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26 NCERT Exemplar Problems Class 9 Maths ideas | class, maths solutions, polynomials

The study material contains an exhaustive explanation to all the questions. These answers are written clearly and step by step to maximise retention. While going through these solutions, students will find themselves understanding the concept better.

Practising regularly is a prerequisite if students want to score well ncert exemplar class 10 maths solutions ch 3 im mathematics. You can consult the guide to brush up your memory or help you if you get stuck. There are 4 Exercises present in this chapter.

Students will learn about real numbers and irrational numbers in the 1st chapter of Class 10 Maths. Exercise 1. There are a total of 4 Exercises including an optional Exercise ncert exemplar class 10 maths solutions ch 3 im the 2nd chapter of class 10 Maths.

The first Exercise is about to find zeros of polynomials p x. In the second Exercise, the students need to find a quadratic polynomial. The third Exercise has questions on division of polynomials. The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2. Exercise 2. The third chapter of class 10 maths is about the linear equations in two variables. It describes what a linear equation in two variables is and how to solve the problems on linear equations in two variables.

In the first Exercise Ex 3. The second Exercise, i. The next four Exercises, Ex 3. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method.

Exercise 3. It contains questions from all the Exercises. This chapter explains what a quadratic equation is and the methods of solving quadratic equations. It also explains the factorization method of solving quadratic equations and the square method.

The chapter gives the details of relationships between discriminant and nature of roots. Also, the problems of real life have been solved as examples in this chapter. Exercise 4. This chapter introduces a new topic to the students - Arithmetic Progression, commonly called as AP. Students will learn what is AP, derivation of nth term, finding the sum ncert exemplar class 10 maths solutions ch 3 im first n terms of the AP and solving the real life problems using AP in this chapter.

The first Exercise of the chapter teaches how to represent a problem or situation in the form of AP, how to find the first term and difference of the AP, and to find whether the given series is Ap or not. The next Exercise, Ex 5.

The third Exercise describes how to find the sum of first n terms of AP and contains questions related to the topic. The last and fourth Exercise have questions related to the topics taught in the chapter. Exercise 5. The chapter 6 of class 10 gives details about the triangles.

The chapter gives details about the figures with the same shape but different sizes. It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles.

Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of pythagoras theorem is explained. Exercise 6. Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers.

The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given. The concept of finding the area of a triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio is explained in the chapter.

Exercise 7. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of ncert exemplar class 10 maths solutions ch 3 im angles. Students will also ncert exemplar class 10 maths solutions ch 3 im to calculate trigonometric ratios for the given angles and also a few trigonometric identities.

Exercise 8. Chapter 9 is the continuation of chapter 8 where the Ncert Solutions Class 10 Maths Ch 10 Study Rankers Name students will learn about the application of trigonometry which they learnt in the previous chapter. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects.

They will also learn how trigonometry is applied and used in navigation, construction and determining the position ncert exemplar class 10 maths solutions ch 3 im any piece of land based on their latitude and longitudes.

Exercise 9. In this chapter, students will be introduced to the concept of tangents and number of tangents from a point on a circle. Exercise Chapter 11 is ncert exemplar class 10 maths solutions ch 3 im of the interesting chapters. This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle.

The methods of construction are well explained in the chapter to clear the concepts. As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle is clarified. This chapter further explains how to find the area of the figures that contains a circle or part of a circle. In the five Exercises of this chapter, finding the surface area of any object which is made up of two or more different solid shapes.

The solid shapes include cuboid, cone, sphere, hemisphere and cylinder. Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions which ask about the conversion from one shape to.

This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone. This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped.

They further learn about finding the mean, median and mode of the given data. In the next Exercise, they will learn about the cumulative frequency distribution and drawing cumulative frequency curves. It elaborates and explains the difference between experimental probability and theoretical probability. The chapter is full of examples to clear the concept of probability to the learners. Students can download the PDF easily and start going through the chapters.

You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score. The exam is of marks where 80 marks is for theory whereas 20 marks is given for internal assessment.

To understand the marking scheme in a better way, you should understand the exam pattern clearly. To score good in the exam, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers and marking schemes so that all the doubts of the students are cleared.

The number of questions are increased and the marks per question are reduced. This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has reduced. CBSE focuses on all-round development of Class 10 students to prepare them for their further education.

To perform well in Class 10 then becomes fairly important. CBSE marking scheme is stepwise so you have scored accordingly. Therefore students should write each step clearly and give a proper conclusion at the end of the answer. The unit wise marks weightage of the mathematics paper is as follows:. The paper has four sections. There are a total of 30 questions for 80 marks.

Number System. Coordinate geometry. Statistics and probability. The question paper design will be:. Sl No. Type of Questions. Total Marks. Memory: Terms, answers, basic concepts and recalling of facts. Understanding: Compare, organize, interpret, translate, describe and stating main ideas. Apply: Solving problems by applying the knowledge, facts, theorems and rules in different ways.

Analyse: Analyse the information provided and making inferences. Evaluate: Opine about the validity of quality of work and validity of ideas. Create: Creating alternative solutions of the given problem and grouping the elements.

Make points:

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Solution: Let a bean arbitrary positive integer. Solution: Let a be an arbitrary positive integer. Question 6 If n is an odd integer, then show that n 2 � 1 is divisible by 8. From eq. Solution: Since, 1, 2 and 3 are the remainders of , and , respectively. Question 11 Show that 12 n cannot end with the digit 0 or 5 for any natural number n.

Solution: If any number ends with the digit 0 or 5, it is always divisible by 5. If 12 n ends with the digit zero or five it must be divisible by 5. This is possible only if prime factorisation of 12 n contains the prime number 5. Question 12 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively.

What is the minimum distance each should walk so that each can cover the same distance in complete steps? Solution: We Ncert Exemplar Class 10 Maths Solutions Ch 8 King have to lind the LCM of 40 cm, 42 cm and 45 cm to get the required minimum distance. Hence, write its decimal expansion, without actual division. Hence, 0. Solution: On dividing n by 3, let q be the quotient and r be the remainder.

So, in this case, only n is divisible by 3. Question 3 Prove that one of any three consecutive positive integers must be divisible by 3. On dividing n by 3, let q be the quotient and r be the remainder. Hence, one of any three consecutive positive integers must be divisible by 3. Question 4 For any positive integer n, prove that n � n is divisible by 6. So, one out of these must be divisible by 2 and another one must be divisible by 3.

Therefore, a is divisible by both 2 and 3. Solution: On dividing n by 5, let q be the quotient and r be the remainder. RD Sharma Class 12 Solutions. Watch Youtube Videos. Hence, the given pair of linear equations are consistent.

We observe that the lines represented by i and ii are coincident. Write the vertices of the triangle formed by these lines and the y-axis. Also, find the area of this triangle? How many such lines can we find? Therefore, the pair of equations has a unique solution.

Hence, these equations are consistent. Find x and y. Question 16 Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now? Now, by first condition, Two years ago, Salim was thrice as old as his daughter.

Question 17 The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father. Solution: Let the present age in year of father and his two children be x, y and z years, respectively. Question 18 Two number are in the ratio 5 : 6, If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5.

Find the numbers. Solution: Let the two numbers be x and y. Question 19 There are some students in the two examination halls A and B.

To make the number of students equal in each hall, 10 students are sent from A to 8. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls. Solution: Let the number of students in halls A and B are x and y respectively. Question 20 A shopkeeper gives books on rent for reading.

She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Find the fixed charges and the charge for each extra day. Jayanti answered questions and got 90 marks. How many questions did she answer correctly? Solution: Let the number of correct answers be x then the number of wrong answers be � x Then, by given condition, Hence, Jayanti answered correctly questions. Find x and y and hence the values of the four angles.

Also find the area of the quadrilateral formed by the lines and the x-axis. Now, from the graph ABCD is the quadrilateral formed by given lines and x � axis. Form the pair of linear equations for the above situation. Find the cost of a pen and Ch 9 Maths Class 10 Ncert Solutions Malaysia a pencil box. On solving lines i and ii , we will get the intersecting point B On multiplying eq.

On solving lines iii and i , we will get the intersecting point A On multiplying in eq. Question 6 Ankita travels 14 km to her home partly by rickshaw and partly by bus.

She takes half an hour, if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer.

Find the speed of the rickshaw and of the bus. Now, time taken to travel 2 km by rickshaw, Ncert Exemplar Class 10 Maths Solutions Ch 8 Que and time taken to travel remaining distance i. Find the speed of the stream. Question 8 A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream. Question 9 A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3.

Find the number. Question 10 A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket.

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