by Rezyo Staff WriterNovember 7, 2025 AI, CBSE, CBSE Class 100 comments

AI Ethics & Project Cycle: CBSE Class 10 (Bias, Privacy, Scoping & Evaluation)

This comprehensive guide covers the key CBSE Class 10 AI chapters on Ethics and the Project Cycle. Explore moral dilemmas, data privacy, and AI bias, then learn the 5-stage project cycle: Problem Scoping (4Ws), Data Acquisition, Data Exploration, Modelling, and Evaluation with interactive charts.

AI Ethics & Project Cycle: CBSE Class 10

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AI Ethics for Class 10: Understanding the Hard Questions

This page covers the moral issues, data privacy concerns, AI bias, and access challenges relevant to your CBSE curriculum.

1. Moral Dilemmas: The Self-Driving Car Problem

Artificial intelligence is not just a technical tool; it makes decisions. Sometimes, these decisions have no clear “right” answer. These are moral dilemmas. Developers must program AI to respond to these situations.

The most famous example is the “self-driving car” scenario, a version of the trolley problem.

Scenario Poll: What Should the Car Do?

A self-driving car’s brakes fail. It is heading towards a crosswalk with five pedestrians. The car can swerve onto the sidewalk, but it will hit one person standing there.

Option A: Stay Course

The car continues straight, hitting the five pedestrians.

Option B: Swerve

The car swerves, hitting the single person on the sidewalk.

What if the single person on the sidewalk is the car’s owner? What if the pedestrians were crossing against a “Don’t Walk” signal? AI must be programmed with a set of rules for these choices. Your learning outcome is to be able to articulate these trade-offs.

Cross-link: These ethical choices are defined in the Problem Scoping stage of the AI Project Cycle (Section 5), where developers must decide *why* the AI is being built.

2. Data Privacy: Permissions, Sensors, and Consent

AI systems need data to learn. Often, this is your personal data. Data privacy involves your right to control who sees and uses your information. Your smartphone is a powerful data collection tool, using sensors like the microphone, camera, and GPS.

Smartphone App Permissions

Apps often ask for permissions. It is important to know what you are agreeing to.

Permission Request	Stated Reason	Potential Privacy Concern
Contacts	“To help you find friends”	The app uploads your entire address book to its servers.
Microphone	“To use voice commands”	The app could be listening even when you are not using it.
Location	“To provide local weather”	The app can track your movements and build a profile of your daily routine.

3. AI Bias: When Data Creates Unfairness

AI bias occurs when an AI system produces results that are unfair to certain groups of people. This is not because the AI “thinks” in a biased way. It happens because the AI learns from human-generated data that already contains bias.

Example (Voice): Early voice assistants were less accurate at understanding female voices. This happened because the training data contained more male voices.
Example (Search): If you search an online job site for “secretary,” the image results might show mostly women. This reflects old stereotypes present in the data, and the AI learns and repeats this pattern.

Interactive Chart: Visualizing AI Bias

This chart shows a hypothetical scenario for a facial recognition system. The error rate (how often the system is wrong) is not the same for all groups. This is a visual example of bias.

Hypothetical Error Rates in a Facial Recognition Model

4. Access & Inclusion: The AI Digital Divide

Who gets to use and build AI? This question is about access and inclusion. There is a risk of a “digital divide,” where people without access to new technology, fast internet, or proper education are left behind.

Downloadable Debate Kit

Debate is a great way to explore these topics. Use these prompts for a class discussion.

Topic 1: “AI will create more jobs than it destroys.”
Topic 2: “Student access to AI writing tools should be restricted.”

Open Debate Kit

Parent & Teacher Guide

This guide helps adults talk to kids and teens about AI. It covers screen time, AI tools in homework, and online safety.

How to set boundaries for AI tools.
Identifying AI-generated content.
Talking about privacy and digital footprint.

Open Parent Guide

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5. The AI Project Cycle

Interactive: The 5 Stages of the AI Project Cycle

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Creating an AI system is not a single step. It is a process called the AI Project Cycle. This cycle provides a structured way to move from an idea to a working, evaluated solution. The main stages are: Problem Scoping, Data Acquisition, Data Exploration, Modelling, and Evaluation.

5.1 Problem Scoping

This is the most important stage. Before writing any code, the team must understand the problem. We use the 4Ws Problem Canvas to guide this.

Interactive: 4Ws Problem Canvas

Fill this out to practice scoping a new AI project.

Who? (Who are the stakeholders?)

What? (What is the problem?)

Where? (What is the context/location?)

Why? (Why is this a problem to solve?)

Download: Problem Statement Template

After the 4Ws, you create a one-page summary. This template helps you structure your idea.

Open Problem Statement Template

5.2 Data Acquisition

AI learns from data. This stage is about collecting the right information. We first identify features, which are the inputs the AI will use (e.g., for a weather-predicting AI, features would be temperature, humidity, wind speed).

Data can come from:

Sensors: Like your phone’s camera, microphone, or GPS.
Databases: Existing records from a company or school.
Web Scraping: Collecting information from websites.
Open Data Portals: Free, public datasets from governments or research (e.g., data.gov.in).

5.3 Data Exploration

Before we can use data, we must understand it. Data Exploration uses charts and statistics to find patterns, errors, and insights. This helps us clean the data (e.g., remove duplicates) and choose the right features. Basic charts are used to visualize the data.

Infographic: Common Data Visualization

Bar Chart

Used to compare quantities across different categories.

Pie Chart

Used to show the proportions (percentages) of a whole.

Scatter Plot

Used to find a relationship (correlation) between two variables.

The “Visualizing AI Bias” chart (in Section 3) is a good example of exploring data to find problems.

5.4 Modelling

This is where the “learning” happens. A model is a program that finds patterns in data. There are two main approaches:

Modelling Approach	How it Works	Example
Rule-Based	Programmers write specific rules (e.g., “IF-THEN” statements).	A chatbot that gives the same 3 answers to a specific question.
Learning-Based	The model “learns” patterns from a large amount of data (Machine Learning).	A spam filter that learns to identify new types of junk email.

5.5 Evaluation

How do we know if the model works? We test it. Evaluation uses a separate set of “testing data” that the model has not seen before. We measure its performance using different metrics.

Accuracy: The percentage of correct predictions. (e.g., “It was right 90% of the time.”)
Precision: Of all the times it predicted “Yes,” how often was it right? (Good for avoiding false positives).
Recall: Of all the actual “Yes” cases, how many did it find? (Good for avoiding false negatives).
F1-Score: A balance between Precision and Recall.

Infographic: Interactive Confusion Matrix

This table helps us see *where* our AI model is right or wrong. Hover over the 4 squares to learn more. (Example: A spam filter)

Predicted: Spam

Predicted: Not Spam

Actual: Spam

50

(True Positive)

5

(False Negative)

Actual: Not Spam

10

(False Positive)

100

(True Negative)

5.5.1 Choosing the Right Metric: Precision vs. Recall

Accuracy isn’t always the best metric. Sometimes, certain types of mistakes are much worse than others. This is where we choose between Precision and Recall.

Focus on Precision

Goal: To minimize False Positives.

Ask: “Of all the times the AI said ‘Yes’, how often was it right?”

Use Case: Email Spam Filter. A False Positive (a real email marked as spam) is very bad. We would rather let a little spam through (a False Negative) than lose an important email.

Focus on Recall

Goal: To minimize False Negatives.

Ask: “Of all the *actual* ‘Yes’ cases, how many did the AI find?”

Use Case: Medical Disease Scan. A False Negative (saying a sick patient is “healthy”) is extremely dangerous. We would rather have some False Positives (telling a healthy person to get more tests) than miss a real case.

5.5.2 Evaluation for Fairness

This is the most important cross-link. The Evaluation stage is not just about numbers like accuracy; it’s our chance to check for the AI Bias we learned about in Section 3.

Here, we must ask: “Is our model’s accuracy good for *all* groups?” We must test our model on data broken down by group.

For example, we would check the error rate for our facial recognition system (from the D3 chart) separately for Group A, Group B, and Group C. If we find the error rate for Group B is much higher (9.8%) than for Group C (3.1%), we have found bias. We must then go back to the Data stages to fix it, perhaps by collecting more data for Group B.

Cross-link: This shows how Evaluation links back to AI Ethics and can force us to repeat the Project Cycle to fix bias.

6. Q&A and Frequently Asked Questions

Filter Questions:

7. Key Chapter Notes

Ethics is the study of what is right and wrong. AI ethics applies this to the decisions made by machines.
Moral Dilemmas are “no-win” scenarios. The goal is not to find a “right” answer but to articulate the trade-offs of each choice.
Data Privacy is about consent and control. Your data is valuable, and you have a right to know how it is used.
AI Bias comes from biased data, not biased machines. It is a technical problem with serious social consequences.
AI Access is an issue of fairness. Everyone should have the opportunity to benefit from and participate in the development of AI.
AI Project Cycle: The 5 stages are Problem Scoping, Data Acquisition, Data Exploration, Modelling, and Evaluation.
Problem Scoping (4Ws): Defines *Who* has the problem, *What* it is, *Where* it happens, and *Why* it needs solving.
Data Visualization: Using charts (Bar, Pie, Scatter) to understand data and find patterns.
Modelling: Can be Rule-Based (explicit rules) or Learning-Based (learning from data).
Evaluation: Uses metrics like Accuracy, Precision, and Recall to test the model.
Precision vs. Recall: Precision minimizes false positives (e.g., spam filter). Recall minimizes false negatives (e.g., medical test).
Fairness Metrics: Evaluation must also check if the model is biased against any group, linking to AI Ethics.

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by Rezyo Staff WriterNovember 7, 2025 AI, CBSE, CBSE Class 100 comments

AI Ethics for CBSE Class 10: Self-Driving Cars, Data Privacy, AI Bias, & Access

Welcome to your complete guide for Chapter 4: AI Ethics, designed for CBSE Class 10 students. As AI becomes part of our daily lives, from self-driving cars to smartphone apps, it is essential to understand the tough questions it brings up. This guide breaks down the core topics, starting with the moral dilemmas of AI, like the famous self-driving car problem. We will then investigate how your data privacy is handled by apps, explore the different sources of AI bias in search results and voice assistants, and discuss how AI access and the digital divide are changing the job market for everyone.

AI Ethics: CBSE Class 10 Chapter 4

CBSE Class 10 / Chapter 4

AI Ethics

This page covers moral issues with self-driving cars, data privacy on your phone, AI bias in search, and how AI access affects jobs.

Updated: October 2025

Learning Outcomes

By the end of this chapter, you will be able to:

Articulate ethical trade-offs in scenario-based problems.
Recognize and describe privacy concerns related to data collection.
Identify different sources of AI bias and their real-world impact.
Explain how unequal access to AI can create new challenges.

1. Moral Dilemmas: The Self-Driving Car

Imagine a self-driving car. Its brakes fail. It must choose between two options: stay on course and hit five people, or swerve and hit one person on the sidewalk. What should it do?

This is a famous thought experiment. It highlights two main ways of thinking about ethics:

Option 1: Focus on the Outcome

This view suggests the best action is the one that causes the least harm. In this case, hitting one person is better than hitting five. The car should swerve.
Option 2: Focus on the Action

This view suggests some actions are just wrong, no matter the outcome. The car swerving is a deliberate choice to hit someone. This view might say the car should do nothing and stay its course.

The key point is this: the car does not “decide” in the moment. Engineers and companies programmed its rules months or years earlier. The real question is not “What will the car do?” but “What values did humans program into the car?”

Scenario Poll

If you were programming the car, what rule would you set?

2. Data Privacy: Your Phone and Your Data

Modern AI runs on data. Your data. Your smartphone is a powerful data collection tool. When you install a “free” app, it often asks for permissions.

Access to your Microphone can capture nearby conversations.
Access to your Location (GPS) tracks where you go.
Access to your Contacts sees who you know.
Access to your Browsing History knows what you read.

Infographic: The Flow of Your Data

This data is used to build a profile of you. This profile helps companies predict your behavior. They use these predictions to show you targeted ads or to keep you on their app longer.

The “I Agree” Problem

You give permission by clicking “I Agree” on a long “Terms of Service” document. Almost nobody reads these. They are often long, confusing, and non-negotiable. This is not meaningful consent. Clicking “Agree” often protects the company more than it informs you.

Beyond the Phone: Smart Sensors and Consent

This problem extends beyond phones. Smart speakers (like Alexa or Google Home) are “always listening” for a wake word. This means they process everything you say. Internet of Things (IoT) devices, like smart TVs or even refrigerators, also collect data about your habits.

This raises a deeper question about informed consent. Did you truly “consent” to your TV tracking your viewing habits if it was in paragraph 72 of a document you clicked “OK” to? Ethical AI design requires consent to be clear, easy to understand, and easy to withdraw.

What App Permissions Really Mean

Permission: Location

What it says: “To provide local weather.”
What it can also mean: “To know where you live, work, shop, and visit. We can sell this data to advertisers who want to target people in those areas.”

Permission: Contacts

What it says: “To help you find friends.”
What it can also mean: “To build a map of your social network. We can target your friends with ads or suggest they use our app.”

Permission: Microphone

What it says: “To enable voice commands.”
What it can also mean: “To listen to ambient sound, conversations, or TV shows you watch to build a more detailed advertising profile.”

3. AI Bias: When AI is Unfair

AI systems are not neutral. They are created by humans and trained on data from our world. This means they can learn, and even amplify, human biases. This is AI Bias.

Interactive: Common Sources of Bias

Where Does Bias Come From?

Filter by source of bias:

Data-Driven Bias

The data used to train the AI is skewed. If a facial recognition system is trained mostly on pictures of one demographic, it will have higher error rates for all other demographics.

Algorithmic Bias

A person’s flawed assumption is built into the AI’s logic. For example, using “zip code” to decide if someone gets a loan. This can be a proxy for race due to historical housing segregation.

Interaction Bias

The AI learns from biased human users. If people searching for “CEO” only click on pictures of men, the AI learns to show only men. This creates a feedback loop.

Infographic: The Interaction Bias Feedback Loop

Examples of AI Bias

Filter by type of harm:

Case Study	Type of Bias	Real-World Harm
Voice Assistants Lower accuracy for non-standard accents	Data-Driven	Exclusion Makes the tech unusable for some groups
Image Search Search for “doctor” shows stereotypes	Interaction / Feedback Loop	Shapes Reality Limits students’ view of what is possible
Facial Recognition Higher error rates for minority groups	Data-Driven	Systemic Injustice Can lead to wrongful arrests

4. Access, Inclusion, and Jobs

AI is changing the job market. This creates a large challenge related to access and fairness.

The Changing Job Market

Task Automation

AI can automate routine tasks, like data entry or simple accounting. This can displace workers in those jobs.
New Roles

AI also creates new, high-skill roles, such as data scientist, AI ethicist, and machine learning engineer.

The problem is that the new jobs require advanced, often expensive, training. It is difficult for a person whose job is automated to “reskill” for these new roles. This can widen the gap between high-income and low-income groups.

The “Digital Divide”

The “Digital Divide” is the gap between those who have access to modern technology and those who do not. This gap is not just about having a computer. It has many layers:

The Infrastructure Gap: Lack of access to high-speed internet and modern devices.
The Literacy Gap: Lack of skills to use technology for creation and critical thinking, not just consumption.
The Educational Gap: Unequal access to high-quality AI education in schools.

This divide is important because it makes all other AI harms worse. A person without digital literacy is less able to spot bias and more vulnerable to data collection. A student without good internet cannot access the “reskilling” tools needed for the new economy.

AI, Age, and Inclusion

Inclusion is also about age. AI systems must be designed for everyone, not just tech-savvy adults.

For Children: AI recommendation algorithms on video platforms or social media can create addictive loops. There are ethical questions about data collection from minors and the need for age-appropriate content filters.
For the Elderly: As services like banking move online, complex AI-driven interfaces can exclude older adults who are less digitally native. This can prevent them from accessing essential services.

Interactive Chart: The Access Gap

Access to key digital resources (example data).

Module: Key Terminology

Stakeholder: Any person or group of people affected by an AI system. This is not just the user, but can include people a decision is made *about*, and even broader society.
Trade-off: An ethical compromise. In the self-driving car case, choosing between one bad outcome and another is a trade-off. There is no “perfect” solution.
Proxy: A feature used as a substitute for another, often sensitive, feature. Using “zip code” as a substitute for “race” is a common example of a harmful proxy in algorithmic bias.
Algorithmic Transparency: The idea that the decisions made by an AI should be understandable and explainable to humans. A “black box” AI is one that is not transparent.
Informed Consent: A clear, knowing, and voluntary agreement to data collection. This is different from just clicking “I Agree” on a long, unreadable document.

Chapter Notes: Key Takeaways

Ethics Involves Trade-offs: AI ethics is rarely about right vs. wrong. It is usually about right vs. right, or choosing the “least bad” option. These rules are programmed by humans.
Data is Power (and a Liability): All AI systems are trained on data. The collection of this data creates privacy risks. “Free” apps are paid for with your personal data.
AI Can Be Biased: Bias can come from skewed data, flawed human logic, or feedback loops from users. This can lead to unfair or discriminatory outcomes.
Access is Not Equal: The benefits of AI (new jobs, tools) and the harms (job automation, digital exclusion) are not distributed fairly. The “Digital Divide” can affect people based on income, location, and age.

5. Questions & Answers (FAQs)

Q: Is AI ethics just about self-driving cars?

A: No. The self-driving car is just one clear example. AI ethics covers any situation where AI makes choices that affect humans. This includes privacy, fairness in loan applications, bias in search results, and impacts on jobs.

Q: Can we just “fix” AI bias by using more data?

A: Not always. Using more data might help if the problem is just data-driven bias. But if the data itself reflects a biased world, “more data” just means “more bias.” It also does not fix algorithmic bias (flawed human logic) or interaction bias (feedback loops).

Q: What can I do about data privacy?

A: You can take small steps. Review your phone’s app permissions. Deny permissions that an app does not truly need (e.g., a calculator app does not need your location). Be aware of what you share online. Support companies and laws that protect user privacy.

Q: Will AI take all of our jobs?

A: This is unlikely. AI will automate certain *tasks*, not necessarily entire *jobs*. This will change many jobs and displace some, but it will also create new jobs that require human skills like creativity, critical thinking, and emotional intelligence. The main challenge is ensuring people can get the training for these new roles.

6. Resources & Next Steps

Download: Classroom Debate Kit

Get scenario-based questions to debate these topics in your class. (Link disabled)

Download: Parent/Teacher Guide

A guide for adults on how to discuss these topics with students. (Link disabled)

Continue Learning:

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by Rezyo Staff WriterNovember 7, 2025 AI, CBSE, CBSE Class 100 comments

AI Domains: Data Science, CV, NLP CH3 | CBSE Class 10 AI (417)

This guide covers Chapter 3 of the CBSE Class 10 AI (417) curriculum: An Introduction to AI Domains. We provide a clear breakdown of the three main branches: Data Science, Computer Vision (CV), and Natural Language Processing (NLP). You will learn to identify the data types and typical tasks for each domain, explained with simple, real-world examples like price comparison websites, smartphone face lock, and smart assistants.

CBSE Class 10 Chapter 3: Introduction to AI Domains | Rezyo.in

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CBSE AI Curriculum

CBSE Class 10 AI (417): Chapter 3 – Introduction to AI Domains

Updated: October 2025

Introduction: The Three Main Areas of AI

Page Objective

This chapter explains the three main areas, or branches, of Artificial Intelligence as specified in the CBSE (Subject Code 417) curriculum. The purpose is to give a clear and structured look at Data Science, Computer Vision (CV), and Natural Language Processing (NLP).

To make these complex topics understandable, this report will explain each area using real-world applications that students see daily. We will look at:

Data Science by checking how price comparison websites work.
Computer Vision by explaining the technology behind smartphone face lock features.
Natural Language Processing by analyzing what happens inside smart assistants like Siri and Google Assistant.

Learning Outcomes

The objectives of this unit are aligned with the CBSE curriculum’s goal of making students “AI-Ready.” By the end of this chapter, a student will be able to:

Identify and explain the differences between the three core areas of AI: Data Science, Computer Vision, and Natural Language Processing.
Match specific types of data (for example, numerical tables, image files, or text messages) to their correct AI area.
Describe the typical tasks and common applications for each area, such as prediction, classification, and recognition.

The Core Concept: AI Areas are Defined by Data

Artificial Intelligence becomes intelligent through training, and this training requires data. A clear and effective way to separate the AI areas is by the specific type of data they are designed to process.

Think of an AI model as a specialized engine: its function is set by the “fuel” it uses. Students can easily understand the difference between a spreadsheet of numbers, a photograph, and a spoken sentence. By linking each area to these data types, we can build a simple and strong framework for understanding AI.

Data Science processes numerical and alpha-numeric data (e.g., spreadsheets, databases, user logs).
Computer Vision processes visual data (e.g., images, videos, camera feeds).
Natural Language Processing processes linguistic data (e.g., text and speech).

This table provides a clear map for the entire chapter, summarizing the core concepts in one place.

t

Domain	Data Type (“What it processes”)	Typical Tasks (“What it does”)	CBSE Example
Data Science	Numerical & Alpha-Numeric Data (e.g., spreadsheets, databases)	Prediction, Classification, Recommendation	Price Comparison Websites
Computer Vision	Visual Data (e.g., images, videos, pixels)	Classification, Object Detection, Recognition	Smartphone Face Lock
Natural Language Processing	Linguistic Data (e.g., text, speech, sentences)	Classification, Translation, Understanding	Smart Assistants (Siri/Alexa)

Filter by Domain

Visualizing the Domains

This graphic shows the three main domains. While we study them separately, many modern applications (like the Google Translate camera) use them together. Hover over a circle for a definition.

Domain Explained: Data Science

Core Concept: The Data to Insight to Decision Pathway

Data Science is an AI area related to “data systems and processes.” At its core, it is a field of study that combines programming skills, mathematics, and statistics to “extract meaningful insights from data.”

This process can be simplified into a three-step pathway: Data to Insight to Decision.

Step 1: Data (Acquisition & Collection) This is the raw material. The system “collects numerous data” and “maintains data sets.” This can be structured data, like sales figures in a spreadsheet, or unstructured data, like user website clicks.
Step 2: Insight (Analysis & Modeling) This is the “science” part. The AI “derives meaning/sense” from the raw data. It uses statistics, data analysis, and machine learning to find answers and “discover hidden patterns.” The purpose is to turn raw, messy data into clean, useful information.
Step 3: Decision (Application) The “information extracted… can be used to make a decision about it.” This extracted insight is used to make an automated prediction (e.g., “this stock will go up”), a recommendation (e.g., “you should watch this movie”), or help a person make a better choice.

Data Pipeline Visualization

This simple chart shows the flow from raw data to a final decision. Hover over the steps to see them highlight and identify.

CBSE Exemplar in Focus: Price Comparison Websites

Price comparison websites are a good, real-world example of the Data Science pathway in action.

How it Works (A Data Science Pipeline):

1. Data: These websites are “driven by lots and lots of data.” They use automated programs called “crawlers” or “scrapers” to collect data from hundreds of different e-commerce sites. This data is numerical (prices, ratings) and alpha-numeric (product names, seller names). This large dataset is collected and stored in a central database.
2. Insight: The Data Science model “unif[ies] statistics [and] data analysis” to instantly process this data when a user searches for a product. The model’s task is to derive meaning by sorting all available prices, identifying the lowest one, and finding the best-rated seller. The “insight” it generates is the answer to the user’s question: “Where can I get the best deal on this product right now?”.
3. Decision: The website presents this structured insight to the user in a clean, sorted list. This “information extracted” allows the user to make an informed “decision” about which vendor to purchase from, saving them time and money. The AI has successfully turned raw, chaotic data from all over the internet into a single, actionable decision.

Data Types and Typical Tasks (Data Science)

Data Types: The primary fuel for Data Science is numeric and alpha-numeric data. This includes tables, spreadsheets, financial data, website user logs, sales figures, and survey results.
Typical Tasks:
- Recommendation: This is used by “Website Recommendations” systems on sites like Amazon and Netflix. The AI analyzes your past data (e.g., what you watched) and compares it to the data of millions of other users to predict what new item you are most likely to enjoy.
- Prediction: This involves using historical data to forecast future outcomes. Examples include predicting the sales of a store, forecasting housing prices, or even optimizing traffic routes in real-time.
- Classification: This task involves sorting data into predefined categories. A critical example is Fraud and Risk Detection. When a credit card transaction occurs, a Data Science model instantly analyzes its data (amount, location, time, user’s purchase history) to classify it as either “legitimate” or “potentially fraudulent.”

Domain Explained: Computer Vision (CV)

Core Concept: Processing the Visual World

Computer Vision (CV) is the AI area that “enables computers and systems to derive meaningful information from digital images, videos, and other visual inputs.” It gives machines a form of sight, allowing them to “get and analyze visual information and afterwards predict some decisions about it.”

The main objective of this AI area is to teach machines how to “collect information from pixels,” which are the smallest building blocks of a digital image.

Data Types and Typical Tasks (Computer Vision)

Data Types: The fuel for Computer Vision is image and visual data. This includes photographs, videos, and real-time streams from cameras or sensors.
Typical Tasks: The two most fundamental tasks in CV, which build upon each other, are Image Classification and Object Detection.

In-Depth Analysis: Classification vs. Object Detection

“Classification” is a foundational task across all AI areas. Data Science classifies transactions (fraud/not fraud), NLP classifies text (spam/not spam), and Computer Vision classifies images. Understanding this concept is key to seeing the connections between the areas.

A. Image Classification

The Question it Answers: “What is this image?”
Definition: The AI model assigns a single label to an entire image.
Example: The AI looks at a photo and provides one label: “cat.” It does not specify where the cat is in the photo, only that the image, as a whole, contains a cat. This is used in medical imaging to classify an entire X-ray as “healthy” or “showing pneumonia.”

B. Object Detection

The Question it Answers: “What objects are in this image, and where are they?”
Definition: This is a more complex and advanced task. It is a two-step process: Classification + Localization. The AI finds multiple objects within a single image, draws a “bounding box” (a rectangle) around each one, and provides a label for each box.
Example (Self-Driving Cars): This is a key CBSE example. An autonomous vehicle cannot simply classify its camera feed as “street.” It must use object detection to find the exact location (the bounding box) of every other “vehicle,” “pedestrian,” and “traffic signal” to navigate the road safely.

CBSE Exemplar in Focus: Smartphone Face Lock

The “Face Lock” or “Facial Recognition” feature on a smartphone is a perfect daily-use example of Computer Vision.

How it Works (A Computer Vision Pipeline):

Data (Acquisition): The user points the smartphone camera at their face. The camera “captures an image or video” of the face, providing the raw visual data.
Task 1 (Face Detection): The CV algorithm first scans the image to answer, “Is there a face here?” It *detects* the presence of a face and separates it from the background (e.g., the wall behind the user). This is a form of object detection.
Task 2 (Feature Extraction): Once a face is detected, the AI analyzes it in detail. It identifies and measures key “facial features” or “landmarks,” such as the distance between the eyes, the shape of the nose, and the position of the mouth. These measurements are converted into a unique mathematical representation (a “face print” or “template”).
Task 3 (Matching & Decision): The system “compares the captured face with stored facial data” (the template created during setup). If the new face print is a statistical match to the stored one, the AI makes the “decision” to verify the user’s identity and unlock the phone.

Domain Explained: Natural Language Processing (NLP)

Core Concept: Understanding Human Language

Natural Language Processing (NLP) is the AI area that “focuses on the ability of a computer to understand human language… as spoken or written.” It is a branch of AI that deals with the “interaction between machine/computers and humans using… natural language.”

NLP processes two distinct types of data:

Text Data (from emails, web pages, books, text messages).
Speech Data (from voice commands, digital phone calls).

CBSE Exemplar in Focus 1: Smart Assistants (Siri, Alexa, Google Assistant)

Smart assistants are a primary CBSE example of NLP, specifically for *speech processing*. It is important to distinguish these from simple *chatbots*. A basic, rule-based chatbot may only follow a predefined script (e.g., “Press 1 for sales”). A *smart assistant* uses complex NLP to understand the *intent* behind a user’s words and can *autonomously perform tasks* like setting reminders, sending messages, or controlling smart home devices.

How it Works (An NLP Speech Pipeline):

Input (Speech): The user speaks a voice command: “Hey Siri, what’s the weather like today?”.
Task 1 (Speech-to-Text): The NLP model “recognize[s] patterns in speech” and transcribes the analog audio waves into digital text: “what’s the weather like today”.
Task 2 (Natural Language Understanding – NLU): This is the “brain” of the operation. The AI analyzes the text to “interpret the natural language request.” It identifies the user’s intent (which is get_weather_forecast) and the key entities (which are location=default/current and time=today).
Action: The assistant’s system queries an external data source (like a weather service) to get the required information (e.g., “25°C, sunny”).
Task 3 (Natural Language Generation – NLG): The AI takes the factual data (“25°C, sunny”) and generates a new, grammatically correct, human-sounding sentence in response (e.g., “It is currently 25 degrees and sunny.”).
Task 4 (Text-to-Speech): The system converts this generated text back into audio, and the device’s speaker plays the response for the user to hear.

CBSE Exemplar in Focus 2: Email Spam Filters

Email spam filters are a key CBSE example of *text processing*. This is a direct application of Text Classification, one of the most common and powerful tasks in NLP.

How it Works (An NLP Text Classification Pipeline):

Data (Training): The AI model is “trained on large datasets of both spam and legitimate email.” This large dataset has been labeled by millions of users (by manually marking emails as “spam”).
Insight (Learning): The machine learning model “learn[s] to distinguish between the two by recognizing subtle patterns.” These patterns are not just simple keywords. The AI learns to identify spam-indicator words (e.g., “free,” “winner,” “urgent”), suspicious sending patterns, and other metadata associated with spam.
Decision (Classification): When a new, unseen email arrives in the inbox, the trained NLP model analyzes its content and metadata. It “classify[s] sentences as spam or not” and assigns a probability score (e.g., “99% chance this is spam”). If the score crosses a certain threshold, the AI makes the “decision” to automatically move the email to the spam folder, keeping the user’s main inbox clean.

Interactive Comparison: AI Domains

Use the filters to compare the domains side-by-side. This table goes beyond the basics to help you see the deeper connections and differences.

Metric	Data Science	Computer Vision	Natural Language Processing
Key Question	“What patterns are in this data?”	“What is in this image?”	“What does this text mean?”
Primary Data	Numbers, Tables, Logs	Pixels, Images, Videos	Words, Sentences, Speech
Key Goal	Find insights, make predictions	See and interpret the world	Understand and generate language
Common Tools	Python (Pandas, Scikit-learn)	OpenCV, TensorFlow	NLTK, spaCy, Transformers
Core Task	Regression, Classification	Object Detection	Natural Language Understanding (NLU)
Future Trend	Automated Machine Learning (AutoML)	Real-time video analysis, AR	Large Language Models (LLMs)

Infographic: AI Application Examples

This chart shows common AI applications. The bubbles are colored by their primary domain. Hover over them to learn more.

Interactive Game: Match the Task to the Domain

Test your knowledge. For each task, select the primary AI domain that powers it.

Loading task…

Test Your Knowledge (Q&A)

Review the key concepts from the chapter. Click on a question to reveal a hint and the answer.

1. What is the main difference between Data Science and NLP data? >

Hint: Think about numbers vs. words.

Answer: Data Science primarily processes numerical and alpha-numeric data (like spreadsheets and databases). NLP processes linguistic data (human language, like text and speech).

2. What are the two steps of Object Detection? >

Hint: It doesn’t just find *what*, but also *where*.

Answer: Object Detection involves two steps: Classification (labeling the object, e.g., “person”) and Localization (drawing a bounding box to show *where* it is).

3. What is the difference between a simple chatbot and a smart assistant? >

Hint: One follows a script, the other understands intent.

Answer: A simple chatbot usually follows a predefined script (e.g., “Press 1 for sales”). A smart assistant uses NLP (specifically NLU) to understand the intent behind your words and can perform new tasks, like setting an alarm or answering a general question.

4. Give an example of a “Classification” task for each of the three domains. >

Hint: Each domain sorts its data type into categories.

Answer:

Data Science: Classifying a credit card transaction as “legitimate” or “fraudulent.”
Computer Vision: Classifying an X-ray image as “healthy” or “showing pneumonia.”
Natural Language Processing: Classifying an email as “spam” or “not spam.”

Key Study Notes

The easiest way to tell the domains apart is by their data type:
- Numbers/Tables = Data Science
- Images/Videos = Computer Vision
- Text/Speech = Natural Language Processing
Classification is a common task in ALL three domains. It means sorting data into groups.
Object Detection (CV) is more advanced than Image Classification (CV) because it finds *where* the object is.
A Smart Assistant (NLP) uses many steps: Speech-to-Text, Natural Language Understanding (NLU), and Text-to-Speech.
The “Rock, Paper, Scissors” AI game is a Data Science example because it analyzes the *data of your past moves* to find a *pattern* and *predict* your next move.

Frequently Asked Questions (FAQs)

What does “NLP” stand for? >

NLP stands for Natural Language Processing. It’s the AI domain that deals with human language.

Is a self-driving car just Computer Vision? >

No. While Computer Vision is its “eyes” (using Object Detection to see pedestrians, cars, and lanes), a self-driving car also uses Data Science. It collects data from many sensors (like LiDAR, radar) and uses prediction models to decide when to brake, accelerate, or turn.

How does the Google Translate camera work? >

It’s a great example of domains working together:

Computer Vision (CV) first “sees” the sign and uses Optical Character Recognition (OCR) to *detect* the visual letters and turn them into digital text (e.g., “Sortie”).
Natural Language Processing (NLP) then *translates* that text from one language (French) to another (English: “Exit”).
Computer Vision (CV) is used again for Augmented Reality (AR) to *overlay* the new word (“Exit”) onto your camera screen.

Conclusion: Domains are Stronger Together

The Big Picture: Domains Work Together

For learning purposes, we separate AI into the distinct areas of Data Science, Computer Vision, and Natural Language Processing. In practice, however, many advanced AI applications *combine* these areas to solve complex problems. They are not isolated silos but building blocks that work together.

Capstone Example: The Google Translate Camera Feature

The “point-and-translate” camera feature in the Google Translate app is a perfect capstone example that shows all three areas working in harmony.

A Step-by-Step Breakdown of Convergence:

A user points their phone’s camera at a sign in a foreign language (e.g., a French “Sortie” sign).
Computer Vision (CV): This is the first step. The AI “sees” the visual data from the camera. It performs a task called Optical Character Recognition (OCR) to detect the text on the sign and convert the visual letters “S-o-r-t-i-e” into digital text.
Natural Language Processing (NLP): This is the second step. The extracted text (“Sortie”) is instantly fed into the NLP engine. This engine translates this text data from French to the user’s chosen language, English (resulting in “Exit”).
Data Science (DS): This is the foundation for the entire process. Both the CV model (trained on millions of images of letters) and the NLP model (trained on billions of translated sentences) were built using Data Science principles.
Computer Vision (Augmented Reality): In the final step, a CV technology called Augmented Reality (AR) seamlessly overlays the translated word “Exit” onto the live camera feed, visually replacing the original word “Sortie.”

Final Takeaway

The three areas are categories that help us *understand* and organize the world of AI. Data Science gives AI its analytical “brain.” Computer Vision gives it “eyes” to see. Natural Language Processing gives it “ears and a mouth” to communicate. The true power of modern AI comes from combining these specializations to create intelligent systems that can see, understand, and predict, solving complex, real-world problems.

Cross-Links

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by Rezyo Staff WriterNovember 6, 2025 AI, CBSE, CBSE Class 100 comments

AI vs ML vs DL Explained: Chapter 2 CBSE Class 10 AI Basics

This guide covers the essential basics of AI for the CBSE Class 10 curriculum. We start with clear definitions from global bodies like NITI Aayog and the WEF. Then, we explore the fundamental relationship between AI, Machine Learning (ML), and Deep Learning (DL), showing you exactly how they are different and how they fit together. This chapter helps you build a strong foundation before exploring complex AI domains.

Chapter 2: The Basics of AI – CBSE Class 10 | Rezyo.in

Chapter 2: The Basics of AI

CBSE Class 10 Artificial Intelligence | Updated: October 2025

The modern world uses complex computation. A phone unlocks with facial recognition. A streaming service suggests a movie. A website chatbot answers questions. The technology behind these experiences is Artificial Intelligence (AI).

This page covers the foundational concepts of AI for Chapter 2 of the CBSE Class 10 curriculum. The official curriculum goal is to help students become “AI-Ready”.

Being “AI-Ready” is different from being an “AI-Expert”. The course objectives focus on “appreciating Artificial Intelligence” and understanding AI applications “in our lives”. This approach builds a mindset for *why* AI matters and *how to think about* its use in society.

Learning Outcomes

After finishing this module, you will be able to:

Define AI using perspectives from groups like NITI Aayog and the World Economic Forum.
Use a K-W-L-H chart as a tool for tracking your learning.
Explain the differences between Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL).
Explain *why* ML and DL are subsets of AI.
Identify the three main domains of AI: Data, Computer Vision, and Natural Language Processing.

What is Artificial Intelligence?

There is no single definition of AI. It is useful to examine definitions from a few sources.

NITI Aayog (India): AI is “the ability of machines to perform cognitive tasks like thinking, perceiving, learning, problem solving and decision making”.

World Economic Forum (WEF): “Broadly speaking, artificial intelligence (AI) is a field of study… characterised by the development and use of machines that are capable of performing tasks that usually would have required human intelligence”.

Encyclopaedia Britannica: “Artificial intelligence (AI) is the ability of a digital computer or computer-controlled robot to perform tasks commonly associated with intelligent beings”.

A simple, consolidated definition is: **Artificial Intelligence is a field of computer science focused on creating systems that perform tasks considered “smart” when done by humans.** These tasks include learning, reasoning, seeing, and understanding language.

AI is Prediction, Not Magic

A common misconception is that AI is equivalent to human intelligence. Kay Firth-Butterfield, Head of AI at the World Economic Forum, clarifies: “AI is not intelligence—it is prediction… it would be a mistake to equate this to human intelligence”.

Current AI systems, known as Artificial Narrow Intelligence (ANI), can only do one task very well at a time. They lack the “common sense” or multi-tasking ability of humans.

AI systems should be viewed as powerful **prediction machines**.

A self-driving car *predicts* the path of a pedestrian.
A streaming service *predicts* the movie a user will enjoy.
A language model *predicts* the most likely next word in a sentence.

This system of learning from data to make statistical predictions is the key to Modern AI. It also forms the logical bridge to understanding Machine Learning.

Activity: Charting The Learning Journey (K-W-L-H)

To build an “AI-Ready” process, this curriculum uses a metacognitive tool: the K-W-L-H Chart. This chart is a graphic organizer for research and self-reflection.

The chart has four columns:

K – What a student already Knows about AI.
W – What a student Wants to know.
H – How the student will find the information.
L – What the student Learned.

This process of “thinking about thinking” is known as **metacognition**. By using the K-W-L-H chart, students practice a structured process of inquiry.

Download K-W-L-H Chart Template

(Students should fill the ‘K’ and ‘W’ columns now.)

The Big Picture: AI vs. Machine Learning vs. Deep Learning

The terms AI, Machine Learning (ML), and Deep Learning (DL) are often used incorrectly. They are not the same. They are not competing concepts. Their relationship is hierarchical.

The Relationship: Subsets

The relationship is best understood as a set of subsets:

Deep Learning is a part of Machine Learning.
Machine Learning is a part of Artificial Intelligence.
Artificial Intelligence is the entire field.

Interactive: AI/ML/DL Relationship

Defining Each Layer

Artificial Intelligence (AI): The “Big Umbrella”
AI includes the entire field of making machines “smart”. AI can be split into two types:

Traditional AI (Rule-Based): A human programmer *explicitly* writes rules (“if-then” statements) for every situation. The machine executes the rules. Example: A simple tic-tac-toe game programmed with rules like, “IF opponent has two-in-a-row, THEN block them.”
Modern AI (Data-Driven): This AI “learns” from data to make decisions. This category is powered by ML and DL. Example: Google Maps learns from real-time traffic data to find the fastest route.

Machine Learning (ML): The “Data-Driven” Subset
ML is a subset of AI defined as giving computers the ability to learn from data without being explicitly programmed. This is a fundamental shift. In Traditional AI, a human writes the rules. In ML, a human provides data and an algorithm. The algorithm studies the data to find patterns and write its own rules. Example: An email spam filter learns from thousands of examples of spam and good emails to identify patterns that predict spam.

Deep Learning (DL): The “Brain-Inspired” Subset
DL is a specialized subset of ML that uses a complex structure called an **Artificial Neural Network (ANN)**. In ML, a human might still need to guide the algorithm by doing “feature extraction” (telling it what features to look for). DL automates this step. It uses deep networks with many layers to learn features on its own. For example, when given an image, the first layer might learn edges, the next layer shapes (like “eye”), and the final layer a “face”. This requires *massive* amounts of training data. Example: A self-driving car identifying a pedestrian from raw camera data.

AI vs. ML vs. DL at a Glance

Feature	Artificial Intelligence (AI)	Machine Learning (ML)	Deep Learning (DL)
Scope	The broad concept of creating “smart” machines.	A subset of AI. A specific way to achieve AI.	A subset of ML. A specific technique within ML.
Core Idea	A machine that simulates human intelligence.	A machine that learns from data to make predictions.	A machine that learns complex patterns using an Artificial Neural Network.
How it Works	Can be “Rule-Based” (explicit “if-then” rules).	Uses statistical algorithms to learn from structured data.	Uses deep neural networks to learn from raw data.
Human’s Job	(Rule-Based): Write all the rules.	Provide data, select algorithm, do “feature extraction.”	Provide massive data, design network. Network does feature extraction.
Data Needs	Varies. Rule-based AI needs no training data.	Requires data. Works well with small to medium datasets.	Requires massive data. Performance improves with more data.
Example	A chess bot with pre-programmed moves.	Netflix’s recommendation engine.	A self-driving car “seeing” a stop sign.

Activity: Where does it belong?

Drag each example into the **most specific** circle it belongs to. A self-driving car uses AI and ML, but its *core technology* is DL, so it belongs in the ‘DL’ circle.

Drag from here:

A simple ‘if-then’ chatbot

Netflix recommending a movie

Self-driving car recognizing a ‘Stop’ sign

Email spam filter

Siri/Alexa understanding your voice

FaceID unlocking your phone

The concept of a ‘thinking machine’

Drop here:

Artificial Intelligence (AI)

Machine Learning (ML)

Deep Learning (DL)

Overview of AI Domains (CBSE Class 10)

AI is a vast field. The CBSE curriculum simplifies it into **three main domains** based on the *type of information* the AI processes. These three domains form the core of the AI-specific units.

Domain 1: Data (Data Science)

This AI domain “thinks” using **numbers, text, and data tables.** It finds hidden patterns and makes predictions from data.

Where it is seen:

Streaming service recommendations.
Bank fraud detection.
Business sales predictions.

Domain 2: Computer Vision (CV)

This AI domain allows machines to “see” and understand the world through **images and videos**.

Where it is seen:

FaceID on mobile phones.
Auto-tagging friends in photos.
Autonomous vehicles identifying signs.

Domain 3: Natural Language (NLP)

This AI domain gives machines the ability to understand and generate **human language** (spoken or text).

Where it is seen:

Siri, Alexa, and Google Assistant.
Google Translate.
Customer service chatbots.

Completing the K-W-L-H Chart

This module established the foundational knowledge for AI. It defined AI as a field of “prediction machines,” not “thinking machines,” and clarified the relationship between AI, ML, and DL.

Key Takeaways

AI (Artificial Intelligence) is the broad, “umbrella” field of creating smart machines.
ML (Machine Learning) is a *subset* of AI that *learns from data* to make predictions.
DL (Deep Learning) is a *subset* of ML that uses *brain-inspired neural networks* to solve complex tasks.
The three main AI domains are Data (Data Science), Computer Vision (CV), and Natural Language Processing (NLP).

As a final step, students should return to their K-W-L-H chart. It is time to fill in the most important column: **’L’ — What I Learned.**

This final reflection reinforces the new knowledge. Students should review their ‘W’ (Want to Know) column to see if their questions were answered. This process encourages new questions and builds the curiosity that defines a student as “AI-Ready.”

Continue Your Learning

Now that you understand the basics, explore the next key topics in the curriculum. These modules build directly on what you’ve learned.

Next Up: AI Domains

Take a deeper look at Data Science, Computer Vision, and Natural Language Processing. Explore real-world projects in each domain.

Go to Domains →

Deep Dive: Neural Networks

Understand the technology that powers Deep Learning. Learn how ANNs are inspired by the human brain and how they “learn” from data.

Explore Neural Networks →

AI (Artificial Intelligence): The broad field of making machines simulate human intelligence. Includes rule-based systems.
ML (Machine Learning): A subset of AI where machines learn from data. All ML is AI, but not all AI is ML.
DL (Deep Learning): A subset of ML that uses multi-layered neural networks. All DL is ML.
Rule-Based AI: Programmed with explicit “if-then” rules. Does not learn.
Data-Driven AI: Learns from data. This is where ML and DL operate.
ANN: Artificial Neural Network. The structure that powers Deep Learning.
Domains:
- Data: For numbers/tables (e.g., Netflix recommendations).
- CV: For images/video (e.g., FaceID).
- NLP: For language/speech (e.g., Siri).

Q1: Is a simple calculator an example of AI?

Hint: Does it learn from data or just follow pre-programmed rules?

Q2: Why does Deep Learning require so much data?

Hint: Think about how many layers and connections are in an ANN.

Q3: What AI domain would be used to check for spam emails?

Hint: What kind of information is in an email? Text, images, or numbers?

Q: Can a machine be both ML and DL?

A: Yes. Since Deep Learning is a subset of Machine Learning, any system that uses DL is also an ML system. For example, a self-driving car’s vision system is a DL system, which means it is also an ML system and an AI system.

Q: Is AI the same as robotics?

A: No. AI is the “brain” (the software) that makes decisions. Robotics is the “body” (the hardware) that moves and acts. A robot can be very simple and use no AI (like on a car assembly line). An AI can have no body at all (like a spam filter). When you combine them, you get an AI-powered robot (like a self-driving car).

Q: Will AI take over the world?

A: This is a topic of big debate. The AI we have today is called Artificial Narrow Intelligence (ANI). It is very good at *one* specific task (like playing chess or identifying faces). It has no consciousness, feelings, or “common sense”. The idea of an AI that is smarter than humans in all areas is called Artificial General Intelligence (AGI). AGI does not exist yet, and we are very far from creating it.

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by Rezyo Staff WriterNovember 6, 2025 AI, CBSE, CBSE Class 100 comments

AI Foundations for Class 10: Intelligence & Decision-Making (CBSE Chapter 1)

Welcome to your guide for Chapter 1 of the CBSE Class 10 AI course. This page covers the foundations of Artificial Intelligence. We’ll start by exploring what human intelligence is and how we make decisions. Then, we will define what AI is, how it learns from data, and see examples in your daily life. Finally, we’ll clear up common confusion by comparing AI vs. automation, IoT, and robotics.

AI Foundations for Class 10: Intelligence & Decision-Making (CBSE)

Chapter 1: AI Foundations: Intelligence & Decision-Making

This page covers the basics of human intelligence, decision-making, and how they relate to the core definition of Artificial Intelligence.

1.0 What is Intelligence? Rethinking “Being Smart”

What does it mean to be ‘smart’? We usually think of ‘smart’ people as those who do well on tests. This common idea centers on a single, measurable ability, sometimes called ‘general intelligence.’ This chapter asks you to reconsider that definition. To understand Artificial Intelligence, we first need a better grasp of Natural Intelligence.

1.1 Beyond a Single “IQ”

Psychologist Howard Gardner challenged this old idea in 1983. In his book *Frames of Mind*, he argued for a ‘pluralistic view of intelligence.’ He believed people do not have a fixed amount of ‘smartness.’ Instead, we have many different *kinds* of intelligence.

Gardner defined intelligence as a “biopsychological potential to process information that can be activated in a cultural setting to solve problems or create products that are of value in a culture.”

Let’s break this down:

“Process information”: Intelligence is how we take in and make sense of the world.
“Solve problems”: It is a practical tool for overcoming challenges.
“Create products of value”: This includes writing a poem, building a bridge, or navigating a social situation.

This foundation is important. The official CBSE definition of Artificial Intelligence is a technology that **mimics human intelligence** by performing tasks like “thinking, perceiving, learning, problem solving and decision making.” Therefore, to build AI, we must first identify the human ‘smarts’ we are trying to copy.

1.2 The Many Ways to be Smart

Gardner’s theory names eight distinct intelligences. He argued that everyone possesses all eight, but each person has a unique *profile* of strengths and weaknesses. This “pluralistic” view helps us understand AI.

The AI we use every day, like a chatbot or a navigation app, is not a single, all-knowing ‘general intelligence.’ It is what we call Artificial Narrow Intelligence (ANI), or “Weak AI.”

We can think of today’s AI systems as attempts to copy one or two of Gardner’s multiple intelligences:

An AI chatbot (like ChatGPT) is an attempt to create Artificial Linguistic Intelligence.
An AI navigation system in a self-driving car is an attempt to create Artificial Visual-Spatial Intelligence.

1.3 The 8 Types of Human Intelligence

Here is a breakdown of the eight core intelligences identified by Howard Gardner. Use the filters to explore different categories.

Intelligence Type	Also Known As…	What it is (Simple Definition)	You might be good at…
Linguistic	“Word Smart”	Using words effectively, spoken and written.	Writing stories, debating, explaining ideas.
Logical-Mathematical	“Number/Reasoning Smart”	Using logic, discerning patterns, and abstract thought.	Solving puzzles, math problems, coding.
Visual-Spatial	“Picture Smart”	Thinking in images, pictures, and 3D space.	Drawing, reading maps, navigating, design.
Bodily-Kinesthetic	“Body Smart”	Using your whole body or parts of your body skillfully.	Sports, dancing, acting, building with hands.
Musical	“Music Smart”	Producing and appreciating rhythm, pitch, and melody.	Singing, playing instruments, composing music.
Interpersonal	“People Smart”	Understanding and interacting effectively with other people.	Teamwork, leadership, teaching, understanding others.
Intrapersonal	“Self Smart”	Understanding yourself, your own feelings, values, and goals.	Setting goals, self-assessment, regulating emotions.
Naturalist	“Nature Smart”	Recognizing and categorizing patterns in the natural environment.	Identifying plants/animals, farming, biology.

4.6 Visual Explainer: How AI Learns vs. Automation

This interactive chart shows the key difference between a fixed automation and a learning AI. Use the buttons to change the data.

The dots are data points. The line represents the “rule” the machine follows.

Click a button to see the visualization.

2.0 How Intelligence Solves Problems: The Art of Decision-Making

We’ve seen that ‘solving problems’ is a core part of intelligence. The way we solve problems is by making decisions.

2.1 Why We Can’t Make Decisions Without Information

Decision-making is a basic human skill. It is the process of making a choice. To make a good choice, you need one main thing: information. As the CBSE question bank states, “The basis of decision making depends upon the availability of information and how we experience and understand it.”

If you have no information, you are just guessing. Knowledge or data helps you see the possible outcomes and pick the best one.

Any intelligent agent, human or AI, follows a structured process to make a rational decision:

Define the Problem: State the decision you need to make.
Gather Relevant Information: Collect all the facts and data.
Identify the Alternatives: Brainstorm all possible options.
Weigh the Evidence: Analyze the pros and cons of each option.
Choose the Best Alternative: Select the option that best solves the problem.

This 5-step process is a simple version of the professional AI Project Cycle that we will study later. This shows we teach machines to follow the same rational process we use.

2.2 Logic Puzzle 1: The Three Doors Riddle (The Lion’s Lair)

The Challenge:

“You are locked inside a room with 3 doors… Behind the 1st door is a lake with a deadly shark. The 2nd door has a mad psychopath… and the third one has a lion that has not eaten since the last 2 months. Which door would you choose? and Why?”

Solution: Door 3.

Analysis: Doors 1 and 2 present clear danger. The information for Door 3 is different. An intelligent person must *process* this information. Based on biological knowledge (our “database”), a lion cannot survive for two months without food. Therefore, the lion must be dead. This door is the only safe option. This puzzle was solved by applying a logical rule to the provided information.

2.3 Logic Puzzle 2: The Case of the Strawberry Pie

The Challenge:

“Aarti invited four of her friends… two… died… poisoned… in the strawberry pie. The three surviving friends (Shiv, Seema, and Aarti) told the police that they hadn’t eaten the pie.”

Shiv said, ‘I am allergic to strawberries.’
Seema said, ‘I am on a diet.’
Aarti said, ‘I ate too many strawberries while cooking…’

The Key Information: “The policemen looked at the pictures of the party and immediately identified the murderer.” Who was it?

Solution: Seema.

Analysis: The police cannot make a decision based on the alibis alone. Seema’s alibi is weak, but not proof. They need *more information*. This is where the “pictures of the party” come in. The police *gathered new data* (the photos). The logical inference is that the pictures showed Seema eating other “unhealthy” party foods. This new data directly contradicted her alibi that she was “on a diet.” Her alibi was a lie, exposing her as the murderer.

The Core of AI: A Simple Diagram

The two puzzles show that intelligent decision-making needs two things: Data (Information) and Algorithms (Logic). This is exactly how AI works. This diagram shows how these two ingredients combine.

3.0 What is Artificial Intelligence (AI)?

Artificial Intelligence (AI) is a field of computer science that creates systems to simulate human intelligence. The official CBSE curriculum defines it clearly: AI is any technique that “enables computers to mimic human intelligence.”

A machine has AI when it can “make decisions, predict the future, learn and improve on its own.” In short, AI helps a computer “think” and “act” like a human.

3.1 How a Machine Becomes “Intelligent”

How does a machine “learn”? It’s not magic. It uses the same two things from our puzzles: Data and Algorithms.

Ingredient 1: Data (The “Experience” or “Information”)
A human learns from experience (data). An AI machine learns by being trained with data. This can be millions of pictures, all of Wikipedia, or years of traffic information. This data acts as the “experience” for the machine.
Ingredient 2: Algorithms (The “Logic” or “Recipe”)
An algorithm is simply a set of rules or instructions used to solve a problem. AI uses special statistical algorithms to sift through massive amounts of data to find hidden patterns.

This process of using algorithms to learn patterns from data is called Machine Learning (ML).

ML is the most common and powerful form of AI used today. It is a subset of AI. It gives machines the ability to learn from data and improve at a task without being explicitly programmed for every single step. This is what makes AI different from a normal computer program. A **non-AI program** (like a calculator) follows fixed rules. An **AI program** (like a spam filter) learns the rules from the data.

3.2 AI in Your Daily Life

You use AI dozens of times every day, often without noticing. Here are a few examples.

Example 1: Virtual Assistants (Siri, Google Assistant, Alexa)

These assistants use Natural Language Processing (NLP), a part of AI. NLP is the ability for a machine to understand human language. When you speak to your phone: 1) The AI transcribes your speech to text. 2) The NLP algorithm figures out the *intent* of your command. 3) The AI decides on the correct action and generates a natural-sounding voice to respond.

Example 2: Navigation Apps (Google Maps, Waze)

These apps use Machine Learning to analyze massive, real-time datasets. This data comes from satellites, user-reported incidents, and the location data from millions of other phones. The AI’s job is to: 1) Analyze all this data in real-time. 2) Predict traffic patterns and your estimated time of arrival (ETA). The “fastest route” Google Maps suggests is an AI-driven prediction.

Example 3: Recommendation Engines (Netflix, YouTube, Spotify)

When Netflix suggests a new show, it is an AI system designed to predict what you will enjoy. They primarily use two methods:

Content-Based Filtering: Recommends items based on their features. “You watched The Dark Knight. The AI tags this as ‘superhero.’ Therefore, it recommends Avengers: Endgame because it shares the ‘superhero’ tag.”
Collaborative Filtering: Recommends items based on people with similar tastes. “You and Person X both love The Dark Knight. Person X also loved Squid Game. The AI predicts you will also love Squid Game.”

Every time you watch a show or give a “thumbs up,” you are feeding new data to the AI, which updates its predictions about you.

3.3 Image Strip: Real-World AI Examples

Here are more places you can find AI working around you, often hidden in plain sight.

Phone Face Unlock

AI (computer vision) maps your face and compares it to stored data to verify your identity.

Email Spam Filtering

AI (machine learning) learns the patterns of “spam” emails and automatically filters them out.

Social Media Feeds

AI recommendation engines analyze your behavior to decide what posts to show you first.

Online Advertising

AI predicts which ads are most relevant to you, making it more likely you will click them.

4.0 What is NOT AI? Clearing Up the Confusion

It is important to understand the difference between true AI and other technologies that are often confused with it.

4.1 The Big Misconception

Many devices are “smart,” but this does not make them AI. The key difference, as defined by CBSE, lies in learning and adaptation.

IoT is the SENSES (Eyes, Ears): IoT devices collect data from the real world (temperature, location, video) and send it.
AI is the BRAIN: The AI algorithms receive this data and analyze it to find patterns and make intelligent decisions.

Paired Example: A basic smart thermostat is an IoT device because you can control it from your phone. This is IoT + Automation. An AI-powered smart thermostat also uses IoT, but it feeds that data to an **AI algorithm**. The AI learns your family’s usage patterns and autonomously creates a custom schedule to save energy.

4.3 AI vs. Robotics

Robotics: This is a branch of engineering that deals with the design and operation of *physical machines called robots*.
The Key Distinction (Brain vs. Body):

Robotics is the BODY: A robot is a physical machine that can move and interact with the physical world.
AI is the BRAIN: AI is software. It is the intelligence that can perceive, reason, and make decisions.

You can have one without the other:

AI (No Robot): Pure software. Your email spam filter or the Netflix recommendation engine.
Robot (No AI): A “dumb” robot. A robot arm on a factory assembly line performing automation (a fixed, pre-programmed task).
AI-Powered Robot: An AI “brain” inside a robot “body.” The most famous example is a self-driving car.

4.5 Table 2: Key Differences: AI vs. The “Other” Tech

Technology	What is it? (Core Definition)	Simple Analogy	“Dumb” Example (Automation)	“Smart” Example (AI-Enabled)
Automation	A system that follows fixed, pre-programmed rules.	A To-Do List	A basic calculator.	An AI chatbot that writes new code.
IoT	A network of devices with sensors that collect data.	Senses (Eyes, Ears)	A smart lightbulb you control with your phone.	An AI security camera that identifies intruders.
Robotics	Building physical machines (robots) that move.	A Body	A factory arm painting the same car door.	A self-driving car that decides when to turn.
AI	A system that learns from data to make decisions.	The Brain	(N/A)	A spam filter that learns to block new spam.

What’s Next? (Cross-Links)

Now that you have a solid understanding of what AI is (and isn’t), you’re ready to explore related topics. These links will guide you to the next steps in your AI learning journey.

→ AI Basics & History

Explore the different types of AI (Narrow, General, Super) and the key historical milestones that led to the technology we have today.

→ AI Ethics: Bias & Privacy

An important look at the challenges AI creates, including data privacy concerns and how AI models can learn and repeat human biases.

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by Rezyo Staff WriterNovember 6, 2025 CBSE, Maths0 comments

Quadratic Equations Class 10 Maths: Chapter 4 Guide (CBSE) | Solve, Visualize & Master Roots

This comprehensive guide to CBSE Class 10 Maths Chapter 4, Quadratic Equations, has everything you need to master the topic. Learn the standard form, all three methods for solving equations (factorization, completing the square, and the quadratic formula), and how to find the nature of roots using the discriminant. We’ll also cover word problems and let you see equations in action with an interactive parabola visualizer.

CBSE Class 10 Maths: Chapter 4, Quadratic Equations Guide

Chapter 4

Quadratic Equations

Your complete guide to understanding, solving, and visualizing quadratic equations. Master the concepts for your CBSE Class 10 exams.

1. What is a Quadratic Equation?

The Standard Form

Any equation that can be written in the form:

ax² + bx + c = 0

…is a quadratic equation. Here’s what the letters mean:

a
The Quadratic Coefficient. It’s the number next to x².
Important: a cannot be zero. If a=0, the x² term disappears, and it becomes a linear equation (bx + c = 0).
b
The Linear Coefficient. It’s the number next to x.
c
The Constant Term. It’s the number with no x attached.

The values a, b, and c are all real numbers.

Identifying Quadratic Equations

Sometimes, an equation doesn’t look quadratic at first. You must simplify it to its standard form.

Example: YES

x(x + 1) + 8 = (x + 2)(x – 2)

Simplifies to:
x² + x + 8 = x² – 4
x + 12 = 0
No. The x² terms cancel out. This is a linear equation.

Correct Example: YES

(x + 2)³ = x³ – 4

Simplifies to:
x³ + 6x² + 12x + 8 = x³ – 4
6x² + 12x + 12 = 0
Yes. The highest power of x is 2. (Here, a=6, b=12, c=12).

Example: NO

x²(x + 1) = 5

Simplifies to:
x³ + x² – 5 = 0
No. The highest power of x is 3. This is a cubic equation.

2. How to Solve Quadratic Equations

“Solving” an equation means finding the values of x that make the equation true. These values are called the roots of the equation. A quadratic equation can have two roots, one root, or no real roots.

Method 1

Solution by Factorization

This method involves splitting the middle term (bx) into two terms.

Example: Solve `2x² - 5x + 3 = 0`

Find a × c: 2 × 3 = 6
Find two numbers that multiply to 6 and add up to ‘b’ (which is -5).
These numbers are -2 and -3. (-2 × -3 = 6 and -2 + -3 = -5)
Split the middle term:
2x² - 2x - 3x + 3 = 0
Factor by grouping:
2x(x - 1) - 3(x - 1) = 0
Extract the common factor:
(2x - 3)(x - 1) = 0
Solve for x:
Either 2x - 3 = 0 ➔ x = 3/2
Or x - 1 = 0 ➔ x = 1

Roots are: 1 and 3/2

Method 2

Solution by Quadratic Formula

This formula gives the roots of ax² + bx + c = 0 directly. It always works.

x = [ -b ± √(b² - 4ac) ] / 2a

Example: Solve `2x² - 5x + 3 = 0`

Identify a, b, c:
a = 2, b = -5, c = 3
Plug into the formula:
x = [ -(-5) ± √((-5)² - 4*2*3) ] / (2*2)
Simplify:
x = [ 5 ± √(25 - 24) ] / 4
x = [ 5 ± √1 ] / 4
x = ( 5 ± 1 ) / 4
Find the two roots:
Root 1: (5 + 1) / 4 = 6 / 4 = 3/2
Root 2: (5 - 1) / 4 = 4 / 4 = 1

Roots are: 1 and 3/2 (Same as before!)

Method 3

Solution by Completing the Square

This method converts the equation into the form (x + k)² = m. It’s also the method used to *prove* the quadratic formula.

Example: Solve `2x² - 5x + 3 = 0`

Make a = 1 (Divide by 2):
x² - (5/2)x + 3/2 = 0
Move constant c to the right:
x² - (5/2)x = -3/2
Add (b/2)² to both sides.
Here, b = -5/2, so (b/2) = -5/4, and (b/2)² = 25/16.
x² - (5/2)x + 25/16 = -3/2 + 25/16
Factor the left side (it’s a perfect square):
(x - 5/4)² = -24/16 + 25/16
(x - 5/4)² = 1/16
Take the square root of both sides:
x - 5/4 = ±√(1/16)
x - 5/4 = ± 1/4
Solve for x:
Root 1: x = 5/4 + 1/4 = 6/4 = 3/2
Root 2: x = 5/4 - 1/4 = 4/4 = 1

3. Nature of Roots (The Discriminant)

We can know the *type* of roots an equation has without actually solving it, using a value called the Discriminant.

The discriminant is the part inside the square root from the quadratic formula.

D = b² - 4ac

What ‘D’ tells us:

D > 0 Positive

The equation has TWO distinct, real roots.
(The parabola crosses the x-axis twice).

Example: x² – 5x + 6 = 0
D = (-5)² – 4(1)(6) = 25 – 24 = 1

D = 0 Zero

The equation has ONE real root (or two equal, real roots).
(The parabola just touches the x-axis at one point).

Example: x² – 4x + 4 = 0
D = (-4)² – 4(1)(4) = 16 – 16 = 0

D < 0 Negative

The equation has NO real roots.
(The parabola never crosses the x-axis).

Example: x² + 2x + 3 = 0
D = (2)² – 4(1)(3) = 4 – 12 = -8

4. Relationship Between Roots & Coefficients

If the roots (solutions) of the equation ax² + bx + c = 0 are α (alpha) and β (beta), there is a direct relationship between these roots and the coefficients a, b, and c.

Sum of Roots (α + β)

The sum of the two roots is always equal to -b/a.

α + β = -b / a

Product of Roots (α × β)

The product of the two roots is always equal to c/a.

α × β = c / a

Forming a Quadratic Equation from its Roots

If you are given the roots α and β, you can construct the equation directly.

x² - (α + β)x + (α × β) = 0

or simply: x² – (Sum of roots)x + (Product of roots) = 0

Example: Form an equation whose roots are `4` and `-2`.

Find the Sum (α + β): 4 + (-2) = 2
Find the Product (α × β): 4 × (-2) = -8
Use the formula x² - (Sum)x + (Product) = 0:
x² - (2)x + (-8) = 0
Final Equation: x² - 2x - 8 = 0

5. Interactive Parabola Visualizer

A quadratic equation y = ax² + bx + c forms a U-shaped curve called a parabola. The “roots” are simply the points where this curve crosses the x-axis (where y=0).

Use the sliders to change a, b, and c and see how the graph and roots change in real-time.

Coefficient a 1.0

If a > 0, parabola opens up (Smiley face 😊). If a < 0, it opens down (Frowny face 😟).

Coefficient b -2.0

b and a together shift the vertex (the lowest/highest point) left or right.

Constant c -3.0

c is the y-intercept. It's where the curve crosses the vertical y-axis.

6. Applications & Word Problems

Quadratic equations appear in many real-world scenarios. The key is to translate the words into a mathematical equation in the standard form ax² + bx + c = 0.

Strategy for Solving Word Problems

Represent: Read the problem. Assign a variable x to the primary unknown quantity.
Relate: Express all other unknown quantities in terms of x.
Formulate: Use the conditions given in the problem to write an equation.
Standardize: Simplify the equation into the standard form ax² + bx + c = 0.
Solve: Find the value(s) of x using factorization or the quadratic formula.
Verify: Check if the solutions make sense. For example, age, speed, or length cannot be negative. Discard any invalid solutions.

Common Problem Types

Type 1: Geometry & Area

Involves area of shapes, often rectangles (Area = l × w) or triangles (Area = ½ × b × h).

Problem:

"The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides."

Setup:

Let base = x. Then altitude = x - 7.
Using Pythagoras' theorem (a² + b² = c²):
(x)² + (x - 7)² = 13²
x² + x² - 14x + 49 = 169
2x² - 14x - 120 = 0
x² - 7x - 60 = 0 (Solve this)

Type 2: Speed, Distance, Time

Uses the formula Time = Distance / Speed. Often compares two scenarios.

Problem:

"A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less."

Setup:

Let speed = x.
Original Time (T1) = 360/x
New Speed = x + 5
New Time (T2) = 360/(x+5)
Given: T1 - T2 = 1
(360/x) - (360/(x+5)) = 1
This simplifies to x² + 5x - 1800 = 0.

Type 3: Age Problems

Involves relationships between ages in the past, present, or future.

Problem:

"The sum of the reciprocals of Rehman's age 3 years ago and 5 years from now is 1/3. Find his present age."

Setup:

Let present age = x.
Age 3 years ago = x - 3
Age 5 years from now = x + 5
Given: 1/(x-3) + 1/(x+5) = 1/3
This simplifies to x² - 4x - 21 = 0.

7. Practice Q&A (Check Your Knowledge)

Q1: Is (x - 2)² + 1 = 2x - 3 a quadratic equation? Click to reveal

Yes, it is.

Step 1: Expand (x - 2)² to x² - 4x + 4.
Step 2: The equation becomes x² - 4x + 4 + 1 = 2x - 3.
Step 3: Simplify: x² - 4x + 5 = 2x - 3.
Step 4: Move all terms to one side: x² - 4x - 2x + 5 + 3 = 0.
Final Form: x² - 6x + 8 = 0.

Since the highest power of x is 2 (and a=1, b=-6, c=8), it is a quadratic equation.

Q2: Find the discriminant (D) for the equation 3x² - 2x + 1/3 = 0. Click to reveal

The discriminant (D) is 0.

Step 1: Identify a, b, and c.
a = 3, b = -2, c = 1/3
Step 2: Use the formula D = b² - 4ac.
Step 3: Substitute the values: D = (-2)² - 4(3)(1/3)
Step 4: Calculate: D = 4 - 4
Final Answer: D = 0.

Bonus: Since D = 0, this equation has exactly one real root (or two equal real roots).

Q3: Find the roots of x² - 7x + 10 = 0 using factorization. Click to reveal

The roots are x = 2 and x = 5.

Step 1: We need two numbers that multiply to a*c = 10 and add up to b = -7.
Step 2: The two numbers are -2 and -5.
Step 3: Split the middle term: x² - 2x - 5x + 10 = 0
Step 4: Factor by grouping: x(x - 2) - 5(x - 2) = 0
Step 5: Extract common factor: (x - 5)(x - 2) = 0
Final Answer: Either x - 5 = 0 (so x = 5) or x - 2 = 0 (so x = 2).

Q4: If the roots of 2x² - 8x + k = 0 are equal, what is the value of k? Click to reveal

The value of k is 8.

Step 1: "Equal roots" means the discriminant (D) must be 0.
Step 2: The formula is D = b² - 4ac = 0.
Step 3: Identify a, b, and c from 2x² - 8x + k = 0.
a = 2, b = -8, c = k
Step 4: Substitute into the formula: (-8)² - 4(2)(k) = 0
Step 5: Calculate: 64 - 8k = 0
Step 6: Solve for k: 64 = 8k ➔ k = 8.

Q5: Find the sum and product of the roots for 3x² + 7x - 5 = 0 without solving. Click to reveal

Sum = -7/3 and Product = -5/3.

Step 1: Identify a, b, and c.
a = 3, b = 7, c = -5
Step 2: Use the Sum of Roots formula: α + β = -b / a
Sum: - (7) / 3 = -7/3
Step 3: Use the Product of Roots formula: α × β = c / a
Product: (-5) / 3 = -5/3

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by Rezyo Staff WriterNovember 5, 2025 CBSE, Maths0 comments

Class 10 Maths Ch 1 Real Numbers | CBSE 2025 Syllabus Guide

Welcome to the complete guide for Class 10 Maths Chapter 1: Real Numbers, fully updated for the 2025 CBSE syllabus. This page focuses on the two core topics: the Fundamental Theorem of Arithmetic (HCF/LCM) and Proofs of Irrationality. Test your knowledge with an interactive Q&A bank, visualize concepts with our factor tree generator, and get clear answers on what’s in (and out) of the syllabus this year.

Guide to Class 10 Real Numbers | Rezyo.in

Rezyo.in

Updated: Oct 2025

Guide to Class 10 Chapter 1 – Real Numbers

Your complete guide to the 2025 CBSE syllabus, with interactive tools, Q&A, and FAQs.

1. The 2025 Syllabus: What Has Changed?

The CBSE syllabus for Real Numbers has been updated. The focus has moved away from older algorithms. Your study plan should reflect this. Here is a clear breakdown of what to focus on and what to ignore.

IN (Your Focus)	OUT (Deleted)
Fundamental Theorem of Arithmetic (FTA) The main concept. Used for HCF, LCM, and proofs like 6ⁿ.	Euclid’s Division Lemma The entire topic of the lemma and the HCF algorithm is removed.
Proofs of Irrationality Proving numbers like √3, √5, and 5 + 3√2 are irrational.	Decimal Expansions Questions on terminating and non-terminating decimals are removed.

IN (Your Focus)

OUT (Deleted)

Fundamental Theorem of Arithmetic (FTA)

The main concept. Used for HCF, LCM, and proofs like 6ⁿ.

Euclid’s Division Lemma

The entire topic of the lemma and the HCF algorithm is removed.

Proofs of Irrationality

Proving numbers like √3, √5, and 5 + 3√2 are irrational.

Decimal Expansions

Questions on terminating and non-terminating decimals are removed.

2. The Two Core Pillars of Real Numbers

Your study of this chapter should be built on two main topics. Master these, and you are prepared.

Pillar 1: Fundamental Theorem of Arithmetic

This theorem states that every composite number can be broken down into a product of primes in a unique way. For example, the number 342 will always have the prime factors 2, 3, 3, and 19, no matter how you find them.

This theorem is the basis for finding HCF and LCM and for proofs about number properties.

Finding HCF and LCM

HCF: The product of the smallest powers of all common prime factors.
LCM: The product of the greatest powers of all prime factors.

Pillar 2: Proofs of Irrationality

This topic tests your logical reasoning. You will use a technique called “Proof by Contradiction.” The method involves assuming the opposite of what you want to prove and then showing that this assumption leads to a logical error.

To do this, you must understand these ideas:

Co-prime: Two numbers with no common factors other than 1.
Rational: A number that can be written as p/q.
Divisibility: If a prime p divides a², then p also divides a.

Example Proofs (How-To)

How to prove √3 is irrational:

1. Assume: Assume √3 is rational. So, √3 = a/b, where a and b are co-prime.

2. Square: 3 = a²/b², which means a² = 3b².

3. Deduce 1: This shows a² is divisible by 3. So, a must also be divisible by 3.

4. Substitute: We can write a = 3c. Put this into Step 2: (3c)² = 3b².

5. Deduce 2: This simplifies to 9c² = 3b², or b² = 3c². This means b² is divisible by 3, so b is also divisible by 3.

6. Contradiction: We proved a and b are both divisible by 3. This contradicts our assumption that they are co-prime. Our first assumption was wrong.

7. Result: Therefore, √3 is irrational.

How to prove 5 + 3√2 is irrational:

1. Assume: Assume 5 + 3√2 is rational. So, 5 + 3√2 = a/b.

2. Isolate: Rearrange the equation to get the irrational part (√2) alone.

3√2 = a/b – 5

3√2 = (a – 5b) / b

√2 = (a – 5b) / 3b

3. Contradiction: Since a and b are integers, the right side (a – 5b) / 3b is a rational number.

4. Result: This means √2 is rational, which contradicts the given fact that √2 is irrational. Our first assumption was wrong. Therefore, 5 + 3√2 is irrational.

3. Interactive Tool: Factor Tree Visualizer

This tool helps you see the Fundamental Theorem of Arithmetic in action. Enter a number to generate its prime factor tree. This shows how any composite number is built from unique prime factors.

Note: Please use numbers between 2 and 2000 for best results.

4. HCF/LCM Word Problem Guide

A common challenge is deciding whether to use HCF or LCM. This table shows the keywords and logic to look for in a word problem.

Problem Type	Keywords	Method	Logic
Maximize Groups	“Maximum,” “Greatest,” “Largest”	HCF	The answer must be a factor that divides all given numbers.
Minimize Quantity / Find Next Event	“Minimum,” “Smallest,” “Next time they meet”	LCM	The answer must be a multiple divisible by all given numbers.
Remainder (Different for each)	“leaves remainders 5 and 8”	HCF	Find HCF of (Number 1 – Remainder 1) and (Number 2 – Remainder 2).
Remainder (Same for all)	“leaves remainder 7”	LCM	Find LCM of the divisors and then add the common remainder (7).

5. Interactive Q&A Bank

Test your knowledge. Use the filters to select a topic. Click the “Hint” or “Answer” buttons to see the solutions.

Q1 (MCQ): If two positive integers a and b are written as a = x³y² and b = xy³, where x and y are prime numbers, then the HCF(a, b) is:
(a) xy (b) xy² (c) x³y³ (d) x²y²

Q2 (MCQ): If p and q are positive integers such that p = a²b³ and q = a³b², where a, b are prime numbers, then the LCM(p, q) is:
(a) ab (b) a³b³ (c) a²b² (d) a⁵b⁵

Q3 (Short Answer): Given that HCF (306, 657) = 9, find LCM (306, 657).

Q4 (Case Study): A seminar has 60 Hindi, 84 English, and 108 Mathematics participants. They must be seated in rooms with the same number of participants, all from the same subject.
1. What is the maximum number of participants that can be in each room?
2. What is the minimum number of rooms required?

Q5 (HOTS): Show that 6ⁿ cannot end with the digit 0 for any natural number n.

Q6 (HOTS): Explain why 7 × 11 × 13 + 13 is a composite number.

6. Common Questions (FAQ)

Is Euclid’s Division Lemma on the exam? ➤

No. Euclid’s Division Lemma and the algorithm used to find HCF are deleted from the 2024-25 syllabus. You will not be tested on it. You should find HCF only using the Prime Factorization Method.

Is the topic of terminating/non-terminating decimals included? ➤

No. This entire topic is deleted. You are no longer required to check the denominator’s prime factors to determine if a decimal terminates.

In the irrationality proof, why must we say a and b are co-prime? ➤

The “co-prime” assumption is the target for the contradiction. The proof works like this:
1. We assume a and b have no common factors (co-prime).
2. We follow the steps and prove that a and b *must* have a common factor (like 2 or 3).
3. This is a logical impossibility. A pair of numbers cannot *both* have no common factors *and* have a common factor.
4. This contradiction proves our original assumption (that the number was rational) was false.

Is π (pi) the same as 22/7? ➤

No. This is a common mistake.
π (pi) is an irrational number (3.14159…).
22/7 is a rational number (3.142857…).
22/7 is just a close approximation used for calculations. They are not the same number.

Does the HCF × LCM = Product of Numbers formula work for three numbers? ➤

No. This is a very common error. The formula HCF × LCM = Product only works for two positive integers. It does not work for three or more numbers.

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by Rezyo Staff WriterNovember 5, 2025 CBSE, Maths0 comments

Linear Equations in Two Variables Class 10 Maths Ch 3 Guide (CBSE)

Welcome to the complete guide for Class 10 Maths, Chapter 3: Pair of Linear Equations in Two Variables. This page helps you learn how to solve these equations. We cover the graphical method (intersecting, parallel, and coincident lines) and all algebraic methods, including substitution and elimination. Find help for complex word problems, reducible equations, and practice with our interactive Q&A and graph visualizer.

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by Rezyo Staff WriterNovember 5, 2025 CBSE0 comments

Class 10 Maths Chapter 2 Polynomials: Notes, Q&A, Graphs & FAQs (CBSE)

Welcome to your complete resource for Chapter 2, Polynomials. This guide covers all fundamental concepts, graphical meanings, and problem-solving techniques. Use the navigation above to move to specific sections.

Guide to CBSE Class 10, Chapter 2: Polynomials

Rezyo.in

CBSE Class 10 Maths

Updated till October 2025

A Complete Guide to CBSE Class 10 Polynomials

Welcome to your complete resource for Chapter 2, Polynomials. This guide covers all fundamental concepts, graphical meanings, and problem-solving techniques. Use the navigation above to move to specific sections.

Part 1: The Foundations of Polynomials

What is a Polynomial?

A polynomial in one variable, x, is an algebraic expression where the exponents of the variable are all non-negative integers (0, 1, 2, 3, …). This is the most important rule for identifying a polynomial.

The general form is: p(x) = a_n*x^n + a_(n-1)*x^(n-1) + … + a_1*x + a_0

Examples (Polynomials)

3x^2 + 7x – 2 (Exponents: 2, 1, 0)
8x^3 – 5 (Exponents: 3, 0)

Counter-examples (Not Polynomials)

3x^2 + 7*sqrt(x) (Reason: sqrt(x) = x^(1/2). 1/2 is not an integer)
3x^2 + (7/x) (Reason: (7/x) = 7x^(-1). -1 is negative)

Key Terminology

Coefficients: The real numbers in front of the variables (e.g., a_n, a_(n-1), …). In 3x^2 + 7x – 2, the coefficients are 3, 7, and -2.
Leading Coefficient: The coefficient of the term with the highest degree (a_n). In 3x^2 + 7x – 2, it’s 3.
Constant Term: The term with no variable (the x^0 term). In 3x^2 + 7x – 2, it’s -2.

Classification by Degree and Terms

Polynomials are classified in two primary ways: by the number of terms they contain, and by their degree.

Classification by Number of Terms

Monomial: 1 term (e.g., 5x^3, 7)
Binomial: 2 terms (e.g., 6x + 8, x^2 – 5)
Trinomial: 3 terms (e.g., x^2 – 3x + 2)

Classification by Degree

Degree 1: Linear (e.g., 2y – 3)
Degree 2: Quadratic (e.g., 4x^2 + 5x – 2)
Degree 3: Cubic (e.g., 8x^3 – 5)

The degree of a polynomial is the highest exponent of the variable. This property determines the graph’s shape and the maximum number of zeroes.

Degree	Name	General Form	Max. Zeroes	Graphical Shape
1	Linear	ax + b, a != 0	1	Straight Line
2	Quadratic	ax^2 + bx + c, a != 0	2	Parabola
3	Cubic	ax^3 + bx^2 + cx + d, a != 0	3	Continuous Curve

Polynomials are also classified by terms: **Monomial** (1 term), **Binomial** (2 terms), and **Trinomial** (3 terms).

Value of a Polynomial at a Point

The value of a polynomial p(x) at a specific number x = k is found by replacing x with k in the expression. This value is denoted as p(k).

Example

If p(x) = 4x^2 – 1, find the value at x = 1.

p(1) = 4(1)^2 – 1 = 4 – 1 = 3.

So, the value of p(x) at x=1 is 3.

Zeroes of a Polynomial

A real number k is called a zero (or root) of the polynomial p(x) if the value of the polynomial at k is zero. In other words, p(k) = 0.

Example

For the same polynomial p(x) = 4x^2 – 1, let’s check if x = 1/2 is a zero.

p(1/2) = 4(1/2)^2 – 1 = 4(1/4) – 1 = 1 – 1 = 0.

Since p(1/2) = 0, the number 1/2 is a zero of the polynomial. (Another zero is -1/2).

Part 2: Geometrical Meaning of Zeroes (Drawings)

The Key Concept

The real zeroes of a polynomial are the **x-coordinates** of the points where its graph intersects the **x-axis**.

Interactive D3.js: The Three Cases for a Quadratic (Parabola)

Click the buttons below to see how a parabola’s position relative to the x-axis determines its number of real zeroes. This visualization plots an equation like y = x² + k.

Interactive: Form a Polynomial from its Zeroes (D3.js)

Drag the two red circles (zeroes) along the x-axis. The display below will update in real-time to show the quadratic polynomial formed from those zeroes. This shows how p(x) = (x – z1)(x – z2) changes.

Part 3: Relationship Between Zeroes and Coefficients

There is a direct algebraic relationship between the zeroes of a polynomial and its coefficients. These formulas are useful for verifying zeroes quickly.

Polynomial Type	Zeroes	Sum of Zeroes	Product of Zeroes
Quadratic ax^2 + bx + c	alpha, beta	alpha + beta = -b/a	alpha*beta = c/a
Cubic ax^3 + bx^2 + cx + d	alpha, beta, gamma	alpha + beta + gamma = -b/a	alphabetagamma = -d/a

For a cubic, there is one more relationship: alpha*beta + beta*gamma + gamma*alpha = c/a.

Deep Dive: Cubic Polynomial Relationships

For a cubic polynomial p(x) = ax^3 + bx^2 + cx + d, with zeroes alpha, beta, and gamma, the relationships are more detailed:

1. Sum of Zeroes:
alpha + beta + gamma = -b/a

2. Sum of Products of Zeroes (taken two at a time):
alpha*beta + beta*gamma + gamma*alpha = c/a

3. Product of Zeroes:
alpha*beta*gamma = -d/a

These three formulas are used to verify the zeroes of a cubic polynomial or to find unknown coefficients.

Forming a Quadratic Polynomial

If you are given the zeroes alpha and beta, you can form the polynomial with this formula:

p(x) = k[x^2 – (alpha + beta)x + alpha*beta]

(where k is any non-zero real number)

Part 4: Division Algorithm for Polynomials

The division algorithm allows us to divide one polynomial, p(x), by another, g(x).

$\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$

p(x) = g(x) * q(x) + r(x)

The division stops when the remainder r(x) is 0 or its degree is less than the degree of the divisor g(x).

Example: Polynomial Long Division

Let’s divide p(x) = -x^3 + 3x^2 – 3x + 5 by g(x) = -x^2 + x – 1.

-x²+x-1 ) -x³+3x²-3x+5 ( x – 2 <-- Quotient q(x)
-x³+ x²- x
(+) (-) (+)
----------------
2x²-2x+5
2x²-2x+2
(-) (+)(-)
-----------
3 <-- Remainder r(x)

Here, q(x) = x – 2 and r(x) = 3. This is a key tool for finding remaining zeroes of a polynomial.

Part 5: Interactive Q&A Bank

Filter by difficulty:

Q.1: A graph cuts the x-axis at three points. What is the number of zeroes?

Hint: The zeroes are the x-coordinates of the points where the graph intersects the x-axis.

Answer: The number of zeroes is 3.

Q.2: What is the maximum number of zeroes a cubic polynomial can have?

Hint: The maximum number of zeroes is equal to the degree of the polynomial.

Answer: A cubic polynomial has a degree of 3, so it can have at most 3 zeroes.

Q.3: Find the zeroes of 6x^2 – 7x – 3 and verify the relationship with coefficients.

Hint: Factor the polynomial by splitting the middle term. Then use the formulas alpha + beta = -b/a and alpha*beta = c/a.

1. Factoring: 6x^2 – 9x + 2x – 3 = 3x(2x – 3) + 1(2x – 3) = (3x + 1)(2x – 3).

The zeroes (alpha, beta) are x = -1/3 and x = 3/2.

2. Verification: Here a = 6, b = -7, c = -3.

Sum: alpha + beta = (-1/3) + (3/2) = 7/6. Formula: -b/a = -(-7)/6 = 7/6. (Verified)

Product: alpha*beta = (-1/3) * (3/2) = -1/2. Formula: c/a = -3/6 = -1/2. (Verified)

Q.4: Find a quadratic polynomial whose sum of zeroes is 2 and product of zeroes is -15.

Hint: Use the formula p(x) = k[x^2 – (sum)x + (product)].

Using the formula p(x) = k[x^2 – (alpha + beta)x + alpha*beta].

p(x) = k[x^2 – (2)x + (-15)] = k[x^2 – 2x – 15].

Letting k=1, a valid polynomial is x^2 – 2x – 15.

Q.5: If 4 is a zero of p(x) = x^3 – 3x^2 – 10x + 24, find its other two zeroes.

Hint: If 4 is a zero, then (x – 4) is a factor. Use polynomial long division to divide p(x) by (x – 4). The zeroes of the resulting quotient are the other two zeroes.

1. Divide (x^3 – 3x^2 – 10x + 24) by (x – 4) using long division.

2. The division gives a quotient q(x) = x^2 + x – 6 and a remainder of 0.

3. Find the zeroes of the quotient by setting q(x) = 0:

x^2 + x – 6 = 0

(x + 3)(x – 2) = 0

The other two zeroes are x = -3 and x = 2.

Q.6: Obtain all zeroes of p(x) = 3x^4 + 6x^3 – 2x^2 – 10x – 5, if two zeroes are sqrt(5/3) and -sqrt(5/3).

Hint: First, find the quadratic factor g(x) from the given zeroes. g(x) = (x – sqrt(5/3))(x + sqrt(5/3)) = x^2 – 5/3. For easier division, use 3g(x) = 3x^2 – 5. Divide p(x) by 3x^2 – 5 to get the quotient q(x). The zeroes of q(x) are the remaining zeroes.

1. The factor from the given zeroes is g(x) = (x – sqrt(5/3))(x + sqrt(5/3)) = x^2 – 5/3.

2. We can use 3g(x) = 3x^2 – 5 as the divisor.

3. Dividing p(x) = 3x^4 + 6x^3 – 2x^2 – 10x – 5 by g(x) = 3x^2 – 5 gives the quotient q(x) = x^2 + 2x + 1.

4. Find the zeroes of q(x): x^2 + 2x + 1 = 0 (x + 1)(x + 1) = 0

The remaining zeroes are x = -1 and x = -1 (a repeated root).

The four zeroes are {sqrt(5/3), -sqrt(5/3), -1, -1}.

Part 6: Frequently Asked Questions (FAQs)

The “degree” is a property of the whole polynomial (the highest exponent). The “value” is the result you get after substituting a number for x.

Both. Geometrically, it is one distinct zero (one point of contact). Algebraically, it is considered two equal zeroes (a “repeated root”). For example, p(x) = x^2 – 4x + 4 factors to (x – 2)(x – 2). The only zero is 2.

A remainder of 0 means the division is exact. This proves that the divisor, g(x), is a perfect factor of the dividend, p(x). This is the main principle used to find unknown zeroes.

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CBSE

AI Ethics & Project Cycle: CBSE Class 10 (Bias, Privacy, Scoping & Evaluation)

AI Ethics for Class 10: Understanding the Hard Questions

1. Moral Dilemmas: The Self-Driving Car Problem

Scenario Poll: What Should the Car Do?

Option A: Stay Course

Option B: Swerve

2. Data Privacy: Permissions, Sensors, and Consent

Smartphone App Permissions

3. AI Bias: When Data Creates Unfairness

Interactive Chart: Visualizing AI Bias

4. Access & Inclusion: The AI Digital Divide

Downloadable Debate Kit

Parent & Teacher Guide

5. The AI Project Cycle

Interactive: The 5 Stages of the AI Project Cycle

5.1 Problem Scoping

Interactive: 4Ws Problem Canvas

Download: Problem Statement Template

5.2 Data Acquisition

5.3 Data Exploration

Infographic: Common Data Visualization

Bar Chart

Pie Chart

Scatter Plot

5.4 Modelling

5.5 Evaluation

Infographic: Interactive Confusion Matrix

Title

5.5.1 Choosing the Right Metric: Precision vs. Recall

Focus on Precision

Focus on Recall

5.5.2 Evaluation for Fairness

6. Q&A and Frequently Asked Questions

7. Key Chapter Notes

Class Debate Kit

Topic 1: “AI will create more jobs than it destroys.”

Topic 2: “Student access to AI writing tools should be restricted.”

Parent & Teacher Guide to AI

1. Setting Boundaries for AI Tools

2. Identifying AI-Generated Content

3. Talking About Privacy & Digital Footprint

Problem Statement Template

Our project aims to solve… (The Problem)

For… (The Stakeholders / Who)

In… (The Context / Where)

By… (The Proposed Solution)

To… (The Impact / Why)

AI Ethics for CBSE Class 10: Self-Driving Cars, Data Privacy, AI Bias, & Access

AI Ethics

Learning Outcomes

1. Moral Dilemmas: The Self-Driving Car

Option 1: Focus on the Outcome

Option 2: Focus on the Action

Scenario Poll

2. Data Privacy: Your Phone and Your Data

Infographic: The Flow of Your Data

The “I Agree” Problem

Beyond the Phone: Smart Sensors and Consent

What App Permissions Really Mean

3. AI Bias: When AI is Unfair

Interactive: Common Sources of Bias

Where Does Bias Come From?

Infographic: The Interaction Bias Feedback Loop

Examples of AI Bias

4. Access, Inclusion, and Jobs

The Changing Job Market

Task Automation

New Roles

The “Digital Divide”

AI, Age, and Inclusion

Interactive Chart: The Access Gap

Module: Key Terminology

Chapter Notes: Key Takeaways

5. Questions & Answers (FAQs)

6. Resources & Next Steps

Download: Classroom Debate Kit

Download: Parent/Teacher Guide

Continue Learning:

AI Domains: Data Science, CV, NLP CH3 | CBSE Class 10 AI (417)