Applied Mathematics · Class 11 Commerce
Ch 1Numbers and Quantification — Class 11 Applied Mathematics, concept-first.
This concept map shows how the chapter fits together. The study of integers opens onto three ideas with real-life uses: the binary system, which underlies how computers store and process information; indices and logarithms, the tools for handling very large and very small quantities; and primes and factorisation, which…
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Introduction
You've been solving problems your whole life. When you see a new type of question, you first figure out what it's asking, then decide which tools to use, then carry out the steps.
Most relevant Q&A
- Write the following numbers in decimal notation: $(1010101100110)_2$, $(101011000110)_2$, $(101111100110)_2$, $(1000000000110)_2$.Free
- Write the following numbers in decimal notation: $654321$, $1000001$, $56237801$, $2468097531$, $963258741$.Free
- Simplify the following and write in decimal notation: $(1000101111100)_2 + (1100101000100)_2$, $(11101100100)_2$.Preview
- Simplify the following and write in binary notation: $(1111000110000)_2 \times 5642371$.Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Concept Map
This concept map shows how the chapter fits together. The study of integers opens onto three ideas with real-life uses: the binary system, which underlies how computers store and process information;…
Introduction
In today's world of computers and digital communication, keeping information secure often comes down to number theory — and prime numbers sit right at the heart of that security.
Prime Numbers
Prime numbers are the fundamental building blocks of all natural numbers — every integer greater than 1 can be broken down into a unique product of primes.
Why Prime Numbers Are Important?: Encryptions Using Prime Numbers
Prime numbers are the building blocks of all natural numbers, but their true power emerges when we need to keep information secret.
Binary Numbers
We use the decimal system every day, but computers and digital systems speak a different language — one built on just two digits: 0 and 1.
+−Exercise 1.1i4 questions
- Q1Write the following numbers in decimal notation: $(1010101100110)_2$, $(101011000110)_2$, $(101111100110)_2$, $(1000000000110)_2$.Free
- Q2Write the following numbers in decimal notation: $654321$, $1000001$, $56237801$, $2468097531$, $963258741$.Free
- Q3Simplify the following and write in decimal notation: $(1000101111100)_2 + (1100101000100)_2$, $(11101100100)_2$.Preview
- Q4Simplify the following and write in binary notation: $(1111000110000)_2 \times 5642371$.Preview
Complex Numbers (Preliminary Idea Only)
You already know how to count, measure, and even handle negative numbers and fractions. But what happens when you try to solve an equation like ? No real number squares to give , so we need a new kind…
+−Exercise 1.2i2 questions
Indices, Logarithm and Antilogarithm
Numbers grow fast when you multiply them repeatedly, and indices give us a compact language to describe that growth.
Logarithms
Logarithms are the inverse of exponentiation — just as subtraction undoes addition, a logarithm undoes raising a number to a power.
Laws and Properties of Logarithms
4 QLogarithms are not arbitrary rules — they are a direct consequence of the way exponents work. Every law of logarithms mirrors a corresponding law of exponents, so understanding one gives you the other…
+−Worked Examplesi2 questions
- Example 1There was an earthquake with a wave amplitude 2020 times the [standard] wave. Calculate the Richter scale with two decimal digits.Free
- Example 2A scientist running an experiment finds that a particular bacterial colony doubles its population every 20 hours. The experiment starts with…Preview