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

Practice Questions – Factorization – Class VIII

Mathematics Class VIII Factorisation Practice Questions – Factorization – Class VIII

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Question 1 of 15

1. Question
The factors of \(x^4+y^4+x^2y^2 \) are
- \((x^2+y^2)\ \text{and}\ (x+y) \)
- \((x^2+y^2)^2 \)
- \((x^2+y^2+xy),(x^2+y^2-xy) \)
- \((x^2-y^2)^2 \)
Correct

Incorrect

Hint

$x^4+y^4+x^2y^2\\ \\ x^4+y^4+2x^2y^2-x^2y^2\\ \\ (x^2+y^2)^2-(xy)^2\\ \\ =(x^2+y^2+xy)\ (x^2+y^2-xy)$
Question 2 of 15

2. Question
The factors of \(15x^2-26x+8 \) are
- \((3x-4),(5x+2) \)
- \((3x-4),(5x-2) \)
- \((3x+4),(5x-2) \)
- \((3x+4),(5x+2) \)
Correct

Incorrect

Hint

$15x^2-26x+8\\ \\ 15x^2-20x-6x+8\\ \\ 5x(3x-4)-2(3x-4)\\ \\ (3x-4)\ (5x-2)$
Question 3 of 15

3. Question
The coefficient of ‘a’ when \(9a^2+18a \) is divided by \((a+2) \) is
- \(18 \)
- \( 9\)
- \(\dfrac{1}{2} \)
- \(2 \)
Correct

Incorrect

Hint

$\dfrac{9a^2+18a}{a+2}=\dfrac{9a(a+2)}{a+2}=9a$
Question 4 of 15

4. Question
When \((p^2+7p+10) \) is divided by \((p+5) \), the quotient is
- \(p-5 \)
- \(p-2 \)
- \(p+2 \)
- \(p+5 \)
Correct

Incorrect

Hint

$\dfrac{p^2+5p+2p+10}{p+5}=\dfrac{(p+5)(p+2)}{p+5}=p+2$
Question 5 of 15

5. Question
The correct statement is
- \((3m+4)^2=3m^2+6m+16 \)
- \( n(3n+2)=3n^2+2n\)
- \((x-2)\ (x-8)=x^2-16 \)
- \((p+2)(p+4)=p^2+8 \)
Correct

Incorrect

Hint

$n(3n+2)=3n^2+2n\\ \\ (3m+4)^2=9m^2+16+2\times3m\times4=9m^2+16+24m\\ \\ (x-2)\ (x-8)=x^2-2x-8x+16=x^2-10x+16\\ \\ (p+2)(p+4)=p^2+2p+4p+8\\ \\ p^2+6p+8$
Question 6 of 15

6. Question
If \((x^3+3x+5)\ (x^2-3x+5)=m^2-n^2 \). The value of \(m \) is
- \(x^2-3x \)
- \(3x \)
- \(x^2+5 \)
- \(x^2+3x \)
Correct

Incorrect

Hint

$(x^2+3x+5)\ (x^2-3x+5)\\ \\ =(x^2+5+3x)\ (x^2+5-3x)\\ \\ =(x^2+5)^2-(3x)^2\\ \\ =m^2-n^2\\ \\ m=x^2+5$
Question 7 of 15

7. Question
Divide \(6p^5+18p^4-3p^2 \) by \(3p^2 \)
- \(6p^3-6p^2+1 \)
- \(2p^3-6p^2-1 \)
- \(2p^3+6p^2-1 \)
- \(2p^3+6p^2+1 \)
Correct

Incorrect

Hint

$\dfrac{6p^5+18p^4-3p^2}{3p^2}=\dfrac{3p^2(2p^3+6p^2-1)}{3p^2}=2p^3+6p^2-1$
Question 8 of 15

8. Question
Which is the exponential form of factors of \( a^2+4a+4\)?
- \((a+2)^2 \)
- \((a+1)^2 \)
- \((a-2)^2 \)
- \( (a-1)^2\)
Correct

Incorrect

Hint

$a^2+4a+4=a^2+2\times a\times2+2^2=(a+2)^2$
Question 9 of 15

9. Question
The result when \(x^3+6x^2+9x \) is factorised
- \(x^2(x+2)^2 \)
- \(x(x+3)^2 \)
- \(x(x+3) \)
- \(x^2(x+3) \)
Correct

Incorrect

Hint

$x(x^2+6x+9)\\ \\ x(x^2+2\times x\times3+3^2)\\ \\ =x(x+3)^2$
Question 10 of 15

10. Question
Simplify \(\dfrac{-3a^2b\times15\ cab^2}{-10\ cab} \)
- \(\dfrac{3}{2}a^2b^2 \)
- \(\dfrac{9}{2}a^2b^2 \)
- \(1 \)
- \( 0\)
Correct

Incorrect

Hint

$\dfrac{-3a^2b\times15\ cab^2}{-10\ cab}=\dfrac{9}{2}a^2b^2$
Question 11 of 15

11. Question
Find the quotient of \(\dfrac{36x^3y^2z}{-9x^2y^2z} \)
- \(4x \)
- \(4xy^2z \)
- \( -4x\)
- \(1 \)
Correct

Incorrect

Hint

$\dfrac{36x^3y^2z}{-9x^2y^2z}=\dfrac{36}{-9}\left(\dfrac{x^3}{x^2}\right)\left(\dfrac{y^2}{y^2}\right)\left(\dfrac{z}{z}\right)=-4x$
Question 12 of 15

12. Question
Divide \(4p^5-14p^4+6p^3-2p^2 \) by \(2p^2 \)
- \(2p^3+7p^2+3p+1 \)
- \(2p^3-7p^2+3p-1 \)
- \( 2p^3-7p^2-3p-1\)
- \(2p^3+7p^2-3p-1 \)
Correct

Incorrect

Hint

$\dfrac{4p^5}{2p^2}-\dfrac{14p^4}{2p^2}+\dfrac{6p^3}{2p^2}-\dfrac{2p^2}{2p^2}\\ \\ 2p^3-7p^2+3p-1$
Question 13 of 15

13. Question
Simplify \(3xz-4yz-6xp+8yp \)?
- \((3x+4y)(z+2p) \)
- \((3x+4y)(z-2p) \)
- \((3x-4y)(z+2p) \)
- \((3x-4y)(z-2p) \)
Correct

Incorrect

Hint

$3xz-4yz-6xp+8yp\\ \\ z(3x-4y)-2p(3x-4y)\\ \\ (3x-4y)(z-2p)$
Question 14 of 15

14. Question
Simplify \(\dfrac{3\ lm}{8n^2}\times\dfrac{32\ ln^3}{m^2}\div\dfrac{9\ ln^2}{m} \)?
- \(\dfrac{4l}{3n} \)
- \(1 \)
- \(0 \)
- \(\dfrac{9n}{4l} \)
Correct

Incorrect

Hint

$\dfrac{3\ lm}{8n^2}\times\dfrac{32\ ln^3}{m^2}\times\dfrac{m}{9\ l^2}=\dfrac{4\ l}{3n}$
Question 15 of 15

15. Question
Divide \(q(5q^2-80) \) by \(5q(q+4) \)
- \(5q(q-16) \)
- \(q-4 \)
- \(5q(q^2+16) \)
- \(q+16 \)
Correct

Incorrect

Hint

$\dfrac{5q(q^2-16)}{5q(q+4)}=\dfrac{5q(q+4)(q-4)}{5q(q+4)}=q-4$

Practice Questions - Factorization - Class VIII

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