCl → 2AlCl3 + H2O

                Aluminium oxide
                • Metals also reacts with water to form metal oxide. Metal oxide in turn can react with water to form metal hydroxide. For Example

                2Na + 2H2O → 2NaOH + 1H2

                2Al + 3H2O → Al2O3 + 3H2

                • Metals also reacts with dilute acids to form salt and hydrogen. For example, magnesium reacts with dilute hydrochloric acid to form magnesium chloride and hydrogen.

                Metal + Acid → Metal Salt + Hydrogen

                Mg + 2HCl → MgCl2 + H2

                Chemical Properties of Nonmetals

                • Non-metals react with oxygen to form non-metal oxide.

                Non-metal + Oxygen → Non-metal oxide

                C + O2 → CO2

                • Non-metals do not react with water and acids to evolve hydrogen gas.
                • Non-metals can react with salt solution; more reactive elements will displace the less reactive non-metal.

                2 NaBr (aq) + Cl2(aq) → 2NaCl (aq) + Br2 (aq)

                • Non-metals can also react with hydrogen to form hydrides.

                H2(g) + S(l) → H2S(g)

                Reactivity Series

                The series in which metals are arranged in the decreasing order of reactivity, it is known as Reactivity Series.

                Reactivity Series

                Fig.1. Reactivity Series

                Ionic Compounds

                Compounds formed due to the transfer of electrons from a metal to a non-metal are known as Ionic Compounds.

                Ionic Compounds

                Covalent Bond

                Bond formed by sharing of electrons between the two atoms. They share their valence electrons to gain stability.

                Covalent Bond

                Properties of Ionic Compounds

                • They are generally hard and solid.
                • They have a high melting and boiling point.
                • They are soluble in water but insoluble in inorganic solvents such as ether etc.
                • They are conductors of electricity in molten and solution state.

                Occurrence of Metals

                Elements or compounds which occur naturally in earth crust are known as Minerals. Minerals from which pure metals can be extracted are known as Mineral Ores.

                Ore

                Extraction of pure metals from its ores/steps for extraction of metals from its ore

                • The first step is enrichment of the ore.
                • Second step includes extraction of metals
                • Third steps involve refining of metal

                Gangue – Ores contain different impurities in it such as sand, soil etc. These impurities are known as Gangue.

                Extracting Metals which are low in activity series

                Metals which are low in activity series are unreactive. The oxides of such metals can be reduced to metals by heating alone. For Example, Cinnabar (HgS)

                Cinnabar

                Extracting Metals in the middle of the Activity Series

                These metals are moderately reactive. They exists as sulphides or carbonates in nature. Before reduction, metal sulphides and carbonates must be converted into metal oxides. Sulphide ores are converted into oxides by heating strongly in presence of excess air, this is known as Roasting. Carbonate ores are converted into oxides by heating in limited air. This is known as Calcination.

                Roasting

                Roasting

                Calcination

                Calcination

                Reduction-metal oxides can be reduced to metals using reducing agent such as such as Carbon.

                Extracting metals towards the top of the activity series

                The metals are highly reactive. They cannot be obtained by heating. For Example, Sodium, magnesium and calcium are obtained by the electrolysis of their molten chlorides.

                At cathode  Na+ + e– → Na

                At anode   2Cl– → Cl2 + 2e–

                Refining of Metals

                Refining of impure metal is done using electrolytic refining. Impure copper is used as anode and strip of pure copper is used as Cathode. Acidified copper sulphate is used as electrolyte. When electric current is passed through this, impure metal from the anode gets deposited in the electrolyte solution, whereas pure metal from the electrolyte is deposited at cathode.

                Deposition of insoluble residue formed from the dissolution of anode during commercial electrolysis.

                Electrolytic refining

                Electrolytic refining

                Corrosion

                Metals when exposed to moist air for a long period of time, they become corroded. This is known as Corrosion. For Example, Silver reacts with moist air and becomes black in colour due to silver sulphide coating.

                Iron + oxygen → Iron (III) oxide

                Fe + O­ 2 → Fe2O3

                Prevention of Corrosion

                • Rusting of iron can be prevented by oiling, galvanising, painting, greasing etc.
                • To protect steel and iron from rusting, a thin layer of zinc is coated on them, this is known as Galvanization.

                Alloy

                Mixture of two or more metals or metal and non-metal is known as Alloy. For Example,

                • Brass is an alloy of copper and zinc.
                • Bronze in an alloy of copper and tin.
                • Solder is an alloy of lead and tin.
                • Amalgam is one metal that is mercury.
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