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Mathematics, written down

Worked problems, method notes and exam strategy from the people who teach the classes.

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Latest article Managerial Economics

Monopsony: A Market With One Buyer

A monopsony is a market with a single dominant buyer facing many sellers. Here are its features, why it appears mostly in factor markets, and a supermarket example.

Yeswanth Reddy K 2 min read

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Online Maths Tutor in Hyderabad

Online maths tuition for Hyderabad students from Expresswala Academy: contact details, the concept-first approach, cours...

· 6 min read

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Managerial Economics

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Oligopoly

An oligopoly is a market dominated by a few large, interdependent firms behind high entry barriers. Here are its feature...

· 4 min read

Monopolistic Competition

Monopolistic competition has many sellers of similar but differentiated products. Here are its features and a familiar e...

· 1 min read

The Types of Monopoly

Twelve kinds of monopoly, from pure and natural monopolies to cartels, franchises and patents, with how each arises and...

· 10 min read

The archive

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Illustration for Monopsony: A Market With One Buyer

Managerial Economics

Monopsony: A Market With One Buyer

A monopsony is a market with a single dominant buyer facing many sellers. Here are its features, why it appears mostly in factor markets, and a supermarket example.

2 min read

Illustration for Oligopoly

Managerial Economics

Oligopoly

An oligopoly is a market dominated by a few large, interdependent firms behind high entry barriers. Here are its features, why firms collude, and familiar examples.

4 min read

Illustration for Angle of Elevation and Depression: Class 10 Maths Guide

Some Applications of Trigonometry

Angle of Elevation and Depression: Class 10 Maths Guide

Learn what the line of sight, angle of elevation and angle of depression mean, why the last two are equal, and how one right triangle and one angle give the height of a tower, a ladder, a chimney or a kite.

13 min read contains equations

Illustration for NCERT Class 10 Exercise 6.3 Solutions: Similar Triangles

Triangles

NCERT Class 10 Exercise 6.3 Solutions: Similar Triangles

Step-by-step solutions to all 16 questions of NCERT Class 10 Exercise 6.3, using the AA, SSS and SAS criteria on medians, altitudes, bisectors, a trapezium, a parallelogram and a shadow problem.

21 min read contains equations

Illustration for Monopolistic Competition

Managerial Economics

Monopolistic Competition

Monopolistic competition has many sellers of similar but differentiated products. Here are its features and a familiar example: the restaurants in your locality.

1 min read

Illustration for The Types of Monopoly

Managerial Economics

The Types of Monopoly

Twelve kinds of monopoly, from pure and natural monopolies to cartels, franchises and patents, with how each arises and how governments keep them in check.

10 min read

Illustration for Similarity Criteria of Triangles: AA, SSS and SAS Explained

Triangles

Similarity Criteria of Triangles: AA, SSS and SAS Explained

The AA, SSS and SAS similarity criteria for triangles with proofs from the Basic Proportionality Theorem, the RHS note, and worked examples including the classic lamp-post shadow problem.

13 min read contains equations

Illustration for NCERT Class 10 Exercise 6.2 Solutions: BPT and Its Converse

Triangles

NCERT Class 10 Exercise 6.2 Solutions: BPT and Its Converse

Step-by-step solutions to every question of NCERT Class 10 Exercise 6.2, using the Basic Proportionality Theorem and its converse to find lengths, test for parallel lines and prove trapezium results.

10 min read contains equations

Illustration for Monopoly: One Seller, and What Follows From It

Managerial Economics

Monopoly: One Seller, and What Follows From It

A monopoly has a single seller and no close substitutes. Here is why monopolies arise, their main features, some examples, and how they differ from oligopolies.

3 min read

Illustration for Perfect and Imperfect Competition Compared

Managerial Economics

Perfect and Imperfect Competition Compared

A side-by-side comparison of perfect and imperfect competition: number of firms, market power, products, entry barriers, pricing, efficiency and examples.

3 min read

Illustration for Basic Proportionality Theorem: Proof and Examples, Class 10

Triangles

Basic Proportionality Theorem: Proof and Examples, Class 10

The Basic Proportionality Theorem (Thales) and its converse for Class 10: statement, full area proof, the whole-side form, and worked examples on lengths, parallel tests, trapeziums and isosceles triangles.

12 min read contains equations

Illustration for NCERT Class 10 Exercise 6.1 Solutions: Similar Figures

Triangles

NCERT Class 10 Exercise 6.1 Solutions: Similar Figures

Complete NCERT Class 10 Exercise 6.1 solutions: the fill-in-the-blanks on similar and congruent figures, checked examples of similar and non-similar pairs, and the square and rhombus question.

7 min read contains equations

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