10th maths assignment answer

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Get here the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers all exercises in Hindi and English medium revised and modified for session 2024-25. The solution of chapter 1 class 10th mathematics is updated according to NCERT textbooks published for 2024-25 CBSE exams.

NCERT Solutions for Class 10 Maths Chapter 1

Learning Class 10 Maths Chapter 1, Real Numbers, effectively requires a systematic approach and a clear understanding of the concepts involved. Here are some steps and strategies to help you learn this chapter.

Class 10 Maths Chapter 1 Solutions Class 10 Maths Chapter 1 Main Topics Class 10 Maths Chapter 1 Practice Tests 10th Maths Chapter 1 Question wise Solutions Class 10 Maths Chapter 1 MCQ Class 10 Maths Chapter 1 Assignments

Euclid’s Division Lemma states that for any two positive integers a and b, there exist unique integers q and r such that: a = bq + r, where 0 ≤ r < b.

The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be expressed as a product of prime numbers in a unique way, up to the order of factors.

Methods for proving the irrationality of certain numbers, such as the square root of a prime number, are discussed. Understanding decimal expansions of real numbers. Terminating decimals and recurring decimals. Rationalization is the process of converting an irrational number into a rational one by multiplying or dividing by a suitable number.

According to rationalised syllabus for academic session 2024-25, only two exercises are in chapter 1. The exercise 1.1 deleted and exercise 1.2 become the exercise 1.1. Similarly exercise 1.3 become exercise 1.2 and exercises 1.4 is also deleted. The course structure of class 10 mathematics chapter 1 is given below: Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5.

>> Total Number of Exercises: 2 >> Total Marks in Board Exam: 6 >> Number of Periods needed: 15

Class 10 Maths Chapter 1, titled Real Numbers, is an important chapter that lays the foundation for understanding various mathematical concepts. The main points covered in this chapter include introduction to Real Numbers. Real numbers are a set of numbers that includes all rational and irrational numbers. Real numbers can be represented on the number line.

Utilize online resources like video tutorials, educational websites like Tiwari Academy, and interactive quizzes to reinforce your understanding of the chapter. As you progress, practice solving sample papers or past year question papers. This will help you become familiar with the exam pattern and time management. Periodically test your knowledge by attempting self-assessment quizzes or problems from the chapter. This will help you gauge your progress.

In class 10 Maths Chapter we will learn about understanding square numbers and their properties. Finding the square root of a number using prime factorization. Real numbers are used in various mathematical applications, such as finding the distance between two points in coordinate geometry.

Class 10 Maths Chapter 1 Real Numbers

The chapter provides numerous examples and practice problems to reinforce the concepts discussed. These are the main points covered in Class 10 Maths Chapter 1, Real Numbers. It serves as the building block for further mathematical concepts and is essential for a solid foundation in mathematics. Get here topic wise NCERT Solutions for 10th Mathematics chapter 1 all exercises in Hindi and English medium. Students can take help of videos for solving questions of each exercise.

Class 10 Maths Chapter 1 Solutions for CBSE Board

• Class 10 Maths Chapter 1 Exercise 1.1
• Class 10 Maths Chapter 1 Exercise 1.2

Class 10 Maths Chapter 1 Solutions for State Boards

• Class 10 Maths Chapter 1 Exercise 1.3
• Class 10 Maths Chapter 1 Exercise 1.4
• Class 10 Maths Chapter 1 NCERT Book
• Class 10 Mathematics NCERT Solutions
• Class 10 all Subjects NCERT Solutions

10th Maths Chapter 1 Exercise 1.1 Solutions

Class 10 Maths Chapter 1 Exercise 1.1 Question 1 Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 The step by step solutions of each part is given here with practice questions>. You can discuss with us Part (i) , Part (ii) , Part (iii) , Part (iv) , and Part (v) to learn more about the solution.

Class 10 Maths Chapter 1 Exercise 1.1 Question 2 Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54. Get the solution of question 2 and discuss Part (i) , Part (ii) and Part (iii) with us along with assignments and other doubts for more clarification.

Class 10 Maths Chapter 1 Exercise 1.1 Question 3 Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25. Discuss with part one , two and three in detail and get worksheets to understand the solution in simple way.

Class 10 Maths Chapter 1 Exercise 1.1 Question 4 Given that HCF (306, 657) = 9, find LCM (306, 657). The solution of this question is very simple and usually asked in MCQ type questions. For more revision , please write to us .

Class 10 Maths Chapter 1 Exercise 1.1 Question 5 Check whether 6ⁿ can end with the digit 0 for any natural number n. The solution of question 5 is similar to the example given in textbook. Discuss with us and Practice here more questions based on question 5.

Class 10 Maths Chapter 1 Exercise 1.1 Question 6 Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers. Extra questions for practice based on the solution of question 6 are given here to download. Put your view to discuss with us.

Class 10 Maths Chapter 1 Exercise 1.1 Question 7 There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? Question number 7 is important for exams. Get here the solution and practice assignments with answers for revision.

10th Maths Chapter 1 Exercise 1.2 Solutions

Class 10 Maths Chapter 1 Exercise 1.2 Question 1 Prove that √5 is irrational. To understand the solution of question 1, student need to practice assignments and discuss the explanation in depth.

Class 10 Maths Chapter 1 Exercise 1.2 Question 2 Prove that 3 + 2√5 is irrational. Get here the assignments and practice questions based on the solution of question 2. If still there is any doubt, please visit to discussion forum.

Class 10 Maths Chapter 1 Exercise 1.2 Question 3 Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2 The solution of question 3 is similar to question 1 and 2. Get more practice to learn the concepts in better way. Discuss in detail here.

Use number lines and diagrams to visualize concepts like decimal expansions and the placement of real numbers on the number line. Visual aids can help make abstract concepts more concrete. Don’t hesitate to ask your teacher or a classmate for help if you encounter difficulties. Sometimes, discussing problems with others can provide valuable insights. Maintain a study schedule and allocate specific time slots for learning and practicing this chapter. Consistency is key.

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The complete chapter of 10th Maths chapter 1 is divided in four main parts. The explanation of each part with video explanation is given below. Start by reading the chapter thoroughly and grasp the basic definitions and concepts. Ensure that you understand the definitions of real numbers, Euclid’s Division Lemma, and the Fundamental Theorem of Arithmetic. Take concise notes while reading the chapter. Write down key formulas, definitions, and important points. These notes will be helpful for quick revision.

Learn here how to find the prime factorization of numbers. This skill is essential for various aspects of number theory. Practice finding the prime factorization of different numbers. Practice working with terminating and recurring decimals. Solve problems that involve decimal expansions of real numbers. Familiarize yourself with methods for rationalizing irrational numbers, especially square roots. Practice these techniques with different examples. Remember that learning mathematics often requires patience and persistence. Take your time to understand each concept thoroughly before moving on to the next. By following these steps and strategies, you can effectively learn Class 10 Maths Chapter 1 Real Numbers.

Class 10 Maths Chapter 1 Main Topics Mathematics is best learned through practice. Solve a variety of problems related to real numbers, including examples from your textbook and additional practice questions. Pay attention to different types of questions, such as finding HCF, LCM, prime factorization, and working with decimal expansions.

10th Maths Chapter 1 Practice Test Papers

Euclid’s Division Lemma is a fundamental concept in this chapter. Make sure you understand how it works and can apply it to solve problems related to divisibility and remainders. There are four exercises in chapter 1 covering all the four topics on Real Numbers. Students can practice well using the 6 question papers given below. It will help to prepare the chapter for CBSE exams also.

Class 10 Maths Chapter 1 Practice Tests with Answers

• Class 10 Maths Chapter 1 Practice Test 1
• Class 10 Maths Chapter 1 Practice Test 2
• Class 10 Maths Chapter 1 Practice Test 3
• Class 10 Maths Chapter 1 Practice Test 4
• Class 10 Maths Chapter 1 Practice Test 5
• Class 10 Maths Chapter 1 Practice Test 6
• Download More Assignments with Solution

The word algorithm come from the name of the name of the 9th century Persian mathematician al-Khwarizmi. The word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabr w’al-muqabala.

An equivalent version of Fundamental theorem of Arithmetic was probably first recorded as Proposition 14 of Book IX in Euclid’s Elements, before it came to be known as the Fundamental Theorem of Arithmetic.

However, the first correct proof was given by Carl Friedrich Gauss in his al-Khwarizmi. Carl Friedrich Gauss is often referred to as the ‘Prince of Mathematicians’ and is considered one of the three greatest mathematicians of all time, along with Archimedes and Newton. He has made fundamental contributions to both mathematics and science. Learn here how to make class 10 Maths chapter 1 easy to learn.

How many exercises are there in class 10 Maths chapter 1 Real numbers?

Now there are only 2 exercises in class 10 chapter 1 (Real numbers): In first exercise (Ex 1.1), there are 5 questions. In second exercise (Ex 1.2), there are 7 questions. So, there are in all 18 questions in class 10 chapter 1 (Real numbers). There are in all 11 examples in class 10 chapter 1 (Real numbers).

• Examples 1,2,3,4 are based on Ex 1.1.
• Examples 5,6,7,8 are based on Ex 1.2.

Are there any Theorems or Algorithm in 10th Maths chapter 1?

Yes, there are 7 Theorems and 1 Algorithm in class 10 chapter 1 (Real numbers). First exercise (Ex 1.1) is based on Theorem 1.1 (Euclid’s Division Lemma) and Euclid’s Division algorithm. Theorem 1.2 (Fundamental Theorem of Arithmetic) is used in second exercise (Ex 1.2).

What are the Important questions from Maths class 10 chapter 1 Real numbers?

Important questions from Maths class 10 chapter 1:

• In first exercise (Ex 1.1), all questions are important.
• In second exercise (Ex 1.2), Q2, 4, 5, 7 are important.

Which topics students should recall before starting class 10 Maths chapter 1?

Students should recall some topics of class 9 chapter 1 (Number systems). Topics :

• Types of numbers (Natural number, Whole number, Integers, Rational numbers, Irrational numbers and Real numbers).
• Decimal expansion of Rational numbers (Terminating and Non-terminating recurring) and Irrational numbers (Non-terminating non-recurring).
• HCF (Highest Common Factor) and LCM (Lowest/Least Common Multiple).
• And some other topics like Meaning of Dividend, Divisor, Quotient and Remainder, Prime numbers, Composite numbers, Factors.

Chapter 2: Polynomials »

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Having graduated from Electronics and Communication Engineering from AKTU – Noida, India, in 2021, working for Tiwari Academy as a content writer and reviewer. My main focus is to provide an easy to understand methods in all subjects specially mathematics and making study material with step by step explanation.

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Class 10 Assignments Download Pdf

Please refer to Assignments for Class 10 for all subjects given below. We have given below free printable Assignments for Class 10 for easy and free download in PDF. The assignments have been developed based on the current year’s NCERT Books for Class 10. These Assignments for Grade 10 cover all critical topics which can come in your standard 10 class tests and exams. Free printable Assignments for CBSE Class 10 , school and class worksheets, and practice test papers have been developed by our experienced class 10 teachers. You can free download CBSE NCERT printable assignments for Class 10 with solutions and answers. All assignments and test sheets have been prepared by expert faculty as per the latest curriculum in Class 10. Students can simply click on the links below and download all Pdf assignments for class 10 for free. Latest Kendriya Vidyalaya Class 10 assignments and test papers are provided below.

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NIOS Class 10th Maths (212) English Medium Solved Assignment PDF (TMA) 2023-24 | Nios Maths TMA 2023-24

Maths (212), tutor marked assignment, 20% marks of theory.

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Note:- if you want solved assignment pdf and handwritten scanned assignment click on whatsapp button, 1. answer any one of the following question., (a) i) find five rational numbers between 3/5 and 4/5. ii) are the square roots of all positive integers irrational if not, give an example of the square root of a number that is a rational number., (b) simplify the following (i) 3 (a⁴b³)¹⁰×5(a²b²)³ (ii) (2x-²y³)³, answer: for pdf click on whatsapp button (pdf is paid), 2. answer any one of the following question., (a) (i) solve: (5m-3)/4+ (3m-2)/5 = (m+6)/7 (ii) the sum of two numbers is 82 and their product is 1456, find the two numbers., (b) for the polynomial (x³ + 2x + 1)/5-(7/2)x²-x⁶, write (i) the degree of the polynomial (ii) the coefficient of x³ (iii) the coefficient of x⁶ (iv) the constant term, 3. answer any one of the following question., (a) in fig. 1, lines xy and mn intersect at o. if ∠poy = 90° and a: b = 2 : 3, find c..

(b) In Fig. 1, ∠PQR = ∠PRQ, then prove that that ∠PQS = ∠PRT.

4. Answer any one of the following questions.

(a) find all the angles of a parallelogram if one angle is 80°. in a rectangle, one diagonal is inclined to one of its sides at 25°. measure the acute angle between the two diagonals., (b) prove that the angle bisectors of a parallelogram form a rectangle. in a trapezium abcd, ab||cd. calculate zc and zd if angle a = 55° and angle b = 70°, 5. answer any one of the following questions., (a) (i) prove that the tangents drawn at the ends of a diameter of a circle are parallel. (ii) two concentric circles are of radii 5 cm and 3 cm. find the length of the chord of the larger circle which touches the smaller circle. in the figure 3, de||ac and df||ae. prove that bf/fe = be/ec.

(b) AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

6. Prepare any one Project out of the following projects given below:

(a) draw the frequency polygon for the following data.

(b) The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. which is the most common, and which is the rarest, blood group among these student, leave a reply cancel reply.

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10th Maths Question Bank

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• English Medium – Preview & Download (MAT.NO. 216639)
• 10th Maths Full Question Bank (2 Mark and 5 Mark Questions) | Ms. V. Deepa – English Medium – Preview & Download (MAT.NO. 216012)
• 10th Maths Question Bank (All Chapters Questions) | Shri Krishna Academy – English Medium – Preview & Download (MAT.NO. 214076)
• Tamil Medium – Preview & Download (MAT.NO. 216870)
• English Medium – Preview & Download (MAT.NO. 216871)
• 10th Maths Blueprint and Question Bank (Classification of Questions) | Arthi Tuition Center – English Medium – Preview & Download (MAT.NO. 216835)
• 10th Maths Unit Exercise Questions (Chapter 1 to 8) | MS Centre – English Medium – Preview & Download (MAT.NO. 216292)
• 10th Maths Book Inside Creative 1 Mark Questions (Chapter 1 to 8) | TN SCERT – English Medium – Preview & Download (MAT.NO. 215324)
• 10th Maths Book Inside Creative 1 Mark Questions with Answers | Mr. U. Karthikkumar – English Medium – Preview & Download (MAT.NO. 216436)
• 10th Maths Book Inside Creative Questions – Chapter 1 (Sets and Relations) | Wisdom Coaching Center – English Medium – Preview & Download (MAT.NO. 221544)
• 10th Maths – Chapter 1 Book Inside Creative Questions | Mr. G. Narasimhan – English Medium – Preview & Download (MAT.NO. 213559)
• 10th Maths Book Inside Creative Questions – Chapter 2 (Arithmetic Progression) | Wisdom Coaching Center – English Medium – Preview & Download (MAT.NO. 213861)
• 10th Maths – Chapter 2 Book Inside Creative Questions | Mr. G. Narasimhan – English Medium – Preview & Download (MAT.NO. 214018)
• 10th Maths – Chapter 2 Book Inside Creative Questions | Mr. V. Anish Kumar – English Medium – Preview & Download (MAT.NO. 214314)

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STEP Support Programme

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STEP Support - Assignment 10

Introduction

This STEP support module derives some of the compound trigonometry formula ($\sin(\alpha + \beta)$ etc.) and introduces a new function. Previous assignments can be found here , but you can do this one without having done the others first.

STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").

About this assignment

The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise.

The warm up for this assignment derives the trigonometrical identities for $\sin(\alpha \pm \beta)$ and $\cos(\alpha \pm \beta)$.

The main STEP question (2005 STEP 2 Question 2) introduces a function which will probably be unfamiliar to you. Don't be put off by this; the question starts by asking you to evaluate the function for some specific values so that you get a feel for what it does.

The final question consists of 4 questions taken from examination papers published more than 150 years ago. Needless to say, calculators should not be used!

For more on logical thinking and "if and only if" see Advanced Problem Solving Module 2 . Some more information on Euler's Totient function can be found on Wikipedia and Wolfram Mathworld (as well as many other places!).

You can explore how modular arithmetic and Euler's Totient function can be used to exchange information securely with this Nrich feature .

Can you use this diagram to derive the compound angle formulae for sine and cosine?

Hints, support and self evaluation

The “Hints and partial solutions for Assignment 10” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.

Here is a Worked Video Solution to the STEP question from this assignment.

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)

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• Reach out to the pro(s) you want, then share your vision to get the ball rolling.
• Request and compare quotes, then hire the Landscape Architect & Landscape Designer that perfectly fits your project and budget limits.

A landscape architect designs and plans outdoor spaces based on the client’s needs and preferences. They:

• Create detailed plans and visual representations using computer software.
• Select suitable materials and consider environmental factors like drainage and energy usage.
• Collaborate with other professionals in Pushkino and oversee landscaping project progress.

Landscape architects are typically required to be licensed in order to practice professionally.

By using the expertise of a landscape architect, clients can ensure that their outdoor spaces in Pushkino are carefully designed, functional, and visually appealing.

• Have a degree or certification in landscape design, horticulture, or a related field
• Best for smaller projects like designing a small backyard or creating a beautiful residential garden.
• Have expertise in creating personalized designs, selecting plants, and suggesting features like patios or garden beds.
• Knowledgeable about plant care, garden aesthetics, and creating functional outdoor spaces.
• Hold a professional degree in landscape architecture and are licensed to practice.
• Best for larger-scale projects like designing a large garden or dealing with challenging terrains.
• Specialize in creating master plans for big properties, integrating features like water elements, outdoor structures, and extensive plantings.
• Have a deep understanding of design principles, construction techniques, and environmental considerations.

What does a landscape architect do?

What does a landscape designer do, questions to ask prospective landscapers in pushkino, moscow oblast, russia:.

If you search for Landscape Architect near me you'll be sure to find a business that knows all about the latest trends and styles for your outdoor spaces, such as gardens, parks, or outdoor recreational areas.

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