10th Maths Guide | Ncert Solutions Class 10 Maths

10th Maths Guide aims at developing in students an understanding and evaluation of basic concepts of Algebra, Geometry, Surface Areas, Volumes, Statistics and Probability. The practice is the only way to success in Mathematics. It is very difficult to score good in Mathematics by only reading and memorizing the formulas. So the students are told to practice these continuously to attain a good position in board examination.

10th Maths Guide contains the solutions for all questions and problems available in the textbook.10th Maths Guide cover all the topics present in the book like, Real Numbers, Polynomials,linear equations in two variables,Quadratic Equations, Arithmetic Progression,Triangles, coordinate geometry,Introduction of Trigonometry, Some Applications of Trigonometry, circles ,Area Related to Circles, Surface Areas and Volumes , Statistics and Probability.

The 10th Maths Guide typically covers a broad range of topics related to algebra, geometry, trigonometry, and statistics. It is designed to help students understand mathematical concepts, principles, and formulas in a structured and systematic way. The guide contains examples, exercises, and practice problems that students can use to test their understanding of different topics and enhance their problem-solving skills.

One of the primary goals of the 10th Math Guide is to provide students with a solid foundation in mathematical concepts and principles that they can apply in real-world situations. The guide focuses on building critical thinking skills, problem-solving skills, and logical reasoning skills that are essential for success in higher education and professional careers.

Some of the key topics covered in the 10th Math Guide include algebra, geometry, trigonometry, and statistics. Algebra covers linear equations, quadratic equations, simultaneous equations, inequalities, and graphing functions. Geometry covers the properties of lines, angles, triangles, quadrilaterals, circles, and other shapes. It also includes topics related to transformations, congruence, similarity, and coordinate geometry. Trigonometry covers the properties of trigonometric functions, including sine, cosine, and tangent. It also includes topics related to solving trigonometric equations and using trigonometry to solve real-world problems. Statistics covers the basics of probability, data analysis, and statistical inference. It includes topics related to data representation, measures of central tendency, and probability distributions.

The 10th Math Guide typically starts with an introduction to basic mathematical concepts and principles. This section provides students with an overview of mathematical operations, formulas, and symbols that they will encounter throughout the course. It also includes tips for studying math and strategies for solving different types of math problems.

After the introduction, the guide typically moves on to more advanced topics related to algebra, geometry, trigonometry, and statistics. Each chapter in the guide typically focuses on a specific topic, providing a detailed explanation of the concepts and principles involved. The guide also includes examples and practice problems that students can use to test their understanding of the material.

In addition to providing students with an overview of different mathematical concepts and principles, the 10th-grade math guide also helps students develop essential skills that are necessary for success in higher education and professional careers. These skills include critical thinking, problem-solving, and logical reasoning.

Critical thinking skills are essential for analyzing and interpreting mathematical problems. They involve the ability to analyze information, identify patterns, and draw conclusions based on evidence. Students who develop critical thinking skills are better equipped to solve complex mathematical problems and apply their knowledge in real-world situations.

Problem-solving skills are also essential for success in mathematics. They involve the ability to identify problems, define objectives, and develop solutions based on available information. Students who develop problem-solving skills are better equipped to tackle complex mathematical problems and devise innovative solutions to real-world challenges.

Logical reasoning skills are another key component of success in mathematics. They involve the ability to evaluate arguments, identify logical fallacies, and use evidence to support conclusions. Students who develop logical reasoning skills are better equipped to analyze complex mathematical problems and make informed decisions based on evidence.

Overall, the 10th Math Guide is an essential resource for students preparing for their math exams. It provides a structured and systematic approach to learning mathematical concepts and principles and helps students develop critical thinking, problem-solving, and logical reasoning skills that are essential for success in higher education and professional careers. Students who use the 10th-grade math guide can gain a solid understanding of math and excel in their math exams.

Very important Questions of All chapters class 10 Maths

CLASS – X
CHAPTER – 1 REAL NUMBERS
SESSION: 2023-24

OBJECTIVE TYPE QUESTIONS

1. If the HCF of 210 and 55 is expressible in the form 210 x 5 – 55 y, find y.
2. The LCM and HCF of two rational numbers are equal, then the number must be ___
3. What is the sum of exponents of prime factors in the prime factorisation of 196?
4. What is the product of H.C.F and L.C.M of the smallest prime number and the smallest composite number?
5. What is the remainder when the square of any prime number greater than 3 is divided by 6. ?
6. If n is any natural number, then 6n- 5n always ends with which digits?
7. If two positive integers a and b are expressible in the form a = pq2 and b = p3q; p, q being prime numbers then what is L.C. M (a,b) ?
8. Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).
9. If the HCF of 85 and 153 is expressible in the form 85n – 153, then find the value of n.
10. If a and b are prime numbers, then what is their L.C.M?

SUBJECTIVE TYPE QUESTIONS

11. Explain why 11 X 13 X 15 X 17 + 17 is a composite number?
12. If three pieces of planks 63m, 42m and 49 m long have to be divided into planks of same length, then what will be the least possible number of planks?
13. Three bells toll at intervals of 9, 12, 15 mins respectively. If they start tolling together, after what time will they next toll together
14. Check whether 4n can end with the digit 0 for any natural number n.
15. The L.C.M of two numbers is 14 times their H.C.F. The sum of L.C.M and H.C.F is 600. If one number is 280, then find the other number.
16. Find HCF of 96 and 404 by prime factorization method. Hence find their L.C.M
17. Find the largest positive integer that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
18. Two tankers contain 850 litres and 680 litres of petrol respectively. 19. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.
20. Prove that √8 is irrational.
21. Prove that √2+√5 is irrational
22. Given that √3 is irrational, prove that 5 + 2√3 is irrational.
23. Prove that is irrational.
Direction for following questions: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
24. Assertion (A): If HCF (336, 54) = 6, then LCM (336, 54) = 3000.
Reason (R): The sum of exponents of prime factors in the prime factorization of 196 is 4
25. Assertion (A): HCF of two or more numbers = Product of the smallest power of each common prime factors, involved in the numbers.
Reason (R): The HCF of 12, 21 and 15 is 3.
26. Assertion (A): 6^n ends with the digit 0, where n is a natural number.
Reason(R): Any number ends with the digit zero, if its prime factors are of the form 2m x 5n ,where m,n are natural numbers.

https://sharmatutorial.in

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

MCQ Questions for Class 10 Maths all Chaptershttps://sharmatutorial.in/category/mcq-class-10-maths/

10th Maths Guide

10th Maths Guide 2023-24

Chapter 1. Real Numbers

Chapter 2 . Polynomials

Chapter 3. Pair of Linear equations in two variables

Chapter 4. Quadratic Equations

Chapter 5. Arithmetic Progression

Chapter 6. Triangles

Chapter 7. Coordinate Geometry

Chapter 8. Introduction to Trigonometry

Chapter 9. Some Applications of Trigonometry

Chapter 10. Circles

Chapter 11. Areas related to circles

Chapter 12. Surface Areas and Volumes

Chapter 13. Statistics

Chapter 14. Probability