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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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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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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-
| Metals | Non-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 mercury | They 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 points | They 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-
| Metals | Non-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 mercury | They 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 points | They have low density compared to metals and low melting point except Diamond which has high melting point |
For Example, Copper reacts with oxygen to form copper oxide.
Metal + O2 → Metal oxide
2Cu + O2 → 2CuO
4Al + 3O2 → 2Al2O3
Al2O3 + 6HCl → 2AlCl3 + H2O
2Na + 2H2O → 2NaOH + 1H2
2Al + 3H2O → Al2O3 + 3H2
Metal + Acid → Metal Salt + Hydrogen
Mg + 2HCl → MgCl2 + H2
Non-metal + Oxygen → Non-metal oxide
C + O2 → CO2
2 NaBr (aq) + Cl2(aq) → 2NaCl (aq) + Br2 (aq)
H2(g) + S(l) → H2S(g)
The series in which metals are arranged in the decreasing order of reactivity, it is known as Reactivity Series.
Fig.1. Reactivity Series
Compounds formed due to the transfer of electrons from a metal to a non-metal are known as Ionic Compounds.
Bond formed by sharing of electrons between the two atoms. They share their valence electrons to gain stability.
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.
Extraction of pure metals from its ores/steps for extraction of metals from its ore
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)
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
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 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
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
Mixture of two or more metals or metal and non-metal is known as Alloy. For Example,
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Mind Map Overal Idea Content Speed Notes Quick Coverage An equation isa condition ona variable suchthat two expressions in the variable should have equalvalue. Thevalue of thevariable for whichthe equation issatisfied is called the solution ofthe equation. An equation remains the same if the LHSand the RHSare interchanged. (Scroll down till end of the page)… readmore
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An equation isa condition ona variable suchthat two expressions in the variable should have equalvalue.
Thevalue of thevariable for whichthe equation issatisfied is called the solution ofthe equation.
An equation remains the same if the LHSand the RHSare interchanged. (Scroll down till end of the page)
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In case ofthe balanced equation, if we add the same number to both thesides, or subtract the same number from both the sides,
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multiply both sidesby the same number, or divide both sidesby the samenumber, the balance remains un disturbed,
i.e.,the value of the LHS remains equal to the value of the RHS The above property gives a systematic method of solving an equation.
We carry out a series of identical mathematical operations on the two sides of the equation in such a waythat on oneof the sides we get justthe variable. Thelast step isthe solution of the equation.
Transposing means moving to the other side.
Transposition of a number has the same effect as adding same number to (or subtracting the same number from) both sides of the equation.
Whenyou transpose a number fromone side ofthe equation tothe other side, you change itssign.
For example, transposing +3 fromthe LHS tothe RHS in equation x + 3 = 8 gives x = 8 – 3 (= 5).
We can carry out the transposition of an expression in thesame way as the transposition of a number.
We havelearnt how to construct simple algebraic expressions corresponding to practical situations.
Wealso learnt how,using the technique of doing thesame mathematical operation (for example adding the samenumber) on bothsides, we could build an equation starting fromits solution.
Further, we also learnt that we could relate a given equation tosome appropriate problem/puzzlefrom the equation. practical situation and build a practical word.
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Mind Map Overal Idea Content Speed Notes Quick Coverage The collection, recording and presentation of data help us organiseour experiences and draw inferences from them. Before collecting data we need to know what we would use it for. The data that is collected needs to be organised in a propertable, so that it becomeseasy to… readmore
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The collection, recording and presentation of data help us organiseour experiences and draw inferences from them.
Before collecting data we need to know what we would use it for.
The data that is collected needs to be organised in a propertable, so that it becomeseasy to understand and interpret (Scroll down till end of the page)
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Average is a numberthat represents or shows the central tendencyof a group of observations or data.
Arithmetic mean is one of the representative values of data.
Mean = sum of all observations/ Number of observations.
Mode is another form of central tendency or representative value.
The mode of a set of observations is the observation that occurs most often.
If each of the value in a data is occurring one time, then all are mode.
Sometimes we also say that this data has no mode since none of them is occurring frequently.
Median is also a form of representative value.
It refers to the value which lies in the middle of the data with half of the observations above it and the other half below it.
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A bar graph is a representation of numbers using bars of uniform widths.
Double bar graphshelp to comparetwo collections of data at a glance.
Double bar graphshelp to comparetwo collections of data at a glance.
There are situations in our life, that are certain to happen, some that are impossible and some that may or may not happen.
The situation that may or may not happen has a chanceof happening.
Probability: A branch of mathematics that is capable of calculating the chance or likelihood of an event taking place (in percentage terms).
If you have 10 likelihoods and you want to calculate the probability of 1 event taking place,it is said that its probability is 1/10 or event has a 10% probability of taking place.
Events that have many possibilities can have probability between 0 and 1.
Important Formulae – Data Handling
1. A trial is anaction which results in one or several outcomes. 2. An experiment in whichthe result ofa trial cannot be predicted inadvance is called a random experiment.
3. An event associated to a random experiment is thecollection of someoutcomes of theexperiment.
4. An event associated witha random experiment is said tohappen if anyone of theoutcomes satisfying thedefinition of theevent is anoutcome of theexperiment when it is performed.
5. The Empirical probability ofhappening of an event E is defined as: P(E)= Number of trials in which the event happened/ Total number of trials.
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Mind Map Overal Idea Content Speed Notes Quick Coverage Heat: It is a form of energy, which makes any object hot or cold. The materials which allow heat to pass through them easily are conductors of heat. The materials which do not allow heat to pass through them easily are called insulators. Temperature: The degree… readmore
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Heat: It is a form of energy, which makes any object hot or cold.
The materials which allow heat to pass through them easily are conductors of heat.
The materials which do not allow heat to pass through them easily are called insulators.
Temperature: The degree of hotness of an object is called temperature.
Heat is the cause of temperature.
Our sense of touch is not reliable to measure the temperature. (Scroll down till end of the page)
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Heat:
It is a form of energy, which makes any object hot or cold.
Temperature: The degree of hotness of an object is called temperature. Our sense of touch is not reliable to measure the temperature.
Thermometer is a device used for measuring temperatures.
Heat is the cause of temperature.
Clinical thermometer is used to measure our body temperature.
Transfer of Heat: Heat flows from a hotter object to a colder object until both objects reach the same temperature.
The heat flows from a body at a higher temperature to a body at a lower temperature.
There are three ways in which heat can flow from one object to another.
These are conduction, convection and radiation.
Conduction: It is the process by which heat is transferred from the hotter end to the colder and end of an object.
Convection: It is the flow of heat through a fluid from places of higher temperature to places of lower temperature by movement of the fluid itself.
Radiation: It is the mode of transfer of heat in which energy is directly transferred from one place to another.
It does not need any material medium.
Dark-coloured objects absorb radiation better than the light-coloured objects.
That is the reason we feel more comfortable in light-coloured clothes in the summer.
Woollen clothes keep us warm during winter.
It is so because wool is a poor conductor of heat and it has air trapped in between the fibres.
Thermometer:
Thermometer is a device used for measuring temperatures.
Clinical thermometer:
Clinical thermometer is used to measure our body temperature.
A thermometer used to measure the temperature of our body is called a clinical thermometer.
For other purposes, we use the laboratory thermometers.
The range of these thermometers is usually from –10°C to 110°C.
The normal temperature of the human body is 37°C.
It consists of a long, narrow, uniform glass tube with a bulb containing mercury at one end.
There is a kink near the bulb.
The range of clinical thermometer is from 35°C to 42°C. (Or from 94°F to 108°F).
Laboratory Thermometer:
Laboratory Thermometer: It is a thermometer used to measure the temperature of objects other than our body.
It consists of a column of mercury enclosed in a glass casing.
The column is continuous without any kink.
It measures a range of temperature from -10˚C to 110˚C.
Sea Breeze:
Sea Breeze: Durign the day, the land heats up faster than the sea.
Warm air above the land rises and cold air from sea takes its place.
Warm air from the land moves towards the sea to compele the cycle.
This produces a sea breeze from the sea to the land.
Land Breeze:
Land Breeze: At night the land cools faster than sea.
The warm air above the sea rises.
This warm air is replaced by colder air from the land producing a land breeze.
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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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Mind Map Overal Idea Content Speed Notes Quick Coverage Plane figure The figures which we can be drawn on a flat surface or that lie on a plane are called Plane Figure. Example – Circle, Square, Rectangle etc. Solid figures The 3D shapes which occupy some space are called Solid Figures. Example – Cube, Cuboid,… readmore
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The figures which we can be drawn on a flat surface or that lie on a plane are called Plane Figure.
Example – Circle, Square, Rectangle etc.
The 3D shapes which occupy some space are called Solid Figures.
Example – Cube, Cuboid, Sphere etc. (Scroll down the till the end of the page)
Volume
Space occupied by any solid shape is the capacity or volume of that figure. The unit of volume is a cubic unit.
The area of all the faces of the solid shape is its total surface area. The unit of surface area is a square unit.
The surface area of the solid shape after leaving the top and bottom face of the figure is called the lateral surface of the shape. The unit of lateral surface area is a square unit.
Cube is a solid shape having 6 equal square faces.
| Lateral surface area of a cube | 4s2 |
| Total surface area of a cube | 6s2 |
| The volume of a cube | s3 |
| Diagonal | √3 s, s = edge of the cube = side length of face of cube |
What is the capacity of a cubical vessel having each side of 8 cm?
Solution
Given side = 8 cm So, Volume of the cubical vessel = l3 = (8)3 = 256 cm3.
Cuboid is a solid shape having 6 rectangular faces at a right angle.
| Lateral surface area of a cuboid | 2h(l + b) |
| Total surface area of a cuboid | 2(lb + bh + lh) |
| Volume of a cuboid | lbh |
| Diagonal | l = length, b = breadth, h = height |
What is the surface area of a cereal box whose length, breadth and height is 20 cm, 8 cm and 30 cm respectively?
Given, length = 20 cm, breadth = 8 cm, Height = 30 cm
Total surface area of the cereal box = 2(lb + bh + lh)
= 2(20 × 8 + 8 × 30 + 20 × 30)
= 2(160 + 240 + 600)
= 2(1000) = 2000 cm2.
If we fold a rectangular sheet with one side as its axis then it forms a cylinder. It is the curved surface of the cylinder. And if this curved surface is covered by two parallel circular bases then it forms a right circular cylinder.
| Curved surface area of a Right circular cylinder | 2πrh |
| Total surface area of a Right circular cylinder | 2πr2 + 2πrh = 2πr(r + h) |
| The volume of a Right circular cylinder | πr2h |
| r = radius, h = height |
If a right circular cylinder is hollow from inside then it has different curved surface and volume.
| Curved surface area of a Right circular cylinder | 2πh (R + r) |
| Total surface area of a Right circular cylinder | 2πh (R + r) + 2π(R2 – r2) |
| R = outer radius, r = inner radius, h = height |
Find the Total surface area of a hollow cylinder whose length is 22 cm and the external radius is 7 cm with 1 cm thickness. (π = 22/7)
Given, h = 22 cm, R = 7 cm, r = 6 cm (thickness of the wall is 1 cm).
Total surface area of a hollow cylinder = 2πh(R + r) + 2π(R2 – r2)
= 2(π) (22) (7+6) + 2(π)(72 – 62)
= 572 π + 26 π = 598 π
= 1878.67 cm2
If we revolve a right-angled triangle about one of its sides by taking other as its axis then the solid shape formed is known as a Right Circular Cone.
| Curved surface area of a Right Circular Cone | πrl = πr[√(h2 + r2)] |
| Total surface area of a Right Circular Cone | πr2 + πrl = πr(r + l) |
| The volume of Right Circular Cone | (1/3) πr2h |
| r = radius, h = height, l = slant height |
A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.
| Curved or Lateral surface area of a Sphere | 4πr2 |
| Total surface area of a Sphere | 4πr2 |
| Volume of a Sphere | (4/3) πr3 |
| R = radius |
If we cut the sphere in two parts then is said to be a hemisphere.
| Curved or Lateral surface area of a Sphere | 2πr2 |
| Total surface area of a Sphere | 3πr2 |
| Volume of a Sphere | (2/3) πr3 |
| r = radius |
If we have a metal piece of cone shape with volume 523.33 cm3 and we mould it in a sphere then what will be the surface area of that sphere?
Given, volume of cone = 523.33 cm3
Volume of cone = Volume of Sphere
Volume of sphere = 100 π cm3
125 = r3
r = 5
Surface area of a sphere = 4πr2
= 314.28 cm2.
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Mind Map Overal Idea Content Speed Notes Quick Coverage Linear Equation in One variable: The expressions which form the equation that contain single variable and the highest power of the variable in the equation is one. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Linear Equations in One Variable… readmore
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Linear Equation in One variable: The expressions which form the equation that contain single variable and the highest power of the variable in the equation is one. (Scroll down till end of the page)
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Linear Equations in One Variable
An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side.
The equations we study in Classes VI, VII and VIII are linear equations in one variable. In such equations, the expressions which form the equation contain only one variable. Further, the equations are linear, i.e., the highest power of the variable appearing in the equation is 1.
A linear equation may have for its solution any rational number.
An equation may have linear expressions on both sides. Equations that we studied in Classes VI and VII had just a number on one side of the equation.
Just as numbers, variables can, also, be transposed from one side of the equation to the other.
Occasionally, the expressions forming equations have to be simplified before we can solve them by usual methods. Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.
The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved
using linear equations.
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