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Tamil Nadu (TNBSE)Class 11 Mathematics★ Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

Basic Algebra

Samacheer Kalvi (TN State Board) Class 11 Mathematics — Chapter 2, Basic Algebra. Real numbers, logarithms, quadratic inequalities and absolute value. Study notes, key concepts, worked examples, practice questions and quick revision for exam preparation.

⏱ 30 min readHard difficulty✓ Free · NCERT-aligned

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Study Guide

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Key points, glossary and the questions most likely to show up.

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By the end of this chapter you'll be able to…

1Apply laws of logarithms
2Solve quadratic inequalities
3Work with absolute value expressions

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Why this chapter matters

Basic Algebra is an important chapter in Class 11 Mathematics (Samacheer Kalvi). It covers real numbers, logarithms, quadratic inequalities and absolute value — concepts that are tested in the TN HSC Public Exam and build the foundation for higher-level studies.

Before you start — revise these

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Class 10 Mathematics — Prior concepts

Foundation knowledge required before studying this chapter.

Basic Algebra — Class 11 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 11 Mathematics, Chapter 2. Real numbers, logarithms, quadratic inequalities and absolute value.

1. About this chapter

This chapter covers Basic Algebra as part of the Class 11 Samacheer Kalvi Mathematics curriculum. It deals with real numbers, logarithms, quadratic inequalities and absolute value and builds conceptual understanding essential for the TN HSC Public Exam.

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

Apply laws of logarithms
Solve quadratic inequalities
Work with absolute value expressions

2. Key concepts

Concept 1: Apply laws of logarithms.
Concept 2: Solve quadratic inequalities.
Concept 3: Work with absolute value expressions.

3. Important terms and formulas

Term / Formula	Description
Apply laws of logarithms…	Apply laws of logarithms
Solve quadratic inequalities…	Solve quadratic inequalities
Work with absolute value…	Work with absolute value expressions

4. Worked examples

Example 1. Applying a key concept from this chapter.

Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.

Example 2. A typical exam-style question on basic algebra.

Solution: Break the problem into steps, use the appropriate formula and verify the answer.

5. Common mistakes

Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.

6. Practice (exam-style)

Define the main term or principle covered in Chapter 2.
Give two real-life examples related to basic algebra.
Solve a short numerical or descriptive question from this chapter.
State one important formula and explain each symbol.

7. Answer key (hints)

Refer to section 2 (Key concepts) above for the definition.
Examples should be drawn from daily experience and local context.
Apply the formula from section 3, show all steps clearly.
Formula with units — refer to the textbook glossary for symbol meanings.

8. Quick revision

Class 11 Mathematics — Chapter 2: Basic Algebra.
Core idea: Real numbers, logarithms, quadratic inequalities and absolute value.
Key outcomes: Apply laws of logarithms; Solve quadratic inequalities; Work with absolute value expressions.
Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Key concept from Basic Algebra

Refer to Samacheer Kalvi textbook

Chapter 2 — Real numbers, logarithms, quadratic inequalities and absolute value.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Skipping units in numerical answers

✓ Always state units alongside every numerical answer for full marks.

WATCH OUT

✗ Confusing similar concepts within the chapter

✓ Create a side-by-side comparison table during revision.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

One-mark MCQs testing key definitions and concepts from Basic Algebra.

Questions

Short answer questions

Two-mark and three-mark questions on real numbers, logarithms, quadratic inequalities and absolute value.

Questions

Long answer / Numerical questions

Five-mark questions requiring detailed explanation or problem-solving.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Concept

Define the key term in Chapter 2: Basic Algebra.

▶ Show solution

Refer to the Samacheer Kalvi Class 11 Mathematics textbook definition.

Q2MEDIUM· Application

Give two examples of basic algebra from daily life and explain.

▶ Show solution

Students should draw from familiar, local examples relevant to real numbers, logarithms, quadratic inequalities and absolute value.

Q3HARD· Long Answer

Explain Basic Algebra with a neat diagram (if applicable) and state its significance.

▶ Show solution

A complete answer includes definition, explanation, labelled diagram and conclusion.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Class 11 Mathematics — Chapter 2: Basic Algebra.
•Core topic: Real numbers, logarithms, quadratic inequalities and absolute value.
•Apply laws of logarithms.
•Solve quadratic inequalities.
•Work with absolute value expressions.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Definitions and key facts
Short Answer	2-3	1-2	Explanation and examples
Long Answer	5	1	Detailed explanation, diagram and application

Prep strategy

Read and understand all definitions in Chapter 2
Memorise key formulas and their units
Practice past-paper questions from this chapter
Draw and label all diagrams from the Samacheer Kalvi textbook

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Everyday application of Basic Algebra

Concepts from basic algebra are applied widely in daily life and professional fields.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Read the question carefully before answering
Write definitions precisely and use technical vocabulary
Draw labelled diagrams wherever applicable
Show all steps in numerical problems for full marks

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Explore advanced problems on basic algebra from Olympiad resource books.
Look for cross-connections between this chapter and other subjects.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN HSC Public ExamHigh

School Unit TestsHigh

NTSE / Olympiad (Classes 9–12)Medium

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This chapter focuses on real numbers, logarithms, quadratic inequalities and absolute value as part of the Class 11 Samacheer Kalvi Mathematics curriculum.

Carries marks in the TN HSC Public Exam through MCQs, short-answer and long-answer (5-mark) questions

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