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CONTENTSCLASS – VIII (Mathematics)

Page Number

ALGEBRA:

Chapter 1. Rational Numbers 2Chapter 2. Linear Equations in One variables 7Chapter 3. Square & Square Roots 10Chapter 4. Cube & Cube Roots 15Chapter 5. Comparing Quantities 19Chapter 6. Algebric Expressions 23

STATISTICS & PROBABILITY :

Chapter 7. Data Handeling 27GEOMETRY:

Chapter 8. Understanding Quadrilaterals 34

CLASS – VIII (Science)

Chapter 1. Force & Pressure 40Chapter 2. Friction 45Chapter 3. Sound 51Chapter 4. Metals & Non Metals 57Chapter 5. Coal & Petroleum 61


About Rational NumbersA rational number is a number which can be expressed as a ratio of twointegers.Non-integer rational numbers (commonly called fractions) are

usually written asab , where b is not equal to zero. a is called the numerator

and b is called the denominator.

Rational Number: Any number of the type pq where p and q are

integers and 0q is called a rational number. Eg:4 1,– ,5 & 03 7

are rational numbers.

CHAPTER 1: RATIONAL NUMBERS


Whole Numbers: The counting numbers along with 0 are called wholenumbers or we can say natural numbers and 0 form the whole numbersystem.For example: 0, 1, 2, 3, 4,……

Integers: Whole numbers with their negative images are calledintegers or we can say natural numbers with their negative images and0 form the group of integers.

For example: 0, 1, 2, 3,........ Closure Property: If we combine two elements from a set by some

operation ( , , , ) and the result also falls in the same set, we saythat the two elements are closed under that operation.

Commutative Property: If a b b a where is any operation, forexample , , , then, a and b are said to be commutative.

Associative Property: If * * * *a b c a b c where is any operation,for example then a, b and c are said to be associative.

Properties of Operations(On different types of numbers)1. Under Closure Property:

Properties Numbers

Closed under Addition Subtraction Multiplication Division

Whole numbers Yes No Y es No

Natural numbers Yes Yes/ N o Closed /

Not Closed Both

Y es No

Integers Yes Yes Y es No Rational numbers Yes Yes Y es Yes


2. Under Commutative Property: Properties Numbers

Commutative under

Addition Multiplication Subtraction Division Natural numbers

Yes Yes/ No Commutative / Non Commutative Both

No

No

Integers Yes Yes No No Whole numbers

Yes Yes No Yes

Rational numbers

Yes Yes No No

3. Under Associative Property: P r op er tie s Nu m b e rs

A ssociat ive under

A dd ition M u lt ip licat ion S ubtraction D iv isio n Natu ral numbers

Y e s/ N o A ss ocia tive /

No n As so ciat iv e B ot h

Y es N o No

Integers Y es Y es N o No Who le numbers

Y es Y es N o No

Rationa l numbers

Y es Y es N o No

Properties

Numbers


Properties of Rational Numbers

For any rational number ab , where 0b we have :

P roperty

Example

C onclusion

0 0a a ab b b

2 2 2

0 05 5 5

Zero (0) is calle d the additive identity o f rational num bers.

0a a a ab b b b

1 1 1 103 3 3 3

ab is the n egative or

additive invers e o f ab

or

v ice-versa.

1 1a a ab b b

5 5 51 1

6 6 6

O ne (1) is the m u ltip lica tive iden tity of rational numbers.

1a b b ab a a b

7 3 3 713 7 7 3

ba

is the recipr ocal o r

m ultiplicative inverse of ab

or vice-versa.

Distribution of multiplication over addition and subtraction

For any rational numbers a, b and c,

(i) a b c a b a c

(ii) a b c a b a c

Example (i) : 2 2 2 2 2 343 33 5 3 3 5 15

(ii) : 1 3 2 1 3 1 2 15 4 3 5 4 5 3 60


Representation of rational numbers on the number lineTo represent the rational numbers geometrically, we use a number line. Webegin by drawing a line and marking on it points corresponding to any twoconsecutive integers. If the distance between the two consecutive integersis taken as a unit of length, then the rational numbers can be arranged onthe line in a natural order.

Rational numbers between two rational numbersThere are finite number of integers (natural numbers) between two integers(natural numbers).What about rational numbers between rational numbers?There are infinite number (countless) of rational numbers between tworational numbers.


CHAPTER 2: LINEAR EQUATIONS IN ONE VARIABLE

An algebraic equation is equality involving variables. It has an equalitysign. The expression on the left of the equality sign is the Left Hand Side(LHS), that on the right of the equality sign is the Right Hand Side (RHS). Algebraic Expression: An expression consisting of one or more numbers

and variables along with one or more arithmetic operations.

For example: 6x, 3x – 2, 2x + 5y, 3xy + 1, x + y + xy, x2 + x + 1


Algebraic Equation: An algebraic equation is an equality involvingalgebraic expressions.

For example : 16 1,3 2 3, 4 52

x x xy

Solution of an equation: The value of the variable for which the value ofthe expression on LHS of an algebraic equation equals the value of theexpression on RHS is called the solution of the equation.

Degree of an equation: The degree of an equation having not more thanone variable in each term is the exponent of the highest power to whichthat variable is raised in the equation.

Example:First degree equation : 3x – 17 = 0Second degree equation : 5x2 – 2x + 1 = 0Third degree equation : 5x3 – 2x2 + 1 = 0

Linear Equation in one variable:Equation of first degree in a single variable is called a linear equation in onevariable.

Equation of the type ax + b = 0, where a and b are real numbers and 0a ,is known as a linear equation in one variable ’x’.Example: 3x – 17 = 0, 7x – 1 = 10Solution of a linear equation in one variable

Solution of ax + b = 0 is given by – , 0bx aa

How to find the solution of equations?We assume that the two sides of the equation arebalanced.Hence we perform the same mathematicaloperations on both sides of the equation

A linear equation in onevariable always has a

unique solution i.e. only onesolution


Solution of Linear Equation in one variable having variable on one side only:A ‘solution’ or ‘root’ of an equation is the value which when substituted forthe variable makes the equation true.To solve a linear equation in one variable, we follow some or all of the following:1. Remove brackets, if any ; Eliminate fractions, if any.2. Addition or subtraction of the same quantity on both sides of the equation.3. Multiplication or division by the same non-zero quantity on both sides of

the equation.4. Isolate the variable on one side.5. Divide both sides by the coefficient of the variable so as to make it unity.6. Check the solution in the original equation.Equation obtained after simplifying with the help of any of the aboveoperations is called an equivalent equation.

Solution of linear equations having variable on both sides:When we have a linear equation having variable on both sides, then just asnumbers, variables can also be transposed from one side of the equation tothe other. So, we simplify the equation such that all the terms containing thevariable are on either side of the equation. The equation reduces to a linearequation having constant on one side only.Applications of Linear Equations:Linear equations are used to solve word problems.Example 1: Mr.Gupta’s age is three times his son’s age. Ten years ago, he wasfive times his son’s age. Find their present ages.Solution: Let the present age of son be x years.

Then the present age of father is 3x years.Their ages ten years ago, son’s age = x – 10 years, father’s age = 3x – 10 years. According to the given statement, 3x – 10 = 5 (x – 10) ; 3x = 5x – 40 – 2x = – 40 x = 20 Present age of son is 20 years and present age of father is 60 years.


Exponent: =tim es

y

y

x x × x × ........× x . Here, x is called the base and y is called

the exponent. We read it as ‘x raised to power y’.

For example: 3 raised to power 5 = 5

5 times

(3) 3 3 3 3 3 243 Square numbers:A square number is the number obtained by multiplying any natural numberwith itself.For example: 32 = 3 × 3 = 9.

In general, if x and y are natural numbers and 2 =x y then y is called asquare number.Square numbers are also called ‘perfect squares’.

Properties of square numbers:1. All square numbers can be put in the form of a square. Here are some pictures of the square numbers:

* * * * * * * * * * * * * * * 1 * * * * * * * * * * * * * * 4 * * * * * * * * * * * * 9 * * * * * * * * * 16 * * * * * 252. The unit’s digit of any square number is either 0, 1, 4, 5, 6 or 9.

You can check it with any example. However, converse may not be true.Any number ending with 0, 1, 4, 5, 6 or 9 may not be a square number. Forexample: 11, 24, 15, 26, 19 are some numbers ending with these digits butthey are not perfect squares.

3. Numbers having 2, 3, 7 or 8 in the unit’s place can never be perfectsquares.

CHAPTER 3: SQUARE & SQUARE ROOTS


4. Square numbers having 1 in the unit’s place are squares of numbersending with 1 or 9 and vice-versa.For example: (1)2 = 1; (9)2 = 81;(11)2 = 121; (19)2 = 361

5. Square numbers having 6 in the unit’s place are squares of numbersending with 4 or 6 and vice-versa.For example: (4)2 = 16; (6)2 = 36;(14)2 = 196; (16)2 = 256

6. Square numbers having 5 in the unit’s place are squares of numbersending with 5 and vice-versa.For example: (5)2 = 25; (15)2 = 225

7. Square numbers having 0 in the unit’s place are squares of numbersending with 0 and vice-versa. Moreover, a perfect square always has aneven number of zeros at the end. If a number has an odd number of zerosat the end, it can never be a perfect square.For example: (10)2 = 100. 100 is a perfect square. It has 2 (even number)zeros at the end while 10 is not a perfect square and it has only 1(oddnumber) zero at the end.

8. Squares of even numbers are always even and squares of odd numbersare always odd.

For example: (2)2 = 4; (3)2 = 9; (11)2 = 121; (14)2 = 196

Triangular numbers:Triangular numbers are the numbers whose dot pattern can be arranged asa triangle. * * * * * 1 * * * * * * * * 3 * * * * * * * * * 6 * * * * * * * * 10 * * * * * 151, 3, 6, 10 and 15 are triangular numbers.

Note: Dot pattern of 1 is a single star. It can be considered a triangle as wellas a square. Thus, 1 is both a triangular number and a square number.


Now, two triangles when combined together make a square.

Similarly, if we combine two triangular numbers, we get a square number.For example: 1 + 3 = 22

3 + 6 = 9 = 32

6 + 10 = 16 = 42

Some patterns in square numbers:I. There are 2n non perfect squares between n2 and (n + 1)2.II. Any square number can be expressed as a sum of consecutive odd

numbers starting from 1 and vice-versa.For example:Sum of first two odd numbers = 1 + 3 = 4 = 22

Sum of first three odd numbers = 1 + 3 + 5 = 9 = 32

Sum of first four odd numbers = 1 + 3 + 5 + 7 = 16 = 42

Sum of first five odd numbers = 1 + 3 + 5 + 7 + 9 = 25 = 52

Note: observe that when we add n consecutive odd numbers, we get a squareof n. This can be used as a method to check whether a given number is asquare number or not.

III. Squares of odd numbers can be expressed as a sum of two consecutivenatural numbers.For example: consider 3, 5, and 7Their respective squares are 9, 25 and 49.Now, 9 = 4 + 5 25 = 12 + 13 49 = 24 + 25In terms of n, if n is an odd number then we can

write2 2

2 n – 1 n +1n = +2 2

.

IV. For any natural number n, (n + 1) × (n – 1) = n2 – 1

Note: for any natural number n, (n + 1) × (n – 1) represents a product of twoconsecutive odd or even numbers.


V. For calculating squares of numbers having 1 in each place, you canfollow the pattern shown below.

12 = 1112 = 1 2 11112 = 1 2 3 2 111112 = 1 2 3 4 3 2 1111112 = 1 2 3 4 5 4 3 2 1

Note the pattern: there are 4 one’s in 1111. To calculate its square, go till 4, i.e.1234 and then backwards, i.e. 1234321.

Finding the square of a number without actual multiplicationWe know that the square of a number is the value obtained by multiplying thenumber with itself. There are techniques by which the square can be computedwithout doing the actual multiplication.Algebraic Identities:

2 2 2( ) 2a b a ab b and 2 2 2( ) 2a b a ab b

Pythagorean tripletsA set of three natural numbers m, n and p satisfying the equation m2 + n2 = p2

is called a Pythagorean triplet.For example: (6, 8, 10) is a Pythagorean triplet because 62 + 82 = 102

[62 = 36, 82 = 64, 102 =100 and 36 + 64 = 100]

For any natural number n > 1, we have (2n) 2 + (n2 – 1)2 = (n2 + 1)2.So, 2n, (n2 – 1) and (n2 + 1) always forms a Pythagorean triplet.


Square root of a numberThe square root of a number is the value which when multiplied by itselfgives the original number.

Mathematically, If x2 = y , then we say, ‘y is the square of x’ and ‘x is the

square root of y’. or y x .

3 94 165 25

The symbol is used for square root of a number..

For example: 22 = 4 4 2Note: we know. Also, (– 2)2 = 4

This means. 4 2 or –2

Methods of Finding the square root of a number1) by prime factorization 2) by repeated subtraction 3) by long division

Finding the square root by prime factorisationTo find the square root of a number, we shallfollow the following steps:Step 1: find the prime factors of the given number.Step 2: group the same prime factors in sets of two.Step 3: choose one prime number from each set.Step 4: find the product of the chosen primes.The product is the desired square root.


A cube is a solid three dimensional figure with each face a square. For any real number x, x3 = x × x × x.

Cube NumbersA cube number (also called a cubic number or a perfect cube) is an integerthat can be written as a cube of some other integer.

Mathematically, a number x is a perfect cube if there exists an integer y suchthat x = y3

For example: Some cube numbers are shownbelow.Cube Numbers Explanation1 is a cube number 1 = 1 × 1 × 1= 13

8 is a cube number 8 = 2 × 2 × 2 = 23

125 is a cube number 125 = 5 × 5 × 5 = 53

–8 is a cube number 8 = (–2) × (–2) × (–2) = (–2)3

Properties of Cube Numbers

1. There is no smallest cube number as cube numbers can be negative.

For example, (–8) = (–2)3 is a cube number.

2. Cube numbers of even and odd integers are even and odd respectively.

3. Cube numbers of positive and negative integers are positive and negativerespectively.

CHAPTER 4: CUBE & CUBE ROOTS

Hardy – Ramanujannumber1729 is smalllest Hardy -Ramanujan numberwhich can be expressedas a sum of two cubes intwo diffrent ways1729 = 1728 + 1 = 123 + 13

1000 + 729 = 103 + 93


4. The table below shows the relation between the unit’s digit of the numbersand their cubes.

Unit digit of the num be r 1 2 3 4 5 6 7 8 9Unit's d igit of the re spe ct ive cube 1 8 7 4 5 6 3 2 9

5. Some cube numbers are also square numbers.For example: 64 = 8 × 8 = 82 (Perfect square)Also, 64 = 4 × 4 × 4 = 43 (Perfect cube)This happens when a number is a perfect sixth power.64 = 2 × 2 × 2 × 2 × 2 × 2 = 26

6. Cube numbers can be expressed as some of consecutive odd numbersin the pattern shown below.13 = 1 = 1 (one odd number)23 = 8 = 3 + 5 (two consecutive odd numbers)33 = 27 = 7 + 9 + 11 (three consecutive odd numbers)43 = 64 = 13 + 15 + 17 + 19 (four consecutive odd numbers)53 = 125 = 21 + 23 + 25 + 27 + 29 (five consecutive odd numbers)

7. Numbers such as 1729, 4104, 13832 can be expressed as sum of twocube numbers in two different ways. Such numbers are known asHardy-Ramanujan numbers.

8. Each prime factor of a number occurs three times or in multiples ofthree in the prime factorisation of its cube. For example: Prime factorisation of 10 = 2 × 5

Prime factorisation of 103 (1000) = 2 × 2 × 2 × 5 × 5 × 5


Method to check whether a given number is a cube number (perfect cube)or not Let the number be x.

1. Find the prime factors of the number x.2. Group the factors in triples such that all three factors in each triple

are the same.3. If all the factors are grouped, the number is a cube number

(perfect cube).4. If any factor is left ungrouped, the number is not a cube number

(perfect cube).Cube RootIf x is a cube number such that x = y3, then y is the cube root of x.In other words, the cube root of a given number is the number which whencubed produces the given number. For example: The cube root of 8 is 2because 23 = 2 × 2 × 2 = 8The cube root of 27 is 3 because 33 = 3 × 3 × 3 = 27

We use the symbol 3 to denote cube root.

Cube root of 8 is written as 3 8 . Cube root of 27 is written as 3 27 .Remark:Finding the cube root and finding the cube of any number are inverseoperations of each other.The following table shows some cubes and cube roots. Cubes Cube Roots Symbolic expression 1 1 13 = 1 2 8 23 = 8 3 27 33 = 27 4 64 43 = 64 5 125 53 = 125


Properties of Cube Roots

1. The cube roots of positive and negative cubic numbers are positive andnegative respectively.

2. The cube roots of even and odd perfect cubes are even and oddrespectively.

3. The cube root of product of two perfect cubes is the product of cuberoots of the two cubes.

Let x and y be two perfect cubes. Then 33 3xy x y .

4. The cube root of quotient of two perfect cubes is the quotient of cuberoots of the two cubes.

Let x and y be two perfect cubes. Then 3

33

, .x x x yy y

5. If 31, then .x x x Clearly,, 3 8 2 8 , 3 27 3 27 etc.

6. If 30 1, then .x x x Clearly,, 31 1 18 2 8 , 3

1 1 127 3 27

etc.

7. The cube root of a perfect cube can be found by the method of primefactorisation.


CHAPTER 5: COMPARING QUANTITIES

Comparing Quantities A ratio is a comparison of two numbers, expressed as the quotient we geton dividing the first by the second. If in a team of 15 students, there are 9boys and 6 girls, we can say that the ratio of boys to girls is 9 : 6 or in

fractions it is 9 3 in simplest form6 2 .

The symbol ‘ : ’ is used to denote a ratio.The two quantities being compared must be expressed in the same unitbefore ratio is taken.The ratio a : b is different from b : a.Two ratios are said to be equivalent if their corresponding fractions areequal. ‘Per cent’ means ‘per 100’ and is denoted by the symbol %.

Evaluating Ratios and PercentagesPercentages can be expressed as fractions or ratios and vice-versa.Consider the following situation and its interpretation in terms of ratio,fraction and percentage.


Increase and decrease in PercentThere are many situations when we talk of increase or hike, decrease orreduction in price of commodities.

To Calculate Decrease/Reduction Percent

To Calculate Increase/Hike Percent

Reduction = Current price – Reduced price

Reduction percent = Reduction

100CurrentPrice

Hike/Increase = Increased price – Current price

Increase percent = Increase/Hike

100CurrentPrice

Example: If 35 is reduced to 20, Reduction = 35 – 20 = 15

15Reduction percent 10035300 42.86% app7

Example: If 35 is increased to 50, Increase = 50 – 35 = 15

15Increase percent 10035300 42.86% app7

DiscountsOften we come across advertisements reading huge ‘sale’ on commodities:‘sale up to 50% off’, ‘10% discount on Marked Price’ etc. The meaning andmethod of computing such terms is shown below.a) Marked Price (List Price or Retail Price): The marked price of an article

is the price at which the commodity is sold.b) Discount: Discount is the reduction given on the marked price of the

commodity.c) Net Selling Price: The price of the commodity obtained by subtracting

discount from the marked price is called net selling price.To Calculate Discount and Discount PercentDiscount = Marked price – Net selling price

Discount percent = Discount 100

Marked Price


Profit (Gain) and Loss

Cost Price, abbreviated as C.P is the price at which an article is

purchased.

Selling Price, abbreviated as S.P is the price at which an article is sold.

There are three cases:

Cases: When C.P < S.P When C.P > S.P When C.P = S.P

Result: There is a profit (gain). There is a loss.

Neither profi t nor loss

Formulae:

Profit (Gain) = S.P – C.P

Profit % = Profit 100 %C.P

Loss = C.P – S.P

Loss % = Loss 100 %C.P

Remark: The expenses made in addition to the C.P like expenses madeon transportation, repairs or modification are called overhead charges.They need to be added to the C.P before doing any other calculations.

Simple InterestWhen someone borrows money from a person or a bank for a period oftime, he pays back some extra money for the use of that money. This extramoney is called ‘Interest’.The amount of money that was borrowed is called ‘Principal’.The percentage of the principal charged as interest for one year is called‘Rate of Interest’.The total money paid back (Principal + Interest) is called ‘Amount’.


Calculating Simple Interest (Formula)The simple interest is calculated from the formula:

Interest (S.I) = Principal (P) × Rate (R %) × Time (T)

The sum of the principal (amount borrowed) and interest (extra money) iscalled Amount. Amount (A) = Principal (P) + Interest (S.I)

Compound InterestIf the interest is not paid after the decided time period, then we computecompound interest.With compound interest, the money you earn in interest becomes part of theprincipal, and also starts to earn interest. Each time interest is paid; it isadded to the principal. The interest is then calculated for the next time periodon the new principal.The time period after which the interest is compounded (added to theprincipal) is called the ‘Conversion period’.This time period is generally taken in years but it can be compounded yearly,half yearly (semi-annually), quarterly (after 3 months) or even monthly.

Calculating Compound Interest (Derivation of formula)Let a principal P be borrowed at rate of interest R% per year for n years. Weshall calculate the compound interest and amount payable after n years.

Interest for first year 1R PRI P 1=

100 100

And so on, Amount to be paid after n years = nRP 1

100

Compound Interest for n years = Amount – Principal nR= P 1 – P

100

Note :(i) Simple interest and compound interest are equal for the first year.(ii) CI formula is used for calculating increase or decrease in population.


CHAPTER 6: ALGEBRIC EXPRESSIONS

SOME BASIC FORMULAE

(i) 2 2 22a b a ab b

(ii) 2 2 22a b a ab b

(iii) 2 2a b a b a b

(iv) 2x a x b x x a b ab

(v) 2 2 2 2 2 2 2a b c a b c ab bc ac

(vi) 3 3 2 2 33 3a b a a b ab b

(vii) 3 3 2 2 33 3a b a a b ab b

(viii) 3 3 2 2a b a b a ab b

(ix) 3 3 2 2a b a b a ab b

(x) 3 3 3 3x y z xyz

= 2 2 2x y z x y z xy yz zx

= 2 2 212

x y z x y y z z x

(xi) If 0x y z , then 3 3 3 3x y z xyz


Basic Algebraic Terms Variable: A term or a quantity which can take different numeric values

is called a variable. Variables are generally denoted by alphabets like x,y, z, etc.

Constant: A number whose value does not change is called a constant.For example: 2, 4, 5.6, etc.

Algebraic expression: An algebraic expression is an expression thatcontains one or more numbers or variables or both combined by somearithmetic operations.

Examples of Algebraic expressions:26 , 1, 2 4, 5 3 1,x x xy x x etc are all algebraic expressions.

Terms and Coefficients:The symbols + or – in an algebraic expression separate it into parts, each ofwhich is called a Term.A term may be either a variable or a constant or a variable (or variables)multiplied by a constant.In the latter case, when a term is formed of factors, the constant in it is calledthe coefficient of the variable.Example: Consider the expression 5x2 + 3xy – 2.

25 3 2

Term TermTerm

x xy

This expression has 3 terms.Term 1: 5x2: Coefficient of x2 = 5.

It has 2 factors:5 and x2

Term 2: 3xy: Coefficient of xy =3 It has 3 factors:3, x and y

Term 3: 2: It is a constant term.


Types Definition Number of terms

Example

Monomia l An algebraic expression which has only one term is called a monomial.

1 4x

Binomial An algebraic expression which has two terms is called a binomial.

2 4x – 3y

Trinomial An algebraic expression which has three terms is called a trinomial.

3 2x – 3y + z

Polynomia l Any algebraic expression which has or more than one terms is called a polynomial.

1, 2, 3 or more

w + x + y + z

Types of Algebraic Expressions:

Multiplication of Algebraic Expressions:While multiplying two algebraic expressions, each of the terms of onealgebraic expression is multiplied by each term of the other algebraicexpression and the result is simplified by adding the like terms.I. Multiplication of Monomials:To find the product of any number of monomials, the following rule is applied:Step 1: Rearrange the terms such that all the numerical factors are put into

one group and the variables into another.Step 2: The coefficient of the product of all the monomials is the product of

the numerical coefficients of all the monomials.Step 3: Algebraic factors are multiplied such that exponents of like variables

are added using the following law of exponents:

. . m n p m n px x y x y

where x, y and z are variables and m, n and p are numeric constants.


II. Multiplication of Monomial and a Binomial:To multiply a monomial and a binomial, we use the following distributiveproperties:(1) X (Y + Z) = XY + XZ (2) X (Y – Z) = XY – XZ(3) (X + Y) Z = XZ + YZ (4) (X – Y) Z = XZ – YZwhere X, Y and Z are monomials (and so X + Y, X – Y, etc are binomials).Multiplication of Binomials:To multiply a binomial with a binomial , we can use the following property:(X + Y) (Y + Z) = X (Y +Z) + Y (Y + Z) = XY + XZ + YY + YZ

Or(X + Y) (Y + Z) = (X + Y) Y + (X + Y) Z = XY + YY + XZ + YZMultiplication of a Binomial and a Trinomial:To multiply a binomial with a trinomial, we can use the following property:(X + Y) (Y + Z + W) = X (Y +Z + W) + Y (Y + Z + W)

Or(X + Y) (Y + Z + W) = (X + Y) Y + (X + Y) Z + (Y + Z) W

A lg ebr a ic E qua ti on A lg ebra ic Ide n tity D if fer enc e

I t is a m ath em atica l eq ua tion in w hi ch o n e o r bo th sid es is an a l geb ra ic exp ressi on .

I t is an eq ualit y th a t r em ain s tru e r eg ard less of th e va l ues of an y var ia ble s th a t ap pear w ith in it.

T h e d iffe ren c e b e tw e en an eq u atio n an d an id en tity is th a t a n eq u atio n is tr ue on ly fo r cer t ain v a lu e s o f th e v a riab le w h ereas an i den tity is tr ue for an y v a lu e of th e v a riab le .

E xa m pl e:

2 x – y = 3 is tru e for x = 1, y = – 1, x =2 , y = 1 an d m an y su c h va lues b ut it is n ot tru e fo r x = 3 , y = 2,

x = 3, y = 1 an d m an y m o re .

E xa m ple :

(a + b) (a – b) = a 2 – b2 is tru e fo r an y va lu e of a an d b .


Organisation and Representation of DataData is a collection of information,usually the result of experiment orobservation.Presenting numerical information in the form of tables, graphs or charts iscalled organisation of data this help us make inferences from them more easilyand quickly.

Data is Represented in following ways

I. Pictograph II. Bar Graph III. Double bar Graph

Illustrat ion D ef inition

Pictograph/Pictogram- A picture or a sym bol is used to represen t an ass igned am ount of dat a. For example: The fol lowing pictograph shows the sal es of differen t fl avors of ice cream s in the month of August .

I. Graphical Representation of Data

Ice Cream Sold Number Picture

Vanilla 40

Chocolate 60

Strawberry 45

Peanut Butter 35

Almond delight 45

Key to Symbols: Each = 10 ice creams Each = 5 ice creams

CHAPTER 7: DATA HANDLING


Illustration Definition

Bar Graph - It is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them. There are two forms of Bar graph: Vertical and Horizontal. 1. In vertical bar graph, x-axis depicts the variable while the values of the variable are depicted on y-axis. 2. In horizontal bar graph, y-axis depicts

the variable while the values of the variable are depicted on x-axis.

3. Bar graphs are one dimensional.

II. Graphical Representation of Data

Organising Data

Sometimes the data collected during an experiment or investigation is in anunorganized manner (called raw data). It needs to be presented in a formatwhich is easy to understand and interpret. The easiest way to organise thedata is to present it in tabular form.

Frequency Distribution Table:

A frequency distribution table can be used in the following cases:

(i) When the variable takes single numeric values.

III. Double Bar Graph:Double bar graphs are used when wehave two sets of frequency for eachdata group. It is used for comparisonwithin data groups as well as betweendata groups.


(ii) When the variable takes several values.

The number of times a particular observation occurs in the data is termedas frequency of the observation.For example: (i) 20 people were asked how many children they had. Theresults were recorded as follows: 1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 4, 1,0, 0. The frequency distribution table for this data is shown below.

Note: If the number of observations in the given data is large, then wecondense it into groups. These groups are called ‘classes’ or ‘class-intervals’and the table is called a grouped frequency distribution table.Size of the class-interval is called the ‘class-size’.The lowest value of the interval is called the ‘lower class limit’The greatest value of the interval is called the ‘upper class limit’.

Number of children 0 1 2 3 4

Tally

Frequency 4 6 5 3 2

||| |||||| |||||||||

A histogram is a representation of a frequency distribution by means ofrectangles whose widths represent class intervals and whose heights areproportional to the corresponding frequencies.


IV Pie Chart/Circle Graph:A pie chart is a graph in the form of a circlethat is divided into sectors, with eachsector representing a part of the wholedata.

Properties of Circle Graphs: They are circular shaped graphs with

the entire circle representing the whole (100%). The circle is split into parts (or sectors). Each sector represents a part of the whole. Each sector is proportional in size to the amount each sector

represents.Constructing a Pie Chart:A pie chart is constructed by converting theshare of each component into a percentageof 360 degrees.


CHANCE AND PROBABILITY

There are situations in our life that are certain to happen, some are impossibleand some that may or may not happen. The situations that may or may nothappen have a ‘chance’ or ‘probability’ of happening.

Term Definition Example

Experiment An activity which ends in some well defined result is called an experiment.

Tossing a coin.

Trial Performing an experiment only once is called a trial. Tossing a coin only once

Outcome The result of a trial is called an outcome. Possible outcomes are head and tail.

Event All possible outcomes of a trial are called events. Any specific of these is called an event.

Occurrence of head in a toss is an event.

Random experiment

An experiment in which all possible outcomes are known before but the result of a trial cannot be predicted.

The result of tossing a coin cannot be judged before.

Sample Space Set of all possible outcomes of an experiment is called its sample space.

Sample space of tossing a coin ={H,T};

H = Head, T = Tail

Mutually Excusive events

If two events cannot occur together, they are said to be mutually exclusive events.

Head and tail cannot occur together

Equally Likely events

If two events have an equal chance of occurrence, they are said to be equally likely events.

Occurrence of head and tail are equally likely.

"Unbiased” or “fair”

These words show that all the outcomes are equally likely. They are used to clarify that no trick has been played on the object.

The coin is fair. It has head on one side and tail on other.

Terms Associated with Probability


Possibles Outcomes (Sample Space)


Points to Remember1. The value of probability always lies between 0 and 1, i.e.0 < P (event) <

1.2. Probability of an impossible event = 03. Probability of a sure event = 14. If A and B are two events and P (A) = P (B), then events A and B are

equally likely to occur.5. If A and B are two events and P (A) > P (B), then event A is more likely

to occur than event B.


BASIC GEOMETRICAL TERMS : Plane: A flat surface that stretches to infinity. Plane Curve: A curve that lies in a single plane. A plane curve may be

closed or open. Simple Curve: A curve that does not cross itself. Simple Closed Curve: A connected curve that does not cross itself and

ends at the same point where it begins. Example: circle, ellipse. Line Segment: All points between two given points (including the

given points themselves) form a line segment. Example: A line segmentAB is shown below.

CHAPTER 8: UNDERSTANDING QUADRILATERALS


Polygons: A simple closed curve made up of only line segments is called apolygon.

Diagonal of a polygon: A diagonal is a line segment connecting two non-consecutive vertices of a polygon.Classification of Polygons: Polygons are named according to the number ofsides and angles they have. The most familiar polygons are the triangle,rectangle and square. The table shown below lists all the polygons having upto 10 sides.

Polygons No. of sides

No. of angles

No. of vertices Shape No. of

diagonals

Triangle 3 3 3

0

Quadrilateral 4 4 4

2

Pentagon 5 5 5

5

Hexagon 6 6 6

9

Heptagon 7 7 7

14

Octagon 8 8 8

20

Nonagon 9 9 9

27

Decagon 10 10 10

35

Quadrilaterals


Types of Polygons:

I. Convex and Concave Polygons:

A convex polygon has no portion of their diagonals in the exterior. In convexpolygons, no internal angles can be more than 180°.If some portions of any of the diagonals lie in the exterior of a polygon, thenit is a concave polygon. In concave polygons, internal angles are greaterthan 180°.II. Regular and Irregular Polygons:If all angles and sides of a polygon are equal, it is called a regular polygon,otherwise it is called an irregular polygon. In other words, a regularpolygon is both ‘equiangular’ and ‘equilateral’.

Interior Angle Sum Property of a Polygon: Polygons can be separated intotriangles by drawing all the diagonals that can be drawn from a single vertex.A quadrilateral can therefore be separated into two triangles. By the AngleSum Property of a triangle, we know that the sum of the measures of the threeangles of a triangle is 180° and therefore the sum of the measures of the fourangles of a quadrilateral is 2 ×180°, i.e. 360°.


Similarly, we can find the sum of the measures of the interior angles of anypolygon.Sum of interior angles of a polygon having n sides = (n – 2) ×180°

Exterior Angle Sum Property of a Polygon:

The sum of the measures of the exterior angles of any polygon is 360°.

Quadrilateral: Quadrilaterals are polygons with four sides.

Some Terms Associated with Quadrilateral:1. Consecutive or Adjacent Sides: Two sides of a quadrilateral are said to

be consecutive or adjacent if they have a common vertex.2. Opposite sides: Two sides of a quadrilateral are said to be opposite if

they have no common vertex.3. Consecutive Angles: Two angles of a quadrilateral are said to be

consecutive if they have a common arm. 4. Opposite Angles: Two angles of a quadrilateral are said to be opposite

if they do not have a common arm.5. Diagonals: Lines formed by joining the opposite vertices are called the

diagonals.


Kinds of Quadrilaterals:


5. If each pair of opposite sides of a quadri lateral is equal, then it is parallelogram.

6. If each pair of opposite angles in a qua drilateral is equal, then it is a parallelogram.

7. If the diagonals of a quadri latera l bisect ea ch other, then the quadrilateral i s a parallelogram.

Property of Quadrilaterals:

S. No. Statements / Theorems Illustration

1. The sum of the four angles of a quadrilateral is 360. i.e.: A + B + C + D = 360.

2.

(a) A diagonal of a parallelogram divides it into two congruent triangles. i.e.: ABC CDA (b) In a parallelogram, opposite sides are equal. i.e.: AB = DC and AD = BC

3.

(a) The opposite angles of a parallelogram are equal. i.e.: A = C and B = D (b) The adjacent angles in a parallelogram are supplementary.

4. The diagonals of a parallelogram bisect each other. i.e.: OA = OC and OB = OD


CHAPTER 1: FORCE AND PRESSURE

Definitions of basic terms: Distance: The distance travelled by a body is the total length of the

path covered by a moving body irrespective of the direction in whichthe body moves.

The S.I. unit of distance is metre (m) and the C.G.S. unit is centimeter (cm).

Displacement: The shortest (straight line) distance between the initialand final positions of the body, along with direction, is known as itsdisplacement.

The S.I. unit of displacement is meter (m) and the C.G.S. unit is centimeter(cm).

Rest: A body is said to be at rest when it does not change its positionwith respect to time.

Motion: A body is said to be in motion when it changes its positionwith respect to time.

Speed: It describes the rate of motion .,

Speed= distance travelled

time taken

Units used for speed is meter (m/s) and Km/h.

An Introduction to ForceDefinition: Force is an external agency which when acting on a body, changesor tends to change the state of rest or of motion of the body. Force is a vector quantity, has both magnitude and direction.


SI unit of Force is Newton (N) Forces when applied (on an object) in the same direction, they add up

with one another and when applied from opposite directions, the netforce acting on the system becomes the difference of the two forces.

Note:1) Strength of a force is calculated by its magnitude.2) Spring balance is a device used for measuring the force acting on an

object.

Impact of ForceImpact 1

A force applied on a body may change the speed of the body. If the force applied is in the direction of the motion of the body,

then the speed of the body increases. If it is in the direction opposite to the motion of the body, the

speed decreases and if the magnitude of the force is high enough,it can even bring the body to rest.

Impact 2 A force can also change the shape of an object.

Contact forceDefinition: In order to apply a force on an object, the object has to come incontact with the source of generation of the force. Such forces are calledContact forces.There are two types of Contact forces:

1. Muscular Force 2. Frictional Force

Force

Contact Force Non contact force


Muscular force: The force resulting due to the action of muscles is known asmuscular force.Example:

Muscular force enables us to perform all activities involvingmovement or bending of our body.

Animals like bullocks, horses, camels, elephants, donkeys etc.,perform various tasks for humans by using their muscular force.

Frictional force: The force of friction is the force that always acts on allmoving bodies and always acts in the direction opposite to motion of thebody and this force arises due to the contact of the body with the surface onwhich it moves.Example:

A ball rolling on the ground gradually slows down and finally comesto rest.

When a cyclist stops pedaling the cycle, it gradually slows downand finally comes to halt.

Non Contact ForceDefinition: The force that comes into play without coming in contact with theobject on which it acts is called non contact force.

Magnetic force:A magnet attracts another magnet or a magnetic substance even when thetwo are not in contact with each other.

Non contact force

Magnetic force Electrostatic force Gravitational force


Electrostatic force:The force exerted by a charged body on another charged or uncharged bodyis the electrostatic force.Gravitational force:Every object in the universe exerts a force on every other object which iscalled the gravitational force. The sun, the moon, the planets and all other celestial bodies of our universe

are bound to each other by the gravitational force. Gravity or the Force of Gravity is the attractive force of the earth on all

objects or things by which the earth pulls them towards its center. It is due to this gravity, all objects ultimately fall downward on the earth.PressureDefinition: It is defined as force acting on a unit area of a surface.

ForcePressure =Area

Note: Only those forces that act perpendicular to the surface is considered

here. The smaller the area is, the larger is the pressure exerted on the

surface for the same magnitude of force.

Pressure exerted by liquids:Liquid exerts pressure on the walls of the container in which it is stored.

Pressure

Pressure exerted by liquids Pressure exerted by gases Atmosphericpressure


Example: Take an empty plastic bottle and drill four holes, at the bottom ofthe bottle at the same height. Fill the bottle with water. Water will come outof the bottle through four different outlets and will fall at the same distancefrom the bottle.Thus, liquids exert identical pressure at the same depth.

Pressure exerted by gases:Gases also exert pressure on the walls of the container in which they arestored.

Example: If there is a puncture inside the tube of a bicycle tyre, the tyre getsdeflated and the cycle can not be ridden.Atmospheric pressure: The envelope of air around us is the atmosphereand the pressure exerted by the atmosphere is the atmospheric pressure.Magnitude of the atmospheric pressure is very high. Value of atmosphericpressure is 760 mm Hg approx.


Frictional forceDefinition: The force of friction is the force that opposes or tends to opposethe motion of a body and always acts in the direction opposite to that of thebody.Example:A ball rolling on the ground, gradually slows down after sometime and finallycomes to rest. This is also due to the force of friction.Note:

The force of friction always opposes the applied force. It always acts in the direction opposite to which the force of motion

acts. It acts in between the two surfaces in contact, i.e. between the surface

of the body and the surface on which it moves.

Cause of friction:Friction occurs due to the irregularities on the two surfaces in contact. Theseirregularities on the two surfaces actually lock into one another. The rougherthe surface, greater is the force of friction involved.The harder the surfaces are pressed together, greater is the frictional force.Example: It is easier to drag a mattress when no one is sitting on it.

Types of friction:

CHAPTER 2: FRICTION

Friction

Static Friction Sliding Friction


Static friction:It is the force required to overcome friction at the instant the body startsmoving on the surface from rest.

Sliding friction:It is the force required to keep the body in motion on the surface with thesame speed.

Note: Static friction is slightly greater than sliding friction. This is because, the moment a body starts sliding, the contact

points on its surface do not get enough time to lock into the contactpoints of the surface on which the body is moving.

Advantages of frictionFriction actually is a necessary evil. It has both positive and negative effects.First, let the advantages be discussed here.

Example: We are able to walk on earth’s surface because of friction. Had

there been no friction, we would have stumbled every time we triedto walk.

Similarly, the cars, bicycles, scooters etc all sorts of vehicles plyon the road because of friction. Or else the brakes would neverhave worked to bring them to stop or change directions.

We are capable to write with a pen or a pencil because of friction,or else writing would have been impossible.

In the classroom, whenever something is written on the black board,some particles of the chalk gets stuck to it due to friction. Thus ifthere were no friction, we would not have been able to write onblack boards.


The nails are fixed on walls because of friction. Knots that we use for various purposes, would not have been tied

without friction. Buildings are constructed on the soil because of the existence of

friction. We light match sticks by scratching the stick on the match box,

using friction.

Disadvantages of frictionFriction has its negative effects as well. Mostly, it wears out machines andmaterials and results in unnecessary wastage of energy.

Example: Shoe-soles, car tyres wear off due to friction. Ball bearings, screws, etc. machine parts wear out in course of time

due to friction. Roads, stair cases wear out with time due to existence of friction. Friction produces heat which corrodes away heavy machines and

machine parts. This unwanted heat results in unnecessary wastage of energy.

Increasing and Reducing Friction Though friction cannot be totally eradicated, but can be regulated

to some extent. It can both be increased and reduced to maximise efficiency as and

when required.

Increasing friction: Brake pads are used in automobiles and bicycles, such that when it

is in motion, the brake pads do not come in contact with the wheels.But when the brakes are pressed, these pads captivate the motionof the rim of the wheels due to friction.


Our shoe soles are grooved to provide us with more friction on theground surface while walking.

Similarly, the tyres of cars and other heavy automobiles are treadedon the outer surface to provide more friction and better grip on theground surface.

Reducing friction Powder is sprinkled on the carom board to minimise friction to

facilitate maximum movement of the striker on the board. Hinges of doors or windows move smoothly without making much

sound when a few drops of oil is used as lubricant. The ball bearings and the other moving parts of bicycles and motor

vehicles are coated with grease to reduce friction. The mechanical joints of heavy machines in mills and factories are

regularly treated with lubricating oils to minimise friction, so thatthe machine parts do not wear out quickly.

Wheels are device that reduces friction, so large luggage casesand glad stones are attached to small wheels at the bottom whichmake them easier to roll over the ground.

Rolling friction:Definition:When a body rolls over the surface of another body, the rolling surfaceprovides continues resistance to its motion and this resistance is calledrolling friction.

Rolling friction is induced by using ball bearing. Rolling friction is slightly smaller than sliding friction, thus in heavy

machines and devices, sliding is replaced by rolling.


Example: In the bicycles, the ball bearings that are used is an example ofrolling friction.

A ball bearingLubricants:Definition: The agents which when applied in between the moving parts ofa machine, reduce the friction and smoothen the movement are calledlubricating agents or lubricants.Example: Various types of oils, like coconut oil, petroleum jelly, grease andgraphite are commonly used as lubricating agents.

Fluid Friction The common scientific term for liquids and gases is fluids. These fluids exert frictional force on the objects that move through

them, this is called fluid friction. The frictional force exerted by fluids is also known as drag.


The magnitude of this force depends on:Speed of the body with respect to the fluid.Shape of the object.Nature of the fluid.

Streamlined body:Friction results in unnecessary wastage of energy and even when a bodymoves through a fluid, it looses some energy. Thus it is necessary to minimisefriction.This can be done by giving the objects a special shape, which is called thestreamlined shape and the objects having this particular shape are calledstreamlined bodies.Example:

In nature streamlined bodies are seen in fishes and birds, to minimisethe frictional force offered by the water and the air respectively.

Boats, ships, aeroplanes, gliders, etc. are man-made streamlinedobjects, which are so designed to facilitate their smooth movementthrough water and air respectively.


Definition of sound: Sound is a form of energy that produces a sensation ofhearing to the ears.

VibrationDefinition: Vibration is the rapid to and fro movement of an object.

Production of SoundSound is produced by vibrations.For example:Human voice is the result of the vibration of the vocal chords. A rubber bandwhen stretched and plucked, it vibrates producing a faint sound.

A Practical example:

Cut a rubber band and tie two ends to points A and B as shown in the figureabove. Now smoothly pluck the band with a finger.A soft humming sound will be heard.Musical instruments like guitar, sitar, etc. produce music in this way.

CHAPTER 3: SOUND


Human soundSound creation

In humans, voice is produced by the larynx, also called the voicebox.

The hard bump in the throat that seems to move when we swallowis the voice box.

This voice box is the upper end of the wind pipe. Two vocal cords are stretched across this larynx such a way, that it

leaves a narrow slit between them for the passage of air. Whenever lungs force air through this slit, the vocal cords vibrate

producing sound.

Note: Muscles around the vocal cords can make the cords tight or loose,

which results in the formation of two types of sounds. Even the length of the vocal cords creates different sounds in men,

women and children.


Medium of propagationSound waves travel or propagate through a medium.This medium could be solid, liquid or gas.

Speed /Velocity of sound isMaximum in Solids ; Moderate in Liquids ; Least in Air

Note:Sound cannot travel through vacuum.Human ear:

Our outer ear is shaped like a funnel.When a sound enters our ears, it travels down a canal which ends at a thin,well stretched membrane called the eardrum which vibrates on receiving it.These vibrations are sent to the inner ear, which in turn redirects them to thebrain.


Properties of VibrationOscillatory motion: The to and fro motion of a body, which is called vibrationis also called oscillation or oscillatory motion.Two important properties of sound are:1) Amplitude 2) Frequency.

Frequency: The number of oscillations of a body per second is the frequencyof oscillation.S.I.Unit: Hertz (Hz)

Note: The frequency of a body is 1 Hz, means the body experiences 1

oscillation in 1 second. Frequency is also represented by f. Frequency also determines the pitch or the shrillness of a sound.

Amplitude:Definition: Amplitude of sound can be defined as the factor that determinesthe loudness or the softness of it.

It is represented by A. Amplitude is dependent on the force with which an object is made to

vibrate.Loudness of sound: Loudness of sound is directly proportional to the squareof the amplitude of the vibration creating the sound.S.I.Unit: Decibel (dB)Note:

If the amplitude of the vibration is large, then the sound produced islarge and when the amplitude is low, the sound is mild.

If the amplitude of the sound increases by three times, its loudnesswill increase by 9 times.

Above 80 dB, a sound becomes physically painful and unbearable.


Pitch or the shrillness of sound: When the frequency of vibration is higher,the sound produced is said to be shrill or of higher pitch, and if the frequencyof vibration is lower, it is said to be of lower pitch.

Noise and MusicAudible sound:Humans cannot hear sounds created from all vibrating bodies.The human ear can pick up sound ranging between the frequencies 20 Hz to20,000 Hz.

Inaudible sound:Sounds less than 20 Hz (i.e. 20 vibrations per second) are not audible to thehuman ear and are called inaudible sounds.

Ultrasound:Sounds having frequencies higher than 20,000 vibrations per second(20 kHz) is known as ultrasound and is also inaudible to the human ear.Note:

Animals like bats; dogs etc. can follow the ultrasound frequencies. These days ultrasonography is being extensively used in medical

sciences to track down problems like kidney stones, ulcers etc.Noise:Any unpleasant sound that does not create soothing sensation of hearingis noise.Examples: Horns of cars, buses etc.Noise from factories and mills, construction sites, blasting zones etc

Musical sound:Sound that produces a soothing sensation and generally originates fromany musical instrument is musical sound.Example: Sound produced when the chord of a sitar or guitar is pulled,harmonium etc.


Noise pollution:Presence of excessive, unwanted sound in the environment is noise pollution.Major sources of noise pollution: Sounds of vehicles, bursting crackers,blasting zones, loudspeakers, vicinity to airports etc.Domestic sources: Excessive loudness of TVs and music systems, kitchenappliances like mixer-grinder etc.Effects of noise pollution: Noise pollution creates many health related hazards,like lack of sleep, hypertension etc. which may lead to temporary or permanentimpairment of hearing.

Remedies: Zones or areas that perform operations which results in creation of a

lot of unwanted noise, like airports, factories etc must be set out atplaces far from human localities.

Use of motor horns should be minimized and the focus should be onusing air horns.

At the domestic level TVs and other audio systems should be heardat low volumes.

Planting of trees help in negating the harmful effects of noisepollution, so trees should be planted.

Hearing impairment: Hearing impairment is the disease or the abnormal functioning of an

individual’s perception of hearing. Total hearing impairment, though uncommon is generally detected

from birth. Partial impairment may be due to, accident, age, diseases etc.

Treatment: People, specially children suffering from it can be exposed to teaching

sign languages, to help in effective communication. Electronic devices have also been invented these days.


CHAPTER 4: METALS AND NON-METALS

Physical Properties of Metals and Non-metals:1. Metals are hard and lustrous; sodium and potassium are two metals

that are soft and can be cut with a knife and mercury is a metal that isliquid at room temperature.Non-metals are non-lustrous and they are not as hard as metals;most of the non-metals exist in gaseous state.

2. Metals make a characteristic sound (ringing type sound) when hitwith an object. But there are some exceptions to it; sodium andpotassium are soft metals and they are not sonorous.

3. Malleability: It is the property of metals by virtue of which they canbe flattened / beaten into thin sheets.This is a characteristic property of metals.Metals like silver, gold & aluminium are beaten into thin foils andsheets.Non-metals cannot be beaten into thin sheets and they break downinto powdery mass on beating with a hammer i.e. they are brittle.

4. Ductility: It is the property of metals by virtue of which it can bedrawn into thin wires and threads.Non-metals are not ductile.

5. Conduction of heat and electricity: Metals are good conductors ofheat and electricity whereas non-metals are poor conductors of heatand electricity.Thus we can say that metals are materials which are hard, lustrous,malleable, ductile, sonorous and good conductors of heat andelectricity.Non-metals are soft, dull and bad conductors of heat and electricity.Non-metals are neither malleable nor ductile.


Chemical Properties of Metals and Non-metals:A chemical reaction is a process in which chemical substances change intoone or more new substances

1. Reaction with OxygenMetals and non-metals react with oxygen present in air to formoxides.(i) Magnesium burns in air and an ash is obtained (magnesium

oxide), which when dissolved in water results in the formationof a basic solution (magnesium hydroxide) which turns red litmusinto blue.

(ii) Metals like sodium and potassium react vigorously with air anda lot of heat is generated in the reaction. Thus, they are stored inkerosene.

(iii) Copper reacts with moist air to yield a mixture of copper hydroxideand copper carbonate. The mixture formed is of green colour.

Oxides of metals are basic in nature.(i) Sulphur reacts with oxygen to form sulphur dioxide gas which

when dissolved in water gives sulphurous acid. Sulphurousacid turns blue litmus red.Oxides of non-metals are acidic in nature.

2. Reaction with WaterDifferent metals react with water in different ways. Some metalsproduce metal hydroxides and hydrogen gas on reaction with water.(i) Sodium reacts vigorously with water and heat is given out during

the reaction.(ii) Iron reacts very slowly with water.


Non-metals do not react with water and thus, non-metals are storedin water.For example, phosphorous is stored in water to prevent it from comingin contact with air because it catches fire if exposed to air.

3. Reaction with acids:(i) Metals react with acids and result in the production of hydrogen

gas. A ‘pop’ sound is produced which serves as an indicationof the presence of hydrogen gas. In this reaction, metal salts areformed Copper doesn’t react with dilute hydrochloric acid, noteven on heating; it reacts with sulphuric acid.

(ii) Non-metals are not reactive towards acids.

4. Reaction with bases:(i) Metals react with bases to produce hydrogen gas. A ‘pop’ sound

indicates the presence of hydrogen gas.(ii) Reactions of non-metals with bases are complex.

Displacement reactions:Displacement reactions are chemical reactions in which a less reactive elementin a compound is replaced by a more reactive one.For example,Copper Sulphate (CuSO4) + Zinc (Zn)Zinc Sulphate (ZnSO4) + Copper (Cu)

In this reaction, displacement of copper by zinc takes place since zinc is morereactive than copper.Copper Sulphate (CuSO4) + Iron (Fe) Iron Sulphate (ZnSO4) + Copper (Cu)In this reaction, displacement of copper by iron takes place since iron is morereactive than copper.


Note: A more reactive metal can replace a less reactive metal but thereverse process i.e., the replacement of a more reactive metal by a less reactivemetal is not possible.For example,Zinc Sulphate (ZnSO4) + Copper (Cu) Copper Sulphate (CuSO4) + Zinc (Zn)

Iron Sulphate (ZnSO4) + Copper (Cu) Copper Sulphate (CuSO4) + Iron (Fe)These two reactions does not occur since copper is less reactive than zincand iron.Zinc Sulphate (ZnSO4) + Iron (Fe) Iron Sulphate (FeSO4) + Zinc (Zn)Iron being less reactive than zinc is unable to replace it and the reaction doesnot occur.

Uses of metals:(i) Metals are used in making machinery, automobiles, trains, aeroplanes,

cooking utensils, industrial gadgets etc. The various uses of metalsare reflective of their characteristic physical properties.

(ii) Metals like magnesium, iron, sodium, copper, zinc are present inbiological systems where they perform important functions.

Uses of non-metals:(i) Non-metals like nitrogen and phosphorous are used in fertilizers.(ii) Chlorine is a non-metal used in the process of water purification.(iii) Non-metals like oxygen, nitrogen, sulphur are essential for our life.(iv) Alcoholic solution of iodine is used an antiseptic.

NOTE: Most of the elements are metals. The number of non-metals is lessthan 20. There are certain elements which possess characteristics of bothmetals and non-metals. They are called metalloids.


CHAPTER 5: COAL AND PETROLEUM

Natural resources are naturally occurring substances that are consideredvaluable for mankind in their unmodified form.

Natural resources and their classification:

Inexhaustible Natural Resources

* Present in unlimited quantities in nature

* Cannot be used up or consumed completely

* Examples: air, water, sunlight

Exhaustible Natural Resources

* Present in limited quantities in nature

* Likely to get used up or consumed completely

* Examples: Coal, petroleum, natural gas, wildlife, minerals

Nature

Natural Resources

* Obtained directly from nature * used in their unmodified forms

* They have many useful applications In our daily lives


Fossil fuels:(i) The dead and decayed remains of living organisms are known as

fossils.(ii) Fuels that are formed from the dead remains of living organisms

(fossils) are known as fossil fuels.(iii) Coal and petroleum are examples of fossil fuels. The main constituent

of coal is carbon(iv) Fossil fuels like coal and petroleum are exhaustible natural resources.(v) Formation of fossil fuels is an extremely slow process taking millions

of years.(vi) The slow process of conversion of dead vegetation into coal is called

carbonisation.COALCoal is formed by the cabonisation of dead vegetation.When heated in air,coal burns and produces mainly carbon dioxide gas.Coal is processed in industry to get some useful products such as coke, coaltar and coal gas.1. Coke

It is a tough, porous and black substance. It is almost pure form of carbon.Coke is used in the manufacture of steel and in the extraction of manymetals.

2. Coal tarIt is a black, thick liquid with unpleasant smell. It is a mixture of about 200substances. Products obtained from coal tar are used as starting materialsfor manufacturing various substances used in everyday life and inindustry, like synthetic dyes,drugs, explosives, perfumes, plastics,paints,photographic materials, roofing materials, etc. Interestingly,naphthaleneballs used to repel moths and other insects are also obtained from coaltar.


3. Coal gasCoal gas is obtained during the processing of coal to get coke. It is usedas a fuel in many industries situated near the coal processing plants.

Petroleum is an exhaustible natural resource from which fuels like petrol anddiesel are obtained.

Formation of petroleum: Petroleum formed from the dead remains of theorganisms present in sea which were settled at the bottom of the sea. Overgeological time, the dead matter was buried under heavy layers of clay andsand. The high levels of pressure and temperature under anoxic conditionscaused the dead matter to change into petroleum and natural gas.

Refining of petroleum:(i) Petroleum is a dark oily liquid.(ii) Petroleum has an unpleasant smell.(iii) Petroleum is not a pure substance; rather it is a mixture of various

substances.The process of separation of the various constituents of petroleumis called refining and the process is carried out in a petroleum refinery.Some of the oldest petroleum refineries in India are located at Mumbai,Assam, Barauni, Jamnagar and Vishakhapatnam.Various constituents of petroleum obtained after refining are:Liquefied petroleum gas (LPG), Kerosene, Petrol, Diesel, Bitumen,Paraffin wax, Lubricating oil.


Table showing Various constituents of petroleum and their uses

Natural GasNatural gas is a very important fossil fuel because it is easy to transportthrough pipes. Natural gas is stored under high pressure as compressed naturalgas (CNG). CNG is used for power generation. It is now being used as a fuelfor transport vehicles because it is less polluting. It is a cleaner fuel. The greatadvantage of CNG is that it can be used directly for burning in homes andfactories.

Importance of petroleum:Petroleum due to its immense commercial significance is also termed as ‘blackgold’. A class of substances known as petrochemicals is obtained frompetroleum which is used in the manufacture of products like detergents, fibres,polyethene and man made plastics. As natural resources are exhaustible It istherefore necessary that we use these fuels only when absolutely necessary.This will result in better environment, smaller risk of global warming and theiravailability for longer period of time. In India, the Petroleum ConservationResearch Association (PCRA) advises people how to save petrol/diesel whiledriving.

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