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
Introduction
Polygons
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
Introduction
Constructing a Quadrilateral
Some Special Cases
Visualising Solid Shapes
3 Topics | 1 Quiz
Introduction
View of 3D-Shapes
Faces, Edges and Vertices
Concept Checkers – Visualising Solid Shapes – Class VIII
Data Handling
5 Topics | 3 Quizzes
Introduction to Data Handling
Organising Data
Grouping 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
Introduction
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
Introduction
Cubes
Cubes Roots
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
Mensuration
8 Topics | 3 Quizzes
Introduction
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
Introduction
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
Introduction
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
Factorisation
4 Topics | 3 Quizzes
Introduction
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
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Inverse Proportion

Mathematics Class VIII Direct and Inverse Proportions Inverse Proportion

Two quantities a and b are said to be in Inverse proportion if

  1. Increase in a decreases the value of b
  2. Decrease in a increases the value of b

But the ratio of their respective values must be the same.

  • a and b will be in inverse proportion if k= ab
  • In such a case if b1, b2 are the values of b corresponding to the values a1, a2 of a respectively then, a1b1 = a2b2 = k, 
  • When two quantities a and b are in inverse proportion then they are written as a \propto \mathrm{\dfrac{1}{b}}

Example

If 15 artists can make a statue in 48 hours then how many artists will be required to do the same work in 30 hours?

Solution:

Let the number of artists required to make a statue in 30 hours be y.

Number of hours4830
Number of artists15y

We know that as the no. of artists will increase the time to complete the work will reduce. So, the number of hours and number of artists are in inverse proportion.

So \mathrm{48\times15=30\times y\ (a_1b_1=a_2b_2)}

Therefore,

\text y=\dfrac{48\times15}{30}=24

So, 24 artists will be required to make the statue in 30 hours.

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