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Mathematics, written down

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

Illustration for NCERT Class 10 Exercise 3.1 Solutions: Graphical Method

Pair of Linear Equations in Two Variables

NCERT Class 10 Exercise 3.1 Solutions: Graphical Method

Complete NCERT Class 10 Exercise 3.1 solutions: forming equations from word problems, solving them graphically, the coefficient ratio test for consistency, building equations to order and the triangle with the x-axis.

12 min read contains equations

Illustration for Graphical Method for Pair of Linear Equations, Class 10

Pair of Linear Equations in Two Variables

Graphical Method for Pair of Linear Equations, Class 10

Learn to solve a pair of linear equations in two variables by drawing graphs, tell intersecting, parallel and coincident lines apart with the coefficient ratio test, and practise with worked examples.

11 min read contains equations

Illustration for Production and Cost Analysis: Where to Start

Managerial Economics

Production and Cost Analysis: Where to Start

Production turns inputs such as land, labour and capital into goods and services. Here is how firms make production decisions, the factors of production and the production function.

3 min read

Illustration for Market Equilibrium

Managerial Economics

Market Equilibrium

Market equilibrium is the price at which the quantity demanded equals the quantity supplied. See how excess demand and excess supply push a market back to it, and what shifts it.

7 min read

Illustration for NCERT Class 10 Exercise 1.2 Solutions: Irrational Numbers

Real Numbers

NCERT Class 10 Exercise 1.2 Solutions: Irrational Numbers

Step-by-step NCERT Class 10 Exercise 1.2 solutions proving that root 5, 3 + 2 root 5, 1 over root 2, 7 root 5 and 6 + root 2 are irrational, using proof by contradiction and the prime divisor theorem.

7 min read contains equations

Illustration for How to Prove √2 and √3 Are Irrational, Class 10 Maths

Real Numbers

How to Prove √2 and √3 Are Irrational, Class 10 Maths

Step-by-step proofs by contradiction that root 2 and root 3 are irrational, the prime-divides-square theorem they rest on, and how to show numbers like 5 minus root 3 and 3 root 2 are irrational.

10 min read contains equations

Illustration for The Law of Supply, and What Shifts It

Managerial Economics

The Law of Supply, and What Shifts It

The law of supply says producers offer more at higher prices, other things equal. Here are the factors that shift supply, the types of supply, the exceptions and elasticity of supply.

9 min read contains equations

Illustration for What Supply Means

Managerial Economics

What Supply Means

Supply is the quantity of a good that producers are willing and able to sell at each price. Here are its features, the law of supply and supply schedules.

4 min read

Illustration for NCERT Class 10 Exercise 1.1 Solutions: HCF and LCM

Real Numbers

NCERT Class 10 Exercise 1.1 Solutions: HCF and LCM

Full NCERT Class 10 Exercise 1.1 solutions: prime factorisation of five numbers, HCF and LCM of pairs and triples, LCM from a given HCF, why 6ⁿ never ends in 0, two composite numbers and the Sonia and Ravi track problem.

9 min read contains equations

Illustration for Fundamental Theorem of Arithmetic with Examples, Class 10

Real Numbers

Fundamental Theorem of Arithmetic with Examples, Class 10

Why every composite number breaks into primes in exactly one way, and how to use prime factorisation to find the HCF and LCM, decide whether a power can end in 0, and avoid the three-number HCF-LCM trap.

10 min read contains equations

Illustration for Demand Forecasting

Managerial Economics

Demand Forecasting

Demand forecasting estimates future demand for a product. Here are the types, the main techniques from surveys to the Delphi method, and how forecasts help a business.

13 min read

Illustration for The Exceptions to the Law of Demand

Managerial Economics

The Exceptions to the Law of Demand

When a higher price does not reduce demand: Giffen goods, Veblen goods, price expectations, necessities and the other exceptions to the law of demand.

4 min read

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