## CBSE Class 8 Maths Practice – Worksheets, Question Papers

Learning all the fundamental principles of CBSE Class 8 Maths is very imperative. If students are serious about scoring high marks in the higher grades, then CBSE Class 8 Maths Practice Worksheets and Question Papers are beneficial for you. There are numerous advantages that Class 8 Maths Students can experience by studying maths with the help of these Worksheets, Practice papers and Multiple Choice Questions . To start with, one can practice each topic and questions by following a extensive detailed and stepwise approach. Moreover, Students gets to practice each chapter and gauge their understanding of a particular topic by attempting various types of questions present in worksheets and practice papers.

#### RATIONAL NUMBERS

- A number that can be expressed in the form p/q, where p and q are integers and q≠0.
- All integers and all fractions are rational numbers.
- A rational number is said to be in its
**standard form**if its denominator is positive and its denominator and numerator are prime to each other. - 0 is also a rational number, but it is neither positive nor a negative rational number.
- Rational numbers are closed under addition, subtraction, multiplication and division (provided divisor is not 0).
- The commutativity of addition as well as that of multiplication is true for rational numbers i.e. if a/b and c/d are any two rational numbers, then a/b + c/d = c/d + a/b and a/b × c/d = c/d × a/b
- The associativity of addition is true for rational numbers i.e. is a/b, c/d and e/f are any three rational numbers, then (a/b +c/d) + e/f = a/b + (c/d + e/f)
- Subtraction is neither commutative nor associative for rational numbers.
- Commutativity and associativity of division is
**not true**for rational numbers. - The
**sum of 0**and any rational number is the rational number itself i.e. if a/b is any rational number, then a/b + 0 = a/b. - The result of
**subtracting zero**from a rational number is the rational number itself i.e. is a/b is a rational number, then a/b – 0 = a/b. - The
**negative of a rational number**p/q is –p/q. - P/q and –p/q are called negative (or
**additive inverse**) of each other. - Zero is the
**identity element**for addition of rational numbers. - The
**product of 1**and any rational number is the rational number itself i.e. if p/q is a rational number, then p/q × 1 = p/q - The product of 0 and any rational number is 0 i.e. p/q × 0 = 0.
- If a/b and c/d are two rational numbers such that a/b × c/d = 1, then each is called the multiplicative inverse or
**reciprocal**of each other. - Zero has no reciprocal.
- We can get
**countless rational numbers**between any two given rational numbers. - If
*x*and*y*are two rational numbers, then (*x + y)/2*is a**rational number between x and y**such that x < (x + y)/2 < y.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (5) – Rational Numbers

Class 8 Maths Worksheet (4) – Rational Numbers

Class 8 Maths Worksheet (3) – Rational Numbers

Class 8 Maths Worksheet (2) – Rational Numbers

Class 8 Maths Worksheet (1) – Rational Numbers

Class 8 Maths – MCQ Worksheet Rational Numbers – 2

Class 8 Maths – MCQ Worksheet Rational Numbers – 1

Class 8 Maths Unit Test ( RATIONAL NUMBERS )

Class 8 Maths Worksheet- Rational Numbers-2

Class 8 Maths Worksheet- Rational Numbers-1

#### LINEAR EQUATIONS IN ONE VARIABLE

- An equation is a statement of equality which contains an unknown quantity.
- In an equation, the expression on the left of the equality sign is the
**Left-Hand Side (L.H.S)**. The expression on the right of the equality sign is the**Right-Hand Side (R.H.S)**. - Any value of the unknown, which makes L.H.S and R.H.S equal, is called its
**solution**or**not**. - The process of carrying terms from one side to another is called
**transporting**. - We can transpose a term from one side of an equation to the other side b merely changing its sign.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (4) – Linear equation in one variable

Class 8 Maths Worksheet (3) – Linear equation in one variable

Class 8 Maths Worksheet (2) – Linear equation in one variable

Class 8 Maths Worksheet (1) – Linear equation in one variable

Class 8 Maths – Practice Questions Linear Equation in One Variable

Class 8 Maths – MCQ Worksheet Linear Equation in One Variable – 3

Class 8 Maths – MCQ Worksheet Linear Equation in One Variable – 2

Class 8 Maths – MCQ Worksheet Linear Equation in One Variable – 1

Class 8 Maths Unit Test ( Linear Equation in One Variable )

Class 8 Maths Worksheet ( HOTS Linear Equation in One Variable )

Class 8 Maths Worksheet- Linear Equation in One Variable

#### UNDERSTANDING QUADRILATERALS

- A simple closed curve made up of only line segments is called a
**polygon**. **Triangle**is a polygon having 3 sides (or vertices).**Quadrilateral**is a polygon having 4 sides (or vertices).**Pentagon**is a polygon having 5 sides (or vertices).**Hexagon**is a polygon having 6 sides (or vertices).**Heptagon**is a polygon having 7 sides (or vertices).**Octagon**is a polygon having 8 sides (or vertices).**Nonagon**is a polygon having 9 sides (or vertices).**Decagon**is a polygon having 10 sides (or vertices).**N-gon**is a polygon having n sides (or vertices).**Diagonal**is a line segment connecting two consecutive vertices of a polygon.- A
**regular polygon**has sides of equal length and angles of equal measure. - The sum of the measures of the three angles of a triangle is
**180°**. - The sum of the measures of the external angles of the polygon is
**360°**. - The
**trapezium**is a quadrilateral with a pair of parallel sides. - If the non-parallel sides of a trapezium are of equal length, it is called an
**isosceles trapezium**. - A quadrilateral having exact two distinct consecutive pairs of sides of equal length is called a
**kite**. - A
**parallelogram**is a quadrilateral whose opposite sides are parallel. - The opposite sides of a parallelogram are of equal length and the opposite angles are of equal measure.
- The
**diagonals**of a parallelogram bisect each other. - The adjacent angles of a parallelogram are
**supplementary**. - A
**rhombus**is a quadrilateral with sides of equal length. - The
**diagonals**of a rhombus are perpendicular bisectors of one another. - A
**rectangle**is an equiangular quadrilateral. - Each angle of a rectangle is a
**right angle**and its**diagonals**are of equal length. - A square is and
**equilateral rectangle**. - The
**diagonals**of square are perpendicular bisectors of one another. - The
**sum of all the interior angles**of a polygon of*n-sides*is given by (n – 2) × 180°.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (9) – Understanding Quadrilaterals

Class 8 Maths Worksheet (8) – Understanding Quadrilaterals

Class 8 Maths Worksheet (7) – Understanding Quadrilaterals

Class 8 Maths Worksheet (6) – Understanding Quadrilaterals

Class 8 Maths Worksheet (5) – Understanding Quadrilaterals

Class 8 Maths Worksheet (4) – Understanding Quadrilaterals

Class 8 Maths Worksheet (3) – Understanding Quadrilaterals

Class 8 Maths Worksheet (2) – Understanding Quadrilaterals

Class 8 Maths Worksheet (1) – Understanding Quadrilaterals

Class 8 Maths Unit Test ( Understanding Quadrilaterals )

Class 8 Maths Worksheet ( HOTS Understanding Quadrilaterals )

Class 8 Maths Worksheet – Understanding Quadrilaterals

#### DATA HANDLING

- The numerical information collected in various cases is called data.
- A
**pictograph**is a pictorial representation of data using symbols to represent a group of items. - A
**bar-graph**is a representation of information using bars of uniform width, the length (or height) of which is proportional to the given value. - The
**frequency**gives the number of times that a particular entry occurs. - A bar graph having bars of equal width with no gaps in between is called
**histogram**. - The difference between its highest and the lowest value of the data is called its
**range**. - In
**circle graph**(or a**pie chart**) the size of each sector is proportional to the information it represents. - To
**draw a pie graph,**we divide the whole angle (360°) at the centre of a circle in proportion of the fractions. - The number of data items in a certain interval is called its
**frequency**. - The observations of an experiment are called its
**outcomes**. - If each outcome of an experiment is independent of the other and also the chances of getting any one of them are the same, then they are called
**equally likely outcomes**. **Probability**is a measure of the likelihood of getting a certain outcome.- The probability of an event is obtained by dividing the
**number of times**a favourable outcome by the trial number of outcomes. - The probability values of an event lie
**between 1 and 0**. - An event which can never happen is called an
**impossible event**. - The probability of an
**impossible event**is 0. - The event which will certainly happen is called
**sure event**. - The probability of a
**sure event**is 1.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (9) – Data Handling

Class 8 Maths Worksheet (8) – Data Handling

Class 8 Maths Worksheet (7) – Data Handling

Class 8 Maths Worksheet (6) – Data Handling

Class 8 Maths Worksheet (5) – Data Handling

Class 8 Maths Worksheet (4) – Data Handling

Class 8 Maths Worksheet (3) – Data Handling

Class 8 Maths Worksheet (2) – Data Handling

Class 8 Maths Worksheet (1) – Data Handling

Class 8 Maths – Practice Questions Data handling – 1

Class 8 Maths – MCQ Worksheet Data handling – 4

Class 8 Maths – MCQ Worksheet Data handling – 3

Class 8 Maths – MCQ Worksheet Data handling – 2

Class 8 Maths – MCQ Worksheet Data handling – 1

#### SQUARES AND SQUARE ROOTS

- If any number
*m*can be expressed as*n*, then^{2}*m*is a**square number**. - The numbers 1, 4, 9, 16, … … … are square numbers. These numbers are called
**perfect square numbers**. - The
**sum**of first*n*odd natural numbers is n^{2}. **Squares of odd**numbers are always odd.**Squares of even**numbers are always even.- The numbers x, y, z are called
**Pythagorean Triplets**, if x^{2}+ y^{2}= z^{2}. - A number ending in 2, 3, 7 or 8 is
**never a perfect square**. - A number ending in an
**odd number of zeros**is never a perfect square. - If
*n*is a perfect square, then*2n*can never be a perfect square. - The inverse operation of squaring is called
**square roots**. - Every perfect square number has
**two square roots**. - If a perfect square of
*n*-digits and*n*is**even**, then its square root will have (n + 1)/2 digits.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (7) – Squares and Square Roots

Class 8 Maths Worksheet (6) – Squares and Square Roots

Class 8 Maths Worksheet (5) – Squares and Square Roots

Class 8 Maths Worksheet (4) – Squares and Square Roots

Class 8 Maths Worksheet (3) – Squares and Square Roots

Class 8 Maths Worksheet (2) – Squares and Square Roots

Class 8 Maths Worksheet (1) – Squares and Square Roots

Class 8 Maths – Worksheet Squares and Square Roots

Class 8 Maths – Practice Questions Squares and Square Roots

Class 8 Maths – MCQ Worksheet Squares and Square Roots – 3

Class 8 Maths – MCQ Worksheet Squares and Square Roots – 2

Class 8 Maths – MCQ Worksheet Squares and Square Roots – 1

#### CUBES AND CUBE ROOTS

- The numbers 1, 8, 27, 64, 125 … are called
**Perfect cubes**or**cube numbers**. **First ten cube numbers**are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.- The cubes of
**even**numbers are even. - The cubes of
**odd**numbers are odd. - In the
**prime factorisation**of any number, if each factor appears three times, then the number if a perfect cube. - Finding the
**cube root**of a number is the inverse operation of cubing. - The
**symbol**^{3}√ denotes\ ‘cube root’.

###### PRACTICE MATERIAL

Class 8 Maths – Worksheet Cubes and Cube Roots

Class 8 Maths – Practice Questions Cubes and Cube Roots

Class 8 Maths – MCQ Worksheet Cubes and Cube Roots – 3

Class 8 Maths – MCQ Worksheet Cubes and Cube Roots – 2

Class 8 Maths – MCQ Worksheet Cubes and Cube Roots – 1

Class 8 Maths Unit Test ( Cubes & Cube Roots )

Class 8 Maths Worksheet (2) – Cube and Cube Roots

Class 8 Maths Worksheet (1) – Cube and Cube Roots

#### COMPARING QUANTITIES

- The
**ratio**of two quantities, say*a*and*b*, in the same units a/b and written as*a : b*. - A ratio is said to be in the
**simplest form**, if the first and the second temr have no common factor, other than 1. - Ratio has
**no units**. - An equality of two ratios is called
**proportion**. - A fraction with its denominator as 100 is equal to that much
**per cent**as much is the numerator. - x/100 = x%
- To
**change**a fraction into a per cent, we multiply the fraction by 100. - The money paid by the shopkeeper to buy an article is called its
**cost price**. - The money received by a shopkeeper on selling an article is called its
**selling price**. **Actual cost price**= cost price + overhead charges.- The money which is borrowed, is called
**principal**. - The period for the money is borrowed is called
**interest**. - The total money which is paid after the expiry of the time is called the
**amount.** - Amount = Principal + Interest
- If we denote principal by P, rate by R and time by T, then Simple Interest = (P×R×T)/100
- When the interest is added at the end of the year to calculate interest for the next year, the interest so obtained is called
**Compound Interest**(C.I.) - The period after which the interest is added to the principal is called the
**conversion period**. - The compound interest differs every year but simple interest remains the same.
- If ‘
**A**’ stands for the amount, ‘**P**’ stands for period, ‘**R**’ stands for rate and ‘’ stand for number of conversion periods, then A = P (1+R/100)*n*

##### PRACTICE MATERIAL

Class 8 Maths Worksheet (11) – Comparing Quantities

Class 8 Maths Worksheet (10) – Comparing Quantities

Class 8 Maths Worksheet (9) – Comparing Quantities

Class 8 Maths Worksheet (8) – Comparing Quantities

Class 8 Maths Worksheet (7) – Comparing Quantities

Class 8 Maths Worksheet (6) – Comparing Quantities

Class 8 Maths Worksheet (5) – Comparing Quantities

Class 8 Maths Worksheet (4) – Comparing Quantities

Class 8 Maths Worksheet (3) – Comparing Quantities

Class 8 Maths Worksheet (2) – Comparing Quantities

Class 8 Maths Worksheet (1) – Comparing Quantities

Class 8 Maths – MCQ Worksheet Comparing Quantities – 5

Class 8 Maths – MCQ Worksheet Comparing Quantities – 4

Class 8 Maths – MCQ Worksheet Comparing Quantities – 3

Class 8 Maths – MCQ Worksheet Comparing Quantities – 2

Class 8 Maths – MCQ Worksheet Comparing Quantities – 1

Class 8 Maths Sample Paper 2018 ( Comparing Quantities )

Class 8 Maths Worksheet ( HOTS Comparing Quantities )

Class 8 Maths Unit Test ( Comparing Quantities )

Class 8 Maths Sample Paper 2018 ( Comparing Quantities )

#### ALGEBRAIC EXPRESSION AND IDENTITIES

**Expressions**are formed from variables and constants.- A variable takes on different
**values**. - The numerical factor of a term is called its
**coefficient**. - An expression with one or more terms is called a
**polynomial**. - Expressions that contain only one term are called
**monomials**. - Expressions that contain two terms are called
**binomials**. - A three term expression is called
**trinomial**. - Algebraic terms with the same variable and same exponent are called like terms
**similar terms**. **Subtraction**of a number is the same as addition of its additive inverse.- To multiply a
**polynomial by a monomial**multiply each term of the polynomial by the monomial and write the resulting terms with their proper signs. - To multiply a
**polynomial by a polynomial**, multiply each term of the multiplicand each term of the multiplier and take the algebraic sum of these partial products. - An equation is a statement of equality of two algebraic expressions involve unknown quantity called a variable.
- An equation is not true for all values of the variable. It is true for
**only certain values**of the variables in it. - If equality is true for every value of the variables in it, then it is called an identity.
- (x+y)
^{2}= x^{2}2xy + y^{2} - (x – y)
^{2}= x^{2 }– 2xy + y^{2} - (x – y) (x + y) = x
^{2 }– y^{2} - (x + a) (x + b) = x
^{2}+ (a + b)x+ ab - A number which when substituted for the variable in an equation, make
- L.H.S. =R.H.S., is said to satisfy the equation and is called a
**root of the equation**.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (7) – Algebraic Expression

Class 8 Maths Worksheet (6) – Algebraic Expression

Class 8 Maths Worksheet (5) – Algebraic Expression

Class 8 Maths Worksheet (4) – Algebraic Expression

Class 8 Maths Worksheet (3) – Algebraic Expression

Class 8 Maths Worksheet (2) – Algebraic Expression

Class 8 Maths Worksheet (1) – Algebraic Expression

Class 8 Maths – Worksheet ( HOTS) Algebraic Expressions

Class 8 Maths – Practice Questions Algebraic Expressions

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 6

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 5

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 4

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 3

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 2

Class 8 Maths – MCQ Worksheet Algebraic Expressions – 1

Class 8 Maths Worksheet ( HOTS Algebraic Expressions )

Class 8 Maths Unit Test ( Algebraic Expressions)

#### MENSURATION

**Area**of a plane figure is magnitude of the region enclosed by it.- A closed plane figure formed by line segments is called a
**rectilinear figure**. - A rectilinear figure is said to be
**simple**if no two sides of it intersect at a point other than the end point. - The sum of the lengths of all sides of a rectilinear figure is called its
**perimeter**. - Area of a:
- rectangle = length x breadth
- square = side x side
- triangle = ½ x base x height
- rhombus = ½ x product of the diagonals
- quadrilateral = ½ x diagonal x (sum of offsets)
- trapezium = ½ (sum of parallel sides) x (Distance between parallel sides)
- circle = πr
^{2}

- In a cuboidal box there are three pairs of identical rectangular faces.
- In a cubical box, all six faces are squares and identical.
- Total surface area of a cuboid = 2[
*hxl + hxb + bxI*], where*h*,*I*and*b*are the height, length and breadth respectively of the cuboid. - Area of four walls of a rooms (= Lateral surface area of a cuboid) = 2h (l + b).
- Lateral surface area of a cylinder =
*2πrh* - Total surface area of a cylinder = 2πr (r + h)
- Volume of a cuboid = area of base x height =
*I x b x h* - Volume of a cube =1
^{3} - Volume of a cylinder = πr
^{2}x h - Measures of area:
- 1 sq. cm = 100 mm
^{2} - 1 sq. m = 10000 cm
^{2} - 1 dm
^{2}= 100 cm^{2} - 1 dam
^{2}= 100 m^{2} - 1 km
^{2}= 100 hm^{2} - 1 km
^{2}= 1000000 m^{2}

- 1 sq. cm = 100 mm
- Measures of volume:
- 1 cm
^{3 }= 1000 mm^{3} - 1 dm
^{3}= 1000 cm^{3} - 1 m
^{3}=1000 dm^{3} - 1 m
^{3}= 1000 litres - 1 m
^{3}= 1000000 cm^{3} - 1 litre = 1000 millilitres

- 1 cm

##### PRACTICE MATERIAL

Class 8 Maths Worksheet (7) – Mensuration

Class 8 Maths Worksheet (6) – Mensuration

Class 8 Maths Worksheet (5) – Mensuration

Class 8 Maths Worksheet (4) – Mensuration

Class 8 Maths Worksheet (3) – Mensuration

Class 8 Maths Worksheet (2) – Mensuration

Class 8 Maths Worksheet (1) – Mensuration

Class 8 Maths – MCQ Worksheet Mensuration – 5

Class 8 Maths – MCQ Worksheet Mensuration – 4

Class 8 Maths – MCQ Worksheet Mensuration – 3

Class 8 Maths – MCQ Worksheet Mensuration – 2

Class 8 Maths – MCQ Worksheet Mensuration – 1

Class 8 Maths Worksheet (HOTS Mensuration)

Class 8 Maths Unit Test ( Mensurations )

#### EXPONENTS AND POWERS

- If
is a positive integer and a is a rational number, then*m**a*^{m }*= a x a x a x a …….. (**m**factors)*

- a
^{m}is called the*m*th power of*‘a’*. Here*‘a’*is called**base**and*‘m’*is called**exponent.** - A power with negative exponent (a
^{-m}) can also be expressed in terms of a power with positive exponent having the same base*‘a’*as 1/a^{m}. - For any non-zero integer a, a
^{m}x a^{n}= a^{m+n }Where m and n are natural numbers. - For any non-zero integer
a*a,*^{m}/a^{n}= a^{m-n }where m and n are natural numbers and ‘m > n’. - If ‘a’ and ‘b’ are non-zero integers and ‘m’, ‘n’ are any integers, then
- (a
^{m})^{n}= a^{mn} - a
^{m}x b^{m}= (ab)^{m} - a
^{m}/b^{m}= (a/b)^{m}

- (a
- (1)
^{m}= (1)^{n}, for any integer m and n. - For any rational (non-zero) number ‘a’, we have a
^{0}= 1 - For comparing very large numbers or very small numbers, we have to change them in
**standard forms**.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (5) – Exponents and Powers

Class 8 Maths Worksheet (4) – Exponents and Powers

Class 8 Maths Worksheet (3) – Exponents and Powers

Class 8 Maths Worksheet (2) – Exponents and Powers

Class 8 Maths Worksheet (1) – Exponents and Powers

Class 8 Maths – MCQ Worksheet Exponents and Powers – 6

Class 8 Maths – MCQ Worksheet Exponents and Powers – 5

Class 8 Maths – MCQ Worksheet Exponents and Powers – 4

Class 8 Maths – MCQ Worksheet Exponents and Powers – 3

Class 8 Maths – MCQ Worksheet Exponents and Powers – 2

Class 8 Maths – MCQ Worksheet Exponents and Powers – 1

Class 8 Maths Unit Test ( Exponents & Powers )

#### FACTORISATION

- The process of expressing a polynomial as a product of two or more polynomial of smaller degree is called
**factoring polynomials**. - Various types of polynomials to be factorized:
- Polynomial each of whose terms contains a
**common monomial**factor*am* bm * cm = m(a + b + c)* - Trinomial as a
**perfect square**. - x
^{2}+ 2xy+ y^{2}= (x + y)^{2 }= (x + y) (x – y) - x
^{2}– 2xy + y^{2}= (x – y)^{2 }=(x – y) (x – y) - Polynomial as the
**difference of two squares**.- x
^{2}– y^{2}= (x + y) (x – y)

- x
- Second degree trinomial ax
^{2}+ bx + c = (x + p) (x + q) where p + q = b and pq = c - A monomial
**multiplied**by a monomial always gives a monomial. But a monomial**divided**by a monomial may not give a monomial. - Expressions having variables in the denominator, are
**not polynomials**. - Expressions in which variables occur under root signs are
**not polynomials**. - If the remainder is zero, both, the divisor and the quotient, are
**factors**of the dividend.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (4) – Factorisation

Class 8 Maths Worksheet (3) – Factorisation

Class 8 Maths Worksheet (2) – Factorisation

Class 8 Maths Worksheet (1) – Factorisation

Class 8 Maths – Worksheet (HOTS) Factorisation

Class 8 Maths – Practice Questions Factorisation

Class 8 Maths – MCQ Worksheet Factorisation – 4

Class 8 Maths – MCQ Worksheet Factorisation – 3

Class 8 Maths – MCQ Worksheet Factorisation – 2

Class 8 Maths – MCQ Worksheet Factorisation – 1

Class 8 Maths Unit Test Worksheet (Factorisation)

Class 8 Maths Worksheet ( HOTS Factorisations )

#### PLAYING WITH NUMBERS

- Think of any two-digit number and reverse it. Add the two numbers. Divide the sum by 11. The quotient will be equal to the sum of the digits of the
**number that was thought**. - Think of any two-digit number and reverse it. Subtract the smaller number from the larger. Divide the answer by 9. The quotient will be equal to the difference in digits of the
**number which was thought**. - Think of a three digit number. Write it by reversing the digits. Find their difference. Now this Difference + 99 = Difference between the hundreds digit and ones digit.
- A number is divisible by 10 just when its ones digit is 0.
- If we subtract the ones digit of a number from that number, the portion left over is a
**multiple of 10**. - If the ones digit of a number is 0 or 5, then it is
**divisible by 5**. - If the ones digit of a number is
**even**, then the number itself is even. - If the ones digit of a number is
**odd**, then the number itself is odd. - If the sum of the digits of a number is divisible by 9, then the number is
**divisible by 9.** - If the sum of the digits of a number is divisible by 3, then number is
**divisible by 3**. - If a number is divisible
**by both 2 and 3**, it must be divisible by 6. - A number is divisible
**by 4**, if the number formed by tens and units digits is divisible by 4. - A number is divisible
**by 11**, if the difference of the sum of digits at even places and the sum of digits at odd places (beginning from units place) is either 0 or a multiple of 11. - A three-digit number is a multiple
**of 11**, if the sum of its outer two digits minus its middle digit is a multiple of 11.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (5) – Playing With Numbers

Class 8 Maths Worksheet (4) – Playing With Numbers

Class 8 Maths Worksheet (3) – Playing With Numbers

Class 8 Maths Worksheet (2) – Playing With Numbers

Class 8 Maths Worksheet (1) – Playing With Numbers

Class 8 Maths – Worksheet (HOTS) Playing with Numbers

Class 8 Maths – Practice Questions Playing with Numbers

Class 8 Maths – MCQ Worksheet Playing with Numbers – 2

Class 8 Maths – MCQ Worksheet Playing with Numbers – 1

Class 8 Maths Unit Test ( Playing it with Numbers )

#### VISUALISING SOLID SHAPES

- 1. A
**polyhedron**is a solid that is bounded by polygons which are called its**faces**. The faces meet at**edges**which are line segments. The edges meet at**vertices**which are points. - 2. A polyhedron is
**convex**if any two points on its surface can be joined by a line segment that entirely lies inside or on the polyhedrons. - 3. A polyhedron is said to be
**regular**if its faces are made up of regular polygons and the same number of faces meet at each vertex. - 4. A
**prism**is a polyhedron, two of whose faces are congruent polygons in parallel planes and whose other faces are parallelograms. - 5. A
**pyramid**is polyhedron whose base is a polygon (of any number of sides) and whose other faces are triangles with a common vertex. - 6. According to Euler’s formula, the relation:
- [Number of faces (f)] + [Number of vertices (v)] = [Number of edges (e)] + 2 is true for any simple convex polyhedron.

- A
**map**depicts the location of a particular object/place in relation to other objects/places - 8. Maps use a
**scale**which is fixed for a particular map. It reduces the actual distances proportionately to distances on the paper. - 9.
**Visualising solid shapes**(i.e., 3-D shapes) is a very useful skill which enables us to see its ‘hidden’ parts. - 10. Various
**ways**to visualise a solid shape are:- by
**cutting or slicing**the shape which would result in the cross-section of the solid. - by
**observing**a 2-D shadow of a 3-D shape. - by looking at the shape from different angles, i.e., the
**front view**, the**side view**and the**top view**.

- by

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (7) – Visualising Solid Shapes

Class 8 Maths Worksheet (6) – Visualising Solid Shapes

Class 8 Maths Worksheet (5) – Visualising Solid Shapes

Class 8 Maths Worksheet (4) – Visualising Solid Shapes

Class 8 Maths Worksheet (3) – Visualising Solid Shapes

Class 8 Maths Worksheet (2) – Visualising Solid Shapes

Class 8 Maths Worksheet (1) – Visualising Solid Shapes

Class 8 Maths – Practice Questions Visualising Solid Shapes

Class 8 Maths – MCQ Worksheet Visualising Solid Shapes – 4

Class 8 Maths – MCQ Worksheet Visualising Solid Shapes – 3

Class 8 Maths – MCQ Worksheet Visualising Solid Shapes – 2

Class 8 Maths – MCQ Worksheet Visualising Solid Shapes – 1

Class 8 Maths Unit Test ( Visualising Solid Shapes )

#### PRACTICAL GEOMETRY

- We require three measurements (of sides, angles) to draw a unique
**triangle**. - A unique
**quadrilateral**can be constructed when:- Four sides and one diagonal Or
- Two diagonals and three sides Or
- Two adjacent sides and three angles Or
- Three sides and two included angle are given.

- Before constructing the figure, its rough sketch is made using the given measurements.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (1) – Practice Geometry

Class 8 Maths – Worksheet Practical Geometry- 1

#### DIRECT AND INVERSE PROPORTIONS

- Two quantities x and y are in
, if they change together in such a manner that the ratio x/y remains constant.*‘direct proportion’* - Two quantities x and y being in direct proportion are written as
**x****y**. - Two quantities x and y are said to be in
**inverse proportion**, if they change together in such a manner that the product xy remains constant. - If two quantities are in inverse-proportion then an increase in one causes a
**proportional decrease**in the other (and vice-versa). - Two quantities x and y being in inverse proportion are written as
**x****1/y**.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (3) – Direct and Inverse Proportion

Class 8 Maths Worksheet (2) – Direct and Inverse Proportion

Class 8 Maths Worksheet (1) – Direct and Inverse Proportion

Class 8 Maths – Worksheet (HOTS) Direct and Inverse Proportion

Class 8 Maths – Practice Questions Direct and Inverse Proportion

Class 8 Maths – MCQ Worksheet Direct and Inverse Proportion – 4

Class 8 Maths – MCQ Worksheet Direct and Inverse Proportion – 3

Class 8 Maths – MCQ Worksheet Direct and Inverse Proportion – 2

Class 8 Maths – MCQ Worksheet Direct and Inverse Proportion – 1

Class 8 Maths Unit Test ( Direct & Inverse Proportions )

Class 8 Maths Worksheet ( HOTS Direct & Inverse Proportions )

#### INTRODUCTION TO GRAPHS

**Graphs**represent a wide variety of data in an easy-to-read format for quick and ready comprehension.- Three useful
**kinds of graphs**are- Line graphs
- Bar graphs
- Circle graphs

**Line graphs**are usually used to show changes in amounts or results over a period of time.**Bar graphs**are generally used to compare amounts or results. They are used to show categories which are different from each other.**Circle graphs**are designed to show relative proportions. The angle of a sector of a circle is made proportional to the percent of an item of the data list to be displayed. They are used to represent data where all categories or groups are specified.- The
**position of a point**on a plane is fixed by specifying its distances from two fixed lines perpendicular to each other. - In an ordered pair the x-coordinate is always stated first. The coordinates are always written in this order and thus they are called
**ordered pair**.

###### PRACTICE MATERIAL

Class 8 Maths Worksheet (4) – Introduction to graphs

Class 8 Maths Worksheet (3) – Introduction to graphs

Class 8 Maths Worksheet (2) – Introduction to graphs