Index Laws in Class 10 Maths definition formulas properties and solved examples
We all enjoy Maths both as a subject as well as a learning point of view. It always tests our application capabilities and makes us good problem solvers. In Class 10th, Maths takes some interesting turns as a subject by adding some new chapters such as trigonometry. In this article, we are going to learn about the chapters present in Class 10th Maths NCERT in detail. The NCERT Maths book for Class 10 has its index given below.
Chapters
Class 10 Maths all chapter names are given below with proper description of sub topics.
Chapter - 1: Real Numbers
1.1 Introduction
1.2 The Fundamental Theorem of Arithmetic
1.3 Revisiting Irrational Numbers
1.4 Summary
Chapter - 2: Polynomials
2.1 Introduction
2.2 Geometrical Meaning of the Zeroes of a Polynomial
2.3 Relationship between Zeroes and Coefficients of a Polynomial
2.4 Summary
Chapter - 3: Pair of Linear Equations in Two Variables
3.1 Introduction
3.2 Graphical Method Solution for a Pair of Linear Equations
3.3 Algebraic Methods of Solving a Pair of Linear Equations
3.3.1 Substitution Method
3.3.2 Elimination Method
3.4 Summary
Chapter - 4: Quadratic Equations
4.1 Introduction
4.2 Quadratic Equations
4.3 Solution of a Quadratic Equation using Factorisation
4.4 Nature of Roots
4.5 Summary
Chapter - 5: Arithmetic Progressions
5.1 Introduction
5.2 Arithmetic Progressions
5.3 nth term of an AP
5.4 The Sum of First n terms of an AP
5.5 Summary
Chapter - 6: Triangles
6.1 Introduction
6.2 Similar Figures
6.3 Similarity of Triangles
6.4 Criteria for Similarity of Triangles
6.5 Summary
Chapter - 7: Coordinate Geometry
7.1 Introduction
7.2 Distance Formula
7.3 Section Formula
7.4 Summary
Chapter - 8: Introduction to Trigonometry
8.1 Introduction
8.2 Trigonometric Ratios
8.3 Trigonometric Ratios of Some Specific Angles
8.4 Trigonometric Identities
8.5 Summary
Chapter - 9: Some Applications of Trigonometry
9.1 Heights and Distances
9.2 Summary
Chapter - 10: Circles
10.1 Introduction
10.2 Tangent to a Circle
10.3 The Number of Tangents from a Point on a Circle
10.4 Summary
Chapter - 11: Areas Related to Circles
11.1 Areas of Sector and Segment of a Circle
11.2 Summary
Chapter - 12: Surface Areas and Volumes
12.1 Introduction
12.2 Surface Area of a Combination of Solids
12.3 Volume of a Combination of Solids
12.4 Summary
Chapter - 13: Statistics
13.1 Introduction
13.2 Mean of Grouped Data
13.3 Mode of Grouped Data
13.4 Median of Grouped Data
13.5 Summary
Chapter - 14: Probability
14.1 Probability — A Theoretical Approach
14.2 Summary
Answers and Hints
This part of Class 10 Maths NCERT consists of solutions of the exercises from each chapter and hints for difficult questions.
Appendix
Appendix A1: Proofs in Mathematics
A1.1 Introduction
A1.2 Mathematical Statements Revisited
A1.3 Deductive Reasoning
A1.4 Conjectures, Theorems, Proofs, and Mathematical Reasoning
A1.5 Negation of a Statement
A1.6 Converse of a Statement
A1.7 Proof by Contradiction
A1.8 Summary
Appendix A2: Mathematical Modelling
A2.1 Introduction
A2.2 Stages in Mathematical Modelling
A2.3 Some Illustrations
A2.4 Why is Mathematical Modelling Important?
A2.5 Summary
To learn more about the Class 10 Maths Index, explore the NCERT TextBook! Also Check out and practise Class 10 Maths Quiz, and learn deeper into your learning journey!
Conclusion
There are fifteen chapters in Class 10 Maths NCERT along with two appendices and solutions and hints for all chapters. The chapters include real numbers, polynomials, pair of linear equations in two variables, quadratic equations, arithmetic progressions, triangles, coordinate geometry, introduction to trigonometry, some applications of trigonometry, circles, constructions, circles and areas related to them, volumes and surface areas, probability, and statistics. Appendix is divided into two parts, i.e., A1 and A2, which are proofs in Mathematics and mathematical modelling, respectively.
Important Materials for Class 10 Maths
To excel in Class 10 Maths, having the right study materials is essential. Below is a list of the most important resources designed by our expert teachers to make your preparation simple and effective.
FAQs on Class 10 Maths Index Laws and Exponents Guide
1. What are the laws of exponents in Class 10 Maths?
The laws of exponents are rules used to simplify expressions with powers having the same base.
The main laws of exponents for Class 10 Maths are:
- am × an = am+n
- am ÷ an = am−n (a ≠ 0)
- (am)n = amn
- (ab)m = ambm
- a0 = 1 (a ≠ 0)
- a−m = 1/am
2. What is the formula for a negative exponent?
A negative exponent means taking the reciprocal of the base raised to the positive exponent.
The formula is:
a−m = 1/am (where a ≠ 0).
Example:
- 2−3 = 1/23 = 1/8
3. Why is any non-zero number raised to the power 0 equal to 1?
Any non-zero number raised to the power 0 equals 1 because of the division law of exponents.
Using the rule:
- am ÷ am = am−m = a0
- But am ÷ am = 1 (for a ≠ 0)
4. How do you simplify expressions using laws of exponents?
To simplify expressions using laws of exponents, apply the correct exponent rule step by step.
Steps:
- Check if bases are the same.
- Apply multiplication or division law accordingly.
- Simplify powers using am+n or am−n.
23 × 24 = 23+4 = 27 = 128.
5. What is the difference between (am)n and am × an?
The expression (am)n multiplies the exponents, while am × an adds the exponents.
Formulas:
- (am)n = amn
- am × an = am+n
- (23)2 = 26 = 64
- 23 × 22 = 25 = 32
6. What is the value of a fractional exponent?
A fractional exponent represents a root of the number.
The formula is:
am/n = (√[n]{a})m
Example:
- 272/3 = (∛27)2 = 32 = 9
7. How do you divide powers with the same base?
When dividing powers with the same base, subtract the exponents.
The rule is:
am ÷ an = am−n (a ≠ 0).
Example:
- 57 ÷ 53 = 54 = 625
8. What are common mistakes in solving exponent problems?
Common mistakes in exponent problems usually involve incorrect application of laws.
Students often:
- Add exponents when bases are different (which is incorrect).
- Forget that a0 = 1 (a ≠ 0).
- Misapply (am)n as am+n instead of amn.
9. How are exponents used in scientific notation?
Exponents in scientific notation represent very large or very small numbers as powers of 10.
The standard form is:
a × 10n where 1 ≤ a < 10.
Example:
- 4,500 = 4.5 × 103
- 0.0032 = 3.2 × 10−3
10. Can you give an example of solving a mixed exponent expression?
A mixed exponent expression can be solved by applying multiple laws of exponents step by step.
Example:
(32 × 33) ÷ 34
Step 1: Multiply powers → 32+3 = 35
Step 2: Divide powers → 35−4 = 31
Final Answer: 3
This method uses both multiplication and division laws of exponents correctly.
