Mathematics Class VIII

Rational Numbers

4 Topics | 3 Quizzes

Introduction – Rational Numbers

Properties of Rational Numbers

Representation of Rational Numbers on the Number Line

Rational Number between Two Rational Numbers

Concept Checkers – Rational Numbers – Class VIII

Practice Questions – Rational Numbers – Class VIII

Olympiad Questions – Rational Numbers – Class VIII

Linear Equations in One Variable

6 Topics | 3 Quizzes

Introduction – Linear Equation in One Variable

Linear Equation in One Variable

Some Important points related to Linear Equations

Applications of Linear Equation

Reducing Equations to Simpler Form

Equations Reducible to the Linear Form

Concept Checkers – Linear equations in one variable – Class VIII

Practice Questions – Linear equations in one variable – Class VIII

Olympiad Questions – Linear equations in one variable – Class VIII

Understanding Quadrilaterals

5 Topics | 3 Quizzes

Some of the Measures of the Exterior Angles of a Polygon

Kinds of Quadrilaterals

Some Special Parallelograms

Concept Checkers – Understanding quadrilaterals – Class VIII

Practice Questions – Understanding quadrilaterals – Class VIII

Olympiad Questions – Understanding Quadrilaterals – Class VIII

Practical Geometry

3 Topics

Constructing a Quadrilateral

Some Special Cases

Visualising Solid Shapes

3 Topics | 1 Quiz

View of 3D-Shapes

Faces, Edges and Vertices

Concept Checkers – Visualising Solid Shapes – Class VIII

5 Topics | 3 Quizzes

Introduction to Data Handling

Organising Data

Circle Graph or Pie Chart

Chance and Probability

Concept Checkers -Data Handling – Class VIII

Practice Questions -Data Handling – Class VIII

Olympiad Questions – Data Handling – Class VIII

Squares and Square Roots

4 Topics | 3 Quizzes

Properties of Square Numbers

Square Roots of Perfect Squares

FINDING SQUARE ROOTS BY Prime Factorization

Concept Checkers – Square and Square Roots – Class VIII

Practice Questions – Square and Square Roots – Class VIII

Olympiad Questions -Square and Square Roots – Class VIII

Cubes and Cube Roots

3 Topics | 3 Quizzes

Concept Checkers -Cubes and Cube roots – Class VIII

Practice Questions -Cubes and Cube roots – Class VIII

Olympiad Questions -Cubes and Cube roots – Class VIII

Comparing Quantities

6 Topics | 2 Quizzes

Recalling Ratios and Percentages

Finding the Increase and Decrease Percent

Finding Discounts

Terms Related to Buying and Selling (Profit and Loss)

Simple Interest and compound interest

The Formula for Compound Interest

Concept Checkers – Comparing Quantities – Class VIII

Olympiad Questions – Comparing Quantities – Class VIII

Algebraic Expressions and Identities

10 Topics | 3 Quizzes

What are Expressions?

Terms, Factors and Coefficients

Monomials, Binomials and Polynomials

Like and Unlike Terms

Addition and Subtraction of Algebraic Expressions

Multiplication of Algebraic Expressions: Introduction

Multiplying a Monomial by a Monomial

Multiplying a Monomial by a Polynomial

Multiplying a Polynomial by a Polynomial

What is an Identity?

Concept Checkers -Algebraic expression and identities – Class VIII

Practice Questions – Algebraic expressions and identities – Class VIII

Olympiad Questions – Algebraic expressions and identities – Class VIII

8 Topics | 3 Quizzes

Area of Trapezium

Area of General Quadrilateral

Area of Special Quadrilaterals (Rhombus)

Solid Shapes and Surface Area

Surface Area of Cube, Cuboid and Cylinder

Volume of Cube, Cuboid and Cylinder

Volume and Capacity

Concept Checkers -Mensuration – Class VIII

Practice Questions -Mensuration – Class VIII

Olympiad Questions – Mensuration – Class VIII

Exponents and Powers

4 Topics | 3 Quizzes

Powers with Negative Exponents

Laws of Exponents

Comparing Very Large and Very Small Numbers

Concept Checkers – Exponents and Powers – Class VIII

Practice Questions – Exponents and Powers – Class VIII

Olympiad Questions – Exponents and Powers – Class VIII

Direct and Inverse Proportions

3 Topics | 3 Quizzes

Direct Proportion

Inverse Proportion

Concept Checkers -Direct and inverse proportion – Class VIII

Practice Questions – Direct and inverse proportions – Class VIII

Olympiad Questions – Direct and inverse proportions – Class VIII

4 Topics | 3 Quizzes

Factors of Algebraic Expressions

Methods of Factorisation

Division of Algebraic Expressions

Concept Checkers – Factorization – Class VIII

Practice Questions – Factorization – Class VIII

Olympiad Questions – Factorization – Class VIII

Playing with Numbers

3 Topics | 3 Quizzes

Numbers in General Form

Letters for Digits

Divisibility Rules

Concept Checkers – Playing with numbers – Class VIII

Practice Questions – Playing with numbers – Class VIII

Olympiad Questions – Playing with numbers – Class VIII

Mock Test 1 – Class VIII

Mock Test 2 – Class VIII

Mock Test 3 – Class VIII

Concept Checkers – Square and Square Roots – Class VIII

Mathematics Class VIII Squares and Square Roots Concept Checkers – Square and Square Roots – Class VIII

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Question 1 of 18

1. Question
What is the least Perfect square which is divisible by 2,4,6 ?
- 36
- 64
- 16
- 18
Correct

Incorrect
Question 2 of 18

2. Question
What is the number of digits in the square root of 390625 ?
- 4
- 6
- 5
- 3
Correct

Incorrect

Hint

$\sqrt{390625}=625$
Question 3 of 18

3. Question
What is the least perfect square exactly divisible by each of the numbers 6, 9, 15, 20 ?
- 3600
- 900
- 400
- 225
Correct

Incorrect

Hint

LCM $=2\times2\times3\times3\times5=180\\ \\ 180=2\times2\times3\times3\times5$
To make it a perfect square we multiply 180 with 5 to get 900
Question 4 of 18

4. Question
What is the least number which must be subtracted from 2509 to make it a perfect square ?
- 6
- 9
- 12
- 14
Correct

Incorrect

Hint

So, 9 will be subtracted
Question 5 of 18

5. Question
What is the square root of \(42\dfrac{583}{1369} \)?
- \(6\dfrac{19}{37} \)
- \(4\dfrac{2}{11} \)
- \(7\dfrac{2}{121} \)
- \(6\dfrac{12}{37} \)
Correct

Incorrect

Hint

$\sqrt{\dfrac{58081}{1369}}=\dfrac{241}{37}=6\dfrac{19}{37}$
Question 6 of 18

6. Question
If \(\sqrt{1+\dfrac{27}{169}}=1+\dfrac{x}{13} \), The value of x is
- 1
- 14
- 10
- 12
Correct

Incorrect

Hint

$\sqrt{1+\dfrac{27}{169}}=\sqrt{\dfrac{196}{169}}=\dfrac{14}{13}=1\dfrac{1}{13}=1+\dfrac{1}{13}\\ \\ x=1$
Question 7 of 18

7. Question
What is the value of \((501)^2-(500)^2 \)
- 1
- 101
- 1001
- 100
Correct

Incorrect

Hint

$(501)^2-(500)^2=(501+500)(501-500)\\ \\ =1001$
Question 8 of 18

8. Question
Which of the following is a pythagorean triplet?
- 6, 8, 10
- 3, 4, 7
- 5, 12, 18
- 2, 3, 6
Correct

Incorrect

Hint

Form of Pythagorean triplet
$=2m,\ m^2-1,\ m^2+1$
Let m = 3
$2m=6,\ m^2-1=8,\ m^2+1=10$
Question 9 of 18

9. Question
What is the value of 1+3+5+7+9+……+25 ?
- 196
- 625
- 225
- 169
Correct

Incorrect

Hint

The given expression is the sum of 13 odd numbers. The required value is $(13)^2=169$
Question 10 of 18

10. Question
What is the smallest number by which 396 must be multiplied so that the product is a perfect square?
- 5
- 11
- 3
- 2
Correct

Incorrect

Hint

$396=3\times3\times2\times2\times11$
Question 11 of 18

11. Question
If \(x\times y=\sqrt{x^2+y^2} \). The value of \((1\times2\sqrt{2}[1\times(-2\sqrt2)])\) is
- -7
- 0
- 2
- 9
Correct

Incorrect

Hint

$=[\sqrt{1+(2\sqrt2)^2}][\sqrt{1+(-2\sqrt2)^2}]\\ \\ =[\sqrt{1+8}][\sqrt{1+8}]\\ \\ =3\times3=9$
Question 12 of 18

12. Question
Evaluate \(\sqrt{41-\sqrt{21+\sqrt{19-\sqrt9}}} \)
- 3
- 6
- 5
- 8
Correct

Incorrect

Hint

$\sqrt{41-\sqrt{21+\sqrt{19-3}}}\\ \\ =\sqrt{41-\sqrt{21+\sqrt{16}}}=\sqrt{41-\sqrt{21+4}}=\sqrt{41-5}=\sqrt{36}=6$
Question 13 of 18

13. Question
Which of the following is a four digit perfect square number whose first two digits and last two digits taken seperately are also perfect squares?
- 1681
- 1636
- 3664
- 6481
Correct

Incorrect

Hint

$1681=(41)^2$
Question 14 of 18

14. Question
Find the number which when subtracted from its square results is 12
- 6
- 5
- 4
- 8
Correct

Incorrect

Hint

Let x be the required number
$x^2-x=12\\ \\ x(x-1)=12$
By inspection
$4\times(4-1)=12$
So, x=4
Question 15 of 18

15. Question
Which is the smallest naturals numbers which when added to the difference of square of 17 and 13 gives a perfect square?
- 1
- 5
- 11
- 24
Correct

Incorrect

Hint

$(17)^2-(13)^2=289-169=120\\ \\ 120+1=121=(11)^2$
Question 16 of 18

16. Question
If \(\sqrt{\dfrac{16}{49}}=\dfrac{x}{49} \) The value of x is
- 4
- 7
- 16
- 28
Correct

Incorrect

Hint

$\sqrt{\dfrac{16}{49}}=\dfrac{4}{7}=\dfrac{x}{49}\\ \\ \Rightarrow x=\dfrac{4\times49}{7}=4\times7=28$
Question 17 of 18

17. Question
The area of a square field is \( 80\dfrac{244}{729}\)sqm what is the length of each side of the field?
- 8.96 m
- 10.26 m
- 13.54 m
- 9.86 m
Correct

Incorrect

Hint

$\sqrt{\dfrac{58564}{729}}=\dfrac{242}{27}=8.96\ m$
Question 18 of 18

18. Question
If \(\sqrt{2^n}=64 \). The value of n is
- 2
- 4
- 6
- 12
Correct

Incorrect

Hint

$\sqrt{2^n}=64=2^6\\ \\ \Rightarrow 2^{\frac{n}{2}}=2^6\\ \\ \Rightarrow \dfrac{n}{2}=6\Rightarrow n=12$

Concept Checkers - Square and Square Roots - Class VIII

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