case study questions on algebra for class 6

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CBSE Case Study Questions for Class 6 – 10, 12 for Maths, Science, SST

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Important Questions for CBSE Class 6 Maths Chapter 11 - Algebra

• Class 6 Important Question
• Chapter 11: Algebra

CBSE Class 6 Maths Important Questions Chapter 11 - Algebra - Free PDF Download

Class 6 algebra is one of the preliminary stage algebra, which is instrumental in making the perfect knowledge-base for the higher classes. Therefore, they must have crystal clear concepts of the fundamental topics. The best way to prepare algebra is to practice sample questions of each of the topics. The Maths experts at Vedantu have compiled a comprehensive list of questions for the topics covered in chapter 11. In Class 6 Maths Important Questions for Chapter 11 , you will get solved sums covering all the topics. You can download this set of questions for free from the Vedantu. Students face a lot of difficulties while solving problems of the NCERT textbook , as these require logic as well as an understanding of concepts. CBSE solutions (NCERT) give the best possible and easy methods to solve problems with the help of solved questions present in it for each type of question. You can also register Online for NCERT Class 6 Science tuition on Vedantu.com to score more marks in CBSE board examination.

Download CBSE Class 6 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 6 Maths Important Questions for other chapters:

Access IMPQ Solutions for Class 6 Maths Chapter 11- Algebra

Very Short Answer Questions 1 Marks

1. Express algebraically: $\mathbf{3}$ more than $\mathbf{x}$.

Ans: The algebraic expression of the given statement is $x+3$.

2. What is the exponential form of $\mathbf{x}\,\times \,\mathbf{x}\,\times \,\mathbf{x}\,\times \,\mathbf{x}\,\times ....\mathbf{15}\ \mathbf{times}$?

Ans: The given expression $x\times x\times x\times x\times ...15\ times$.

Recall that, $x\times x={{x}^{2}}$,

$x\times x\times x={{x}^{3}}$,

$x\times x\times x\times x={{x}^{4}}$, etc.

Therefore, the number of times $x$ is multiplied with itself equals $x$ to the power that number.

Thus, $x\times x\times x\times x\times ...15\ times={{x}^{15}}$.

3. What is the product form of ${{\mathbf{x}}^{\mathbf{2}}}{{\mathbf{y}}^{\mathbf{7}}}$?

Ans: The given algebraic expression is ${{x}^{2}}{{y}^{7}}$.

Recall that, the number of times $x$ is multiplied with itself equals $x$ to the power that number.

Therefore, ${{x}^{2}}=x\times x$.

Similarly, ${{y}^{7}}=y\times y\times y\times y\times y\times y\times y$.

Thus, ${{x}^{2}}{{y}^{7}}=x\times x\times y\times y\times y\times y\times y\times y\times y$.

4. What is the coefficient of $\mathbf{b}$ in $\mathbf{-8abc}$?

Ans: The given algebraic expression is $-8abc$.

Recall that, the coefficient of any term in an algebraic expression is the multiplication of other terms in that algebraic expression.

Therefore, the coefficient of the term $b$ in the expression $-8abc$ is $-8ac$.

5. What is the numerical coefficient of $\mathbf{4}{{\mathbf{a}}^{\mathbf{2}}}$?

Ans: The given expression is $4{{a}^{2}}$.

It is known that, the numerical coefficient in an algebraic expression is the number multiplied in that expression.

Therefore, the numerical coefficient of $4{{a}^{2}}$ is $4$.

6.  What is the constant term of $\mathbf{2}{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{9}$?

Ans: The constant term of the expression $2{{a}^{2}}-9$ is $-9$.

7. If $\dfrac{\mathbf{y}}{\mathbf{5}}=\mathbf{1}$, then $\mathbf{y}=$?

Ans: The given equation is

$\dfrac{y}{5}=1$.

Multiply $5$ both sides of the equation.

$5\times \dfrac{y}{5}=1\times 5$

$\Rightarrow y=5$.

Short Answer Questions 2 Marks

1. Express algebraically the following statement:

$\mathbf{8}$ times a number $\mathbf{x}$ is less than a number $\ge $.

Ans: The required algebraic expression of the given statement is

2. What are the terms in the following algebraic expression?

$\mathbf{4a}{{\mathbf{b}}^{\mathbf{2}}}\mathbf{+3}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{-5ab+9}$.

Ans: The terms of in the given expression are 

$4a{{b}^{2}},\,3{{c}^{2}},-5ab,$ and $9$.

3. Solve the following equation and evaluate $\mathbf{x}$. Also, justify the result.

$\mathbf{x}-\mathbf{8}=\mathbf{17}$.

Add $8$ both sides of the equation.

$ x-8+8=17+8 $

$ \Rightarrow x=25$ 

Justification:

$ LHS=x-8 $

$ =17$ 

Thus, Left-hand-side $=$ Right-hand-side.

4. Solve the following equation and evaluate $\mathbf{x}$. Also, justify the result.

$\dfrac{\mathbf{4}}{\mathbf{6}}\mathbf{x=18}$.

Ans: The given equation is 

$\dfrac{4}{6}x=18$

Multiply $6$ both sides of the equation.

$6\times \dfrac{4}{6}x=6\times 18$

$\Rightarrow 4x=18\times 6$

Divid both sides of the equation by $4$.

$\dfrac{4x}{4}=\dfrac{18\times 6}{4}$

$\Rightarrow x=27$.

$ LHS=\dfrac{4}{6}x $

$ =\dfrac{4}{6}\times 27 $

Hence, Left-hand-side $=$ Right-hand-side.

Long Answer Questions 3 Marks

1. Sanjit scored $\mathbf{70}$ marks in mathematics and $\mathbf{''x''}$ marks in English. Find the total score in both the subjects?

Ans: He got marks in mathematics $=70$.

He got marks in English $=x$.

Therefore, the total marks in mathematics and English $=x+70$.

2. Let $\mathbf{p}=\mathbf{1},\,\,\mathbf{q}=-\mathbf{1},$ and $\mathbf{r}=\mathbf{3}$ . What is the value of ${{\mathbf{p}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{r}}^{\mathbf{3}}}\mathbf{-3pqr}$?

Ans: The given algebraic expression is 

${{p}^{3}}+{{q}^{3}}+{{r}^{3}}-3pqr$                                             …… (i)

Substituting $p=1,q=-1,$ and $r=3$ into the equation (i) gives

$ {{p}^{3}}+{{q}^{3}}+{{r}^{3}}-3pqr$

$ ={{\left( 1 \right)}^{3}}+{{\left( -1 \right)}^{3}}+{{\left( 3 \right)}^{3}}-3\left( 1 \right)\left( -1 \right)\left( 3 \right) $

 $=1-1+27+9$ 

 $=27+9 $ 

 $ =36 $

3. Choose the similar terms from the following expressions.

$\mathbf{xyz,}\,\,\mathbf{x}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{z,}\,\,\mathbf{xz}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{,}\,\,{{\mathbf{z}}^{\mathbf{2}}}\mathbf{xy,}\,\,{{\mathbf{y}}^{\mathbf{2}}}\mathbf{xz,}\,\,{{\mathbf{x}}^{\mathbf{2}}}\mathbf{yz,}\,\,\mathbf{zx}{{\mathbf{y}}^{\mathbf{2}}}$

The like terms are those which have exactly one square term involved.

Therefore, the similar terms are

$x{{y}^{2}}z,\,\,xz{{y}^{2}},\,\,{{y}^{2}}xz,$ and $zx{{y}^{2}}$.

4. Solve the equation $\mathbf{12x}-\mathbf{30}=\mathbf{6}$.

The given equation is 

Add $30$ both sides of the equation.

$12x-30+30=6+30$

$\Rightarrow 12x=36$

Divide $12$ both sides of the equation.

$\dfrac{12x}{12}=\dfrac{36}{12}$

$\Rightarrow x=3$.

Hence, the solution is $x=3$.

5. Verify whether $\mathbf{y}=\mathbf{4}$ satisfy the equation $\mathbf{3y}-\mathbf{5}=\mathbf{7}$.

Ans: The given equation is $3y-5=7$.

$ LHS=3\left( 4 \right)-5 $

Hence, $y=4$ satisfy the given equation.

6. Solve the equation $\mathbf{6x}+\mathbf{10}=\mathbf{26}-\mathbf{2x}$ and evaluate $\mathbf{x}$ by using the method of transposition. Then justify the answer.

$6x+10=26-2x$

$\Rightarrow 6x=26-2x-10$, by the method of transposition.

$\Rightarrow 6x=16-2x$

$\Rightarrow 6x+2x=16$, by the method of transposition.

$\Rightarrow 8x=16$

Divide $8$ both sides of the equation.

$\dfrac{8x}{8}=\dfrac{16}{8}$

$\Rightarrow x=2$.

$ LHS=6x+10$

$=6\times 2+10 $ 

$ RHS=26-2x $

 $=26-2\times 2 $

$ =26-4$ 

 $=22 $

Hence, $x=2$ is the solution of the given equation.

Long Answer Questions 4 or 5 Marks 

1. Find the algebraic expression of the statements given below.

(a) $\mathbf{6}$ less than the quotient of $\mathbf{x}$ and $\mathbf{y}$.

Ans. The required algebraic expression is 

$\dfrac{x}{y}-6$.

(b) The sum of the quotient of $\mathbf{p}$, $\mathbf{q}$ and the product of $\mathbf{p},\,\,\mathbf{q}$.

Ans: The quotient of $p,q$ is $\dfrac{p}{q}$.

The product of $p,q$ is $pq$.

Therefore, the required algebraic expression is given by

$\dfrac{p}{q}+pq$.

(c) One fourth of the sum of $\mathbf{x}$ and $\mathbf{y}$.

Ans: The sum of $x$ and $y$ is $x+y$.

$\dfrac{1}{4}\left( x+y \right)$.

(d) $\mathbf{8}$ removed from twice the term $\mathbf{x}$.

Ans: Twice the term $x$ is $2x$.

Therefore, the required algebraic expression is $2x-8$.

2. Classify monomials, binomials, and trinomials from the following algebraic expressions.

$\mathbf{y}+\mathbf{5},\,\,\,\mathbf{6}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{y},\,\,\,-\mathbf{8},\,\,\,-\mathbf{3pqr},\,\,\,{{\mathbf{a}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{b}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{2}}}$

Ans: Recall that, sum of two terms is called binomials, sum of three terms is called trinomials and single algebraic term is called monomials.

The following table shows the required classifications.

3. Determine the solution of $\mathbf{3x}=\mathbf{12}$, by using the method of trial and errors.

Ans: The given equation is $3x=12$.

First substitute $x=1$ into the given equation.

$3x=3\times 1=3\ne 12$.

So, $x\ne 1$.

Then, substitute $x=2$ into the equation.

$3x=3\times 2=6\ne 12$.

So, $x\ne 2$.

Again, substitute $x=3$ into the given equation.

$3x=3\times 3=9\ne 12$.

Therefore, $x\ne 3$.

Now, substitute $x=4$ into the given equation.

Then $3x=3\times 4=12$.

Thus, $x=4$ is the solution of the given equation.

4. Solve the following equation and evaluate $\mathbf{x}$ by using the method of isolation.

$\mathbf{a}-\mathbf{7}=\mathbf{5}+\dfrac{\mathbf{a}}{\mathbf{2}}$.

$a-7=5+\dfrac{a}{2}$

Add $7$ on both sides of the equation.

$a-7+7=5+7+\dfrac{a}{2}$

$\Rightarrow a=12+\dfrac{a}{2}$

Add $-\dfrac{a}{2}$  on both sides of the equation.

$a+\left( -\dfrac{a}{2} \right)=12+\dfrac{a}{2}+\left( -\dfrac{a}{2} \right)$

$ \Rightarrow a-\dfrac{a}{2}=12+\dfrac{a}{2}-\dfrac{a}{2} $

$ \Rightarrow \dfrac{2a-a}{2}=12 $ 

$\Rightarrow \dfrac{a}{2}=12 $

Multiply $2$ on both sides of the equation.

$\dfrac{a}{2}\times 2=12\times 2$

$\Rightarrow a=24$.

Hence, the required solution is $a=24$.

5. Solve the following equation and justify the result.

$\mathbf{3}\left( \mathbf{a+3} \right)\mathbf{+3}\left( \mathbf{a-1} \right)=\mathbf{5}\left( \mathbf{a+5} \right)$.

$\text{3}\left( \text{a+3} \right)\text{+3}\left( \text{a-1} \right)=\text{5}\left( \text{a+5} \right)$

$\Rightarrow 3a+9+3a-3=5a+25$, multiplying the terms.

$\Rightarrow 6a+6=5a+25$, adding the like terms.

$\Rightarrow 6a-5a=25-6$, by the method of transposition.

$\Rightarrow a=19$.

$ LHS=3\left( a+3 \right)+3\left( a-1 \right) $

$=3\left( 19+3 \right)+3\left( 19-1 \right)$

$ =3\times 22+3\times 18 $

Also, 

$ RHS=5\left( a+5 \right) $

$ =5\left( 19+5 \right) $ 

$=5\times 24 $ 

Hence, the required solution of the given equation is $a=19$.

6. Determine two numbers so that one is greater by $\mathbf{21}$ than another and sum of them is $\mathbf{91}$.

Ans: Let $x$ be one number.

Then, another number is $x+21$.

By the given conditions,

$x+\left( x+21 \right)=91$

$\Rightarrow 2x+21=91$

Add $-21$ on both sides of the equation.

$2x+21+\left( -21 \right)=91+\left( -21 \right) $ 

$\Rightarrow 2x+21-21=91-21 $ 

$ \Rightarrow 2x=70 $

Divide $2$ on both sides of the equation.

$ \dfrac{2x}{2}=\dfrac{70}{2} $

$\Rightarrow x=35 $

Hence, the required numbers are $35$ and $35+21$, that is $35,\,\,56$.

Important Questions for Class 6 Maths Chapter 11

Cbse class 6 maths chapter 11 - algebra pdf free download.

To prepare for any mathematics concept, the best way to do it is to practice. You must have a set of important questions for class 6 maths chapter 11 to get your concepts cleared about the chapter. The students can download the PDF version of this question set from the Vedantu website onto their system for free. They need to have an account on the website. They can also enroll in some tuition classes to get accustomed to the topics. The students can download these class 6 maths chapter 11 important questions and use them in their preparation before any examinations.

Why is it Important to Practice Important Questions for Algebra?

Every teacher will recommend students practice class 6 maths important questions for chapter 11, and they have valid points to do so. Let us look at some of the reasons why class 6 maths chapter 11 important questions will benefit the students.

More Questions Mean More Practice

Mathematics has always been one of the rare subjects which require a lot of practice. Unlike other subjects where reading the concepts can help the students in their preparation, they have to first know about the concepts and then practice in maths. To help the students in their practice, the set of important questions for class 6 maths chapter 11 has been published. In this set of questions, all the basic principles of algebra are covered. The students will start from scratch and gradually can soak up the increasing complexity of the subject.

The Proper Introduction to a New Topic

Secondly, algebra will be a new chapter for the students in class 6. Chapter 11 will pose another issue for the students. The students will be confused about the type of questions that they will encounter in the examination. By solving these class 6 maths chapter 11 important questions, the students will know the type of questions. They can consider these questions to be the blueprint of what is coming in the examination and plan their preparation accordingly.

Proper Time Management While Solving Questions

Although the questions are not arranged in the exam format, the students can plan their preparation keeping the format in mind. That means they can make different clusters of questions and have a proper plan for managing time while they solve them. This practice will increase their proficiency in proper time management for examinations. They will know how to allocate time to each question. If they can develop these skills, they will not face any problem during the actual examination.

Growth in Confidence

Proper time management and constant practice also play a major role in building confidence in the students. As the students practice solving these class 6 maths chapter 11 important questions, they will grow their confidence in answering such questions. They will also be confident about encountering some unknown questions, as they know the right approach for such questions. Therefore, the students will face no problem when they see any unknown questions in the final exam paper.

Fine-Tuning the Preparation Process

When you start to know about a new topic in maths, you practice a lot to build the concept. You will solve all types of questions related to the topic. However, as you develop your concepts, you will focus more on the important aspects of the topics. Class 6 maths chapter 11 important questions bring you the right set of questions to fine-tune your preparation. As you focus more on these important aspects, your preparation will become more exam-oriented. You will focus more on questions that come in the examination. Therefore, you will know how to approach the questions that you will encounter in the examination.

Last-Minute Exam Preparation

For any other subject, the last-minute exam preparation will involve revision of the important topics. However, Math is such a subject that can only be revised through practice. For the last-minute preparation, you would prefer to look at the problems that are most likely to come in the examination. You might also prefer to solve them to revise the techniques. These questions will be ideal for last-minute preparation before any examination.

Important Questions on Maths Chapter 11 Algebra

Q. What is the algebraic representation of six more than x?

Ans. The problem mentioned above can be best represented as x + 6.

Q. What is the algebraic representation of nine less than three times of x?

Ans. The problem mentioned above can be best represented as 3x - 9. 

Q. What is the algebraic representation of four more than half of x?

Ans. The problem mentioned above can be best represented as (x/2) + 4.

Q. In a horticultural garden, rose plants are arranged in rows. There are seven rose plants in each row. If the total number of rows dedicated to role plants is equal to n, how many rose plants are there in the garden?

Ans. In the problem mentioned above, the following information is obtained.

The number of rose plants in a single row = 7.

The number of rows in the horticultural garden dedicated to rose plants = n.

The total number of rose plants in the horticultural garden = total number of rose plants in each row X total number of rows dedicated to rose plants in the horticultural garden.

Therefore, the total number of rose plants in the horticultural garden = 7n.

Q. In a fruit store, there are different boxes designated for different fruits. There are n boxes of mangoes, each containing 15 mangoes. Apples are present in 4 boxes with x number of apples in each box. Additionally, there are 6 boxes of guavas, each containing 20 guavas. How many fruits are present in the store in total?

Number of mangoes in each box = 15 mangoes

Number of boxes containing mangoes = n boxes

The total number of mangoes in the fruit store = number of mangoes in each box X Number of boxes containing mangoes.

Therefore, the total number of mangoes in the fruit store = 15n.

Number of apples in each box = x apples

Number of boxes containing apples = 4 boxes

The total number of apples in the fruit store = number of apples in each box X Number of boxes containing apples.

Therefore, the total number of apples in the fruit store = 4x.

Number of guavas in each box = 20 guavas

Number of boxes containing guavas = 6 boxes

The total number of guavas in the fruit store = number of guavas in each box X Number of boxes containing guavas.

Therefore, the total number of guavas in the fruit store = 120 guavas.

Finally, the total number of fruits present in the fruit store = total number of mangoes + total number of apples + the total number of guavas

Total number of fruits in the fruit store = 15n + 4x +120.

Q. The speed of a car is x km/ hr. If the car covers a distance of y km by going with that constant speed, how much time will it take to complete the distance?

Speed of the car = x km/hr.

Distance covered by the car at that constant speed = y km.

Time-taken by the car to cover the distance = Distance covered by the car at that constant speed/ Speed of the car.

Therefore, Time-taken by the car to cover the distance = y/x.

Q. Manoj has x number of chocolates. Rahim gave him 4 more. How many chocolates does Manoj have now?

The number of chocolates Manoj has = x chocolates.

The number of chocolates Rahim gave to Manoj = 4 chocolates.

Total number of chocolates that Manoj have = number of chocolates Manoj had previously + number of chocolates Rahim gave to Manoj,

Therefore, the total number of chocolates Manoj has now = x+4.

What are the Benefits of Important Questions from Vedantu for Class 6 Maths Chapter 11 - Algebra

Embark on a mathematical journey with Vedantu's Important Questions, tailored for Class 6 Maths Chapter 11 - Algebra. These targeted resources promise focused learning, exam readiness, strengthened fundamentals, time-efficient study habits, self-assessment tools, strategic exam approach, comprehensive topic coverage, and a confidence boost for every student.

Focused Learning: Delve into key Algebraic concepts for efficient understanding.

Exam Readiness: Feel prepared, reducing anxiety and enhancing performance.

Strengthened Fundamentals: Reinforce core principles through practice.

Time-Efficient Study Habits: Learn to manage time effectively during exams.

Self-Assessment Tools: Evaluate progress and identify areas for improvement.

Strategic Exam Approach: Develop a planned strategy for scoring higher.

Comprehensive Topic Coverage: Cover a spectrum of Algebraic topics comprehensively.

Confidence Boost: Strengthen exam preparation and boost overall confidence.

Important Related Links for CBSE Class 6 Maths 

The compilation of Important Questions for CBSE Class 6 Maths Chapter 11 - "Algebra" is an invaluable resource for students seeking to reinforce their understanding of fundamental algebraic concepts. These questions, curated to cover key topics in the chapter, provide a targeted approach to mastering algebraic expressions, equations, and operations. By engaging with these practice questions, students can enhance their problem-solving skills and gain confidence in applying algebraic principles. The emphasis on varied question formats ensures a comprehensive grasp of the subject. In essence, these important questions serve as a strategic tool for effective revision and preparation, contributing to overall proficiency in algebra for Class 6 students.

FAQs on Important Questions for CBSE Class 6 Maths Chapter 11 - Algebra

1. How to score good marks in Chapter 11 of NCERT Solutions for Class 6 Maths?

Ans: Chapter 11 is important in Class 6 Mathematics. Once students cover the core areas, it will always be easier for them to solve the exercise wise problems. Solving the problems related to this chapter will improve the analytical thinking and logical thinking skills of students. Choosing the right study material plays a vital role in scoring good marks in the Class 6 exam. The main aim of creating NCERT Solutions is to help students analyze the concepts which they are lagging behind and work on them for a better score.

2. Does the Vedantu’s NCERT Solutions for Class 6 Maths Chapter 11 provide accurate solutions as per the CBSE syllabus?

Ans: When it comes to Mathematics, accuracy is an important factor and regular practice is required to achieve that. As there are various study materials available online, selecting the correct one is always a challenging task. By opting for solutions that completely focus on the CBSE syllabus, students will be able to understand the concepts which are important from the exam perspective.

3. What are the terms of an expression Chapter 11 of NCERT Solutions for Class 6 Maths?

Ans: Parts of an expression that are formed separately first and then added or subtracted, are known as terms. In the given example, terms 2x and 5 are added to form the expression (2x+5).

4. How many exercises are there in Chapter 11 ‘Algebra’ of Class 6 Maths?

Ans: There are particularly five exercises in Chapter 11 ‘Algebra’ of Class 6 Maths. The exercises are enlisted as; 

Exercise 11.1- In this exercise there are ten questions. 

Exercise- 11.2- This exercise comprises five questions

Exercise 11.3- It includes six questions

Exercise 11.4- This exercise contains three long type answer type questions

Exercise 11.5- It includes five questions. 

To get answers to these textbook exercise questions, visit Vedantu’s official website (vedantu.com). One can find important questions on the Chapter 11 ‘Algebra’ of Class 6 Maths where you can download the solutions to textbook questions absolutely free of cost.

5. Will Vedantu help me to get decent scores in Chapter 11 ‘Algebra’ of Class 6 Maths?

Ans: Yes, Vedantu will help you to get decent scores in Chapter 11 ‘Algebra’ of Class 6 Maths. It is one of the best online learning platforms that enables students to understand educational concepts better. It provides numerous study materials like notes, a summary of the chapter, answers to the textbook questions mentioned in exercises, sample papers, video lectures, etc, so that you can understand the important concepts of the chapter clearly and score decent marks in your class tests as well as in your exams.

6. What are the benefits of practising important questions of Chapter 11 ‘Algebra’ of Class 6 Maths? 

Ans: It is important to go through the important questions of Chapter 11 ‘Algebra’ of Class 6 Maths as solving these questions will enable you to clarify your doubts and strengthen your concepts. If you practise them then you can test your skills and analyze your performance. This analysis will help you to know how much you have understood the chapter. With this, you can also detect your strong and weak topics. Practising questions of Chapter 11 ‘Algebra’ of Class 6 Maths will store concepts in your brain for the long term. And hence, you’ll be able to revise this chapter in less time. 

7. Is Chapter 11 ‘Algebra’ of Class 6 Maths easy? 

Ans: Chapter 11 ‘Algebra’ of Class 6 Maths is neither easy nor difficult. Its difficulty level is medium as some questions and examples of this chapter are easy to understand whereas you may find difficulty in understanding the rest of the questions. However, students who are good at their studies will comprehend concepts easily. While average and weak students have to struggle a bit to understand this chapter. But, if they practise this chapter continuously then they’ll find it easy. 

8. What concepts are students going to understand in Chapter 11 ‘Algebra’ of Class 6 Maths? 

Ans: The concepts that students are going to understand in Chapter 11 ‘Algebra’ of Class 6 Maths are as follows. 

Understanding patterns with matchsticks

Definition, facts, and examples of a variable

Understanding more examples of patterns with matchsticks

Other examples and applications of variables

Application of variables in common rules

Understanding regulations of geometry and arithmetic

Expressions with variables

Practical uses of expressions

Definition, facts and examples of an equation

 Solution of an equation 

Chapter wise Important Questions for CBSE Class 6 Maths

Cbse study materials.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Extra Questions for Class 6 Maths with Solutions

June 5, 2019 by Veerendra

Extra Questions for Class 6 Maths with Solutions Chapter Wise are given for the students so that they can get to know the answers to the questions in case they are not able to find it. It is important for all the students who are in Class 6 currently. Here we are providing the solutions based on all the chapters of NCERT Mathematics Class 6 Textbook for the students.

Extra Questions for Class 6 Maths

Here is the list of Extra Questions for Class 6 Maths with Solutions and Answers Chapter wise based on latest NCERT syllabus (http://ncert.nic.in/) prescribed by CBSE.

• Chapter 1 Knowing Our Numbers Class 6 Extra Questions
• Chapter 2 Whole Numbers Class 6 Extra Questions
• Chapter 3 Playing With Numbers Class 6 Extra Questions
• Chapter 4 Basic Geometrical Ideas Class 6 Extra Questions
• Chapter 5 Understanding Elementary Shape Class 6 Extra Questions
• Chapter 6 Integers Class 6 Extra Questions
• Chapter 7 Fractions Class 6 Extra Questions
• Chapter 8 Decimals Class 6 Extra Questions
• Chapter 9 Data Handling Class 6 Extra Questions
• Chapter 10 Mensuration Class 6 Extra Questions
• Chapter 11 Algebra Class 6 Extra Questions
• Chapter 12 Ratio and Proportion Class 6 Extra Questions
• Chapter 13 Symmetry Class 6 Extra Questions
• Chapter 14 Practical Geometry Class 6 Extra Questions

NCERT Solutions for Class 6 Maths

You can also refer NCERT Solutions for Class 6 Maths for your homework help.

Free Resources

NCERT Solutions

Quick Resources

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• Latest Chapter Wise Extra...

Latest Chapter Wise Extra Questions for Class 6 Mathematics

Latest Chapter Wise Extra Questions for Class 6 Mathematics  myCBSEguide has just released Chapter Wise Question Answers for class 6 Maths. These Extra Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around 4-5 set of solved Mathematics Extra questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Exam. We have taken care of every single concept given in  CBSE Class 6 Mathematics   syllabus and questions are framed as per the latest marking scheme and blue print issued by CBSE for Class 6. These chapter wise Practice Questions with complete solutions are available for download in  myCBSEguide   website and mobile app.

Chapter Wise Important Questions for Class 6 Mathematics

• Knowing our Numbers
• Whole Numbers
• Playing with Numbers
• Basic Geometrical Ideas
• Understanding Elementary Shapes
• Data handling
• Mensuration
• Ratio and Proportion
• Practical Geometry

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NCERT Solutions for Class 6 Maths Chapter 11 Algebra

NCERT Solutions for Class 6 Maths Chapter 11 Algebra with Practice Tests in updated format for session 2024-25 in Hindi and English Medium. As per the new rationalised syllabus and latest NCERT books for academic year 2024-25, there are only one exercise in chapter 11 of 6th mathematics.

Class 6 Maths Chapter 11 Solutions for CBSE Board

• Class 6 Maths Exercise 11.1 in English
• Class 6 Maths Exercise 11.1 in Hindi
• Class 6 Maths Chapter 11 NCERT Book
• Class 6th Maths Solutions Page
• Class 6 all Subjects Solutions

Class 6 Maths Chapter 11 Solutions for State Boards

• Class 6 Maths Chapter 11 Exercise 11.1
• Class 6 Maths Chapter 11 Exercise 11.2
• Class 6 Maths Chapter 11 Exercise 11.3
• Class 6 Maths Chapter 11 Exercise 11.4
• Class 6 Maths Chapter 11 Exercise 11.5

Class 6 Maths Chapter 11 Practice Test 6th Maths Chapter 11 Test 1 6th Maths Chapter 11 Test 2 6th Maths Chapter 11 Test 3 6th Maths Chapter 11 Test 4 6th Maths Chapter 11 Test 5 6th Maths Chapter 11 Test 6

Class VI Mathematics Exercise 11.1 in English Medium as well as Hindi Medium updated for new CBSE session. Solutions of Prashnavali 11.1 in Hindi Medium PDF file format to free download. Video solutions of each exercises are also given in Hindi Medium and English Medium. Download Books from NCERT (https://ncert.nic.in/) website for the new academic session and NCERT Solutions updated for 2024-25 based on these books. Class 6 solutions Offline Apps for all subjects are given to use it without internet.

Download NCERT Solutions for Class 6 Maths Chapter 11 Algebra in PDF format or use online without downloading. The exercise are updated for CBSE session 2024-25 using the latest NCERT Books. Contact us for any further help in education or educational contents.

In 6 Maths Chapter 11 Algebra, we will study about the terms related to algebra and algebraic expressions. As we know that the branch of mathematics in which we studied numbers is arithmetic and the branch of mathematics in which we studied shapes is geometry. Similarly, in the algebra section, we will study the following thinks. We will study how to use letters in maths. Use of letters will allow us to write rules and formulas in a general way. By using letters, we can talk about any number and not just a particular number.

Since letters stand for numbers, operations can be performed on them as on numbers. This leads to the study of algebraic expressions and their properties. Letters may stand for unknown quantities. By learning methods of determining unknowns, we develop powerful tools for solving puzzles and many problems from daily life. Note: Variables can take different values; they have no fixed value. But they are numbers. That is why as in the case of numbers, operations of addition, subtraction, multiplication and division can be done on them.

Important Questions on Class 6 Maths Chapter 11

Cadets are marching in a parade. there are 5 cadets in a row. what is the rule, which gives the number of cadets, given the number of rows.

Number of rows = n Cadets in each row = 5 Therefore, total number of cadets = 5n

If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes?

Number of boxes = b Number of mangoes in each box = 50 Therefore, total number of mangoes = 50b

The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students?

Number of students = x Number of pencils to each student = 5 Therefore, total number of pencils needed are = 5x

We are trying to provide help to all users at our level best. Gradually, we are updating the website also as per the suggestions, we have received. The changes made above is the result of suggestions and feedback given by users. Post your questions in Discussion Forum to get proper answers.

Which exercise of chapter 11 of Class 6 Maths has the highest number of questions?

According to new syllabus, in chapter 11 of 6th Grade Maths has only one exercise. This exercise (Ex 11.1) has 11 questions. So, exercise 11.1 has the highest number of questions (11 questions).

Is chapter 11 of class 6th Maths easy?

Chapter 11 of class 6th Maths is not easy and not difficult. It lies in the mid of simple and difficult because some examples and questions of this chapter are easy, and some are difficult. However, the difficulty level of any topic/chapter varies from student to student. So, Chapter 11 of class 6th Maths is easy or not depends on students also. Some students find it complex, some find it easy, and some find it in the middle of easy and complex.

Can students complete chapter 11 of 6th Maths in 6-8 days?

Yes, students can complete chapter 11 of grade 6th Maths in 6-7 days if they give 1-2 hours per day to this chapter. This time is an approximate time. This time depends on students also because no students can have the same working speed, efficiency, ability, etc.

Which topics are students going to learn in chapter 11 of grade 6th Maths?

The topics that students going to learn in chapter 11 of grade 6th Maths are: 1. Matchstick Patterns 2. The Idea of a Variable 3. More Matchstick Patterns

When algebra began accourding to chapter 11 of class 6th Maths?

It is said that algebra as a branch of Mathematics began about 1550 BC, i.e. more than 3500 years ago, when people in Egypt started using symbols to denote unknown numbers. The word ‘algebra’ is derived from the title of the book, ‘Aljebar w’al almugabalah’, written about 825AD by an Arab mathematician, Mohammed Ibn Al Khowarizmi of Baghdad.

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Chapter 12: ratio and proportion ».

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Algebra Questions and Problems for Grade 6

Grade 6 algebra questions and problems with detailed solutions are presented. Questions on expanding and simplifying expressions, solving linear equations, factoring expressions,....are included.

Questions and Problems

• List all like terms included in each of the expressions given below. A) 6 x + 5 + 12 x - 6 B) 2 x 2 - 4 + 9 x 2 + 9 C) x / 5 + x / 7 + 7 D) 0.2 x + 1.2 x + x / 2 + 5 E) 5 x - 8 + 7 x - 2 x 2 - 4 + 9 x 2 + 4 x 3 F) 5 a + 8 - 7 a b G) 5 a b+ 8 + 6 b a - a + 3 b Solution
• Evaluate each of the expressions for the given value(s) of the variable(s). A) 6 x + 5   for   x = 2 B) 12 x 2 + 5 x - 2   for   x = 1 C) 2( x + 7) + x   for   x = 0 D) 2 a + 3b - 7   for   a = 2 and b = 4 Solution
• Expand (if needed) and simplify each of the expressions below. A) 3 x + 5 x B) 2( x + 7) + x C) 2(x + 3) + 3(x + 5) + 3 D) 2 (a + 1) + 5b + 3(a + b) + 3 Solution
• Factor each of the expressions below. A) 3 x + 3 B) 8 x + 4 C) a x + 3 a D) (x +1) y + 4 (x + 1) E) x + 2 + b x + 2 b Solution
• Solve each of the equations below and check your answer. A) x + 5 = 8 B) 2 x = 4 C) x / 3 = 2 D) 0.2 x = 1 D) 3 x + 6 = 12 E) 3 (x + 2) + 2 = 8 Solution
• There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag? Solution
• Rewrite the expressions a × a × a - b × b using exponents. Solution
• The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle. Solution
• Two thirds of students in a class study math and the remaining eight students do not study math. What is the total number of students in this class? Solution
• A car travels 60 kilometers in one hour. At the same rate, what distance will be covered by this car in x hour? Solution
• Evaluate the expressions. A) 2 3 + 3 2 B) 0.1 3 C) 6 × (2 / 3) Solution
• A bag contains three red marbles; five blue marbles and seven green marbles. What is the ratio of blue marbles to the total number of marbles? Solution
• Solve the proportion : a / 3 = 5 / 18 Solution
• Which of the following ordered pairs is a solution to the equation 2 x + 3 y = 8? A) (0 , 0) B) (4 , 0) C) (1 , 2) Solution
• List all factors of the following numbers. A) 4 B) 12 C) 50 Solution
• Find the greatest common factor to each pair of the given numbers. A) 6 and 3 B) 18 and 24 C) 50 and 60 Solution
• Write the number " Six hundred seventy-two million two hundred fifty-nine" using the digits 0, 1, 2, ...9. Solution
• Which of the following expressions are equivalent? A) 2(x + 3) - 2 B) 2x + 4 C) 3(x + 3) - x - 5 Solution
• Find the lowest common multiple to each pair of the given numbers. A) 2 and 3 B) 7 and 14 C) 25 and 15 Solution
• Add and / or subtract and simplify A) 1 / 3 + 2 / 3 B) 2/5 - 1 / 7 Solution
• What is 2 / 3 of 21? Solution
• What is 40% of 1 / 4? Solution
• What is 20% of 50%? Solution
• How many seconds are there in one hour? Solution
• How many minutes are there in the month of January? Solution
• What is the location of each of the points: (-2 , 0) , (0 , 3) and (-2 , - 3) in a coordinate plane? Solution
• Order   7 / 5 , 12 / 10 , 21 / 20 and 111%   from the smallest to the largest. Solution

More References and links

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NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF Download

The NCERT Solutions for Class 6 Maths Chapter 11 Algebra provides detailed and explained Solutions for all Questions in the textbook. By referring to the Chapter 11 Algebra answers, students can understand each and every step; accordingly can form their own strategies to solve Questions in a proper and systematic way during further preparations. 

NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF

The NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF prove to be worthy as it provides a lot of Questions to solve; accordingly they can score well. Students can access the Chapter 11 Algebra Questions of Class 6 Maths through the Selfstudys website from their comfort zone. In the process of solving Chapter 11 Algebra Questions, students can build a strong and solid foundation for the chapter. 

Where can Students Find the NCERT Solutions for Class 6 Maths Chapter 11 Algebra?

Students can find the NCERT Solutions for Class 6 Maths Chapter 11 Algebra from the Selfstudys website; steps to download are clearly explained:

• Visit the Selfstudys website. 

• Bring the arrow towards the NCERT Books & Solutions which can be clearly seen in the navigation bar.

• Automatically a drop menu will appear, select NCERT Solutions from the list. 

• A new page will appear, select Class 6th from the list of classes. 
• Now click Maths from the list of subjects and select Chapter 11 Algebra from the list of chapters. 

Characteristics of NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF

The characteristics of NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF is the distinctive quality which each and every student needs to know; some of the important features are discussed below: 

• All the Exercises are Covered: In the NCERT Solutions for Class 6 Maths Chapter 11 Algebra revision, all the exercises of the textbook are covered so that students can get an idea about how to solve Questions. 
• Pictorial Representation is Given: Pictorial representations are often represented as icons, symbols, pictures, etc; these pictorial representations are given in the NCERT Solutions for Class 6 Maths Chapter 11 Algebra theory. 
• Formulas are Included: Formula is a group of signs, letters or numbers that are used to solve Chapter 11 Algebra Questions; these formulas are included in the Class 6 Maths NCERT Solutions. 
• All Topics are Covered: In the Class 6 NCERT Maths Solutions, all the topics of Chapter 11 Algebra are covered so that students can have a deep understanding of the concepts. 
• Available in the PDF: Students can easily access the Maths Chapter 11 Algebra Questions from the Class 6 NCERT Solutions as it is available in portable document format. 
• Step By Step Approach: The Questions of Chapter 11 Algebra in the Class 6 Maths NCERT Solutions are solved in a step by step approach so that students can understand each and every step. 

How Can NCERT Solutions for Class 6 Maths Chapter 11 Algebra Help Students?

The NCERT Solutions for Class 6 Maths Chapter 11 Algebra can help in several ways; those ways are discussed below: 

• Focuses on Fundamental Concepts: The Questions in the NCERT Solutions for Class 6 Maths Chapter 11 Algebra focuses on fundamental concepts; so by solving and referring to it students can have crystal clear knowledge about the concepts. 
• Improves Problem Solving Skills: Problem solving skills helps students determine the source of Chapter 11 Algebra Questions and to find an effective solution; to improve problem solving skills, students can refer to the NCERT Class 6 Maths Solutions.  
• Helps in Better Grades: By using the Class 6 Maths NCERT Solutions of Chapter 11 Algebra, students can develop their understanding of concepts and accordingly they can improve their grades. 
• Explained in a Simple Language: The Chapter 11 Algebra Questions of NCERT Class 6 Solutions are explained in a simple language so that students can understand a lot of complex Questions easily. 
• Designed According to the Exam Pattern: It is believed that the Chapter 11 Algebra Questions from the NCERT Class 6 Maths Solutions are designed according to the latest exam pattern. 
• Saves Time: The Chapter 11 Algebra Questions of Class 6 Maths NCERT Solutions are available ready made which saves most of time; otherwise students would be wasting precious time in searching for answers. 

A Comprehensive Guide to Solve Questions from NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF

To solve Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF in a comprehensive way, students need to follow the given steps; those steps are: 

• Read the Question Carefully: Before attempting the Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra, students need to read the question carefully so that they can understand what is being asked. 
• Understand the Concepts: Students should make sure that they need to understand Chapter 11 Algebra concepts which are related to Questions; then only they can solve Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra revision. 
• Use the Formula or Method: Depending upon the types of Questions in the NCERT Solutions for Class 6 Maths Chapter 11 Algebra theory, students need to use the required formula and method; through this students can score well. 
•  Look for Clues in the Questions: Students are advised to look for clues in the Chapter 11 Algebra Questions in the NCERT Class 6 Maths Solutions so that they can conclude the answers. 
• Check the Answers: After solving the Class 6 Maths Chapter 11 Algebra Questions from the NCERT Solutions, students need to check the answers with their own answers then they can get an idea about the mistakes. 
• Set Some Goals: To solve Chapter 11 Algebra Questions from the NCERT Class 6 Maths Solutions, students need to set some goals rather than just thinking to complete the Questions. 

How to Improve Confidence With the Help of NCERT Solutions for Class 6 Maths Chapter 11 Algebra? 

To improve confidence during the preparations, students can refer to the NCERT Solutions for Class 6 Maths Chapter 11 Algebra; some of the scenarios to improve confidence are discussed below: 

• Questions are Based on the Textbook: The Questions in the NCERT Solutions for Class 6 Maths Chapter 11 Algebra revision are based on the textbook. So by solving Chapter 11 Algebra Questions, students can gain confidence and score well in the test. 
• Enhances the Basic Knowledge: Once students start solving Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra theory it can enhance the basic knowledge and improve their confidence; which can be implemented while attempting the final exams. 
• Covers the Difficult Topics: It is obvious that the NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF covers difficult and complex topics; so by solving these Questions students can have a better understanding of concepts; accordingly they can improve their confidence level. 
• Students Will Learn How to Answer Questions: By solving Chapter 11 Algebra Questions from the NCERT Solutions of Class 6 Maths, students can learn to have different and creative approaches; this can help students to improve their confidence level. 
• Are Great for Revision: The NCERT Class 6 Maths Solutions of Chapter 11 Algebra are great for revising all topics and concepts; automatically they can improve their confidence level. 
• Provide Accurate Answers: The answers of Chapter 11 Algebra Questions of NCERT Class 6 Maths Solutions are accurate so by referring to it; students can improve their confidence level. 

What are the Difficulties Faced While Solving Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF?

Students may face difficulty while solving Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF; some of the difficulties are discussed below: 

• Lack of Understanding of the Concepts: If in case, students don’t have an understanding for the concepts; then they may face difficulty while solving Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra. 
• Difficulty in Calculations: If students are struggling with basic calculations then they can also face the same difficulty while solving Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra revision. 
• Confusions With the Formulas: If in case students are not familiar with the usage of right formulas and right method, then they can face difficulty in attempting Questions from the NCERT Solutions for Class 6 Maths Chapter 11 Algebra PDF. 
• Misreading of the Question: Students may face difficulty in solving Chapter 11 Algebra Questions from the NCERT Class 6 Maths Solutions if they have misunderstood the question or misinterpreted it. 
• Fear of Failure: It is obvious that students may be afraid of making mistakes; for them it may be very difficult in solving Chapter 11 Algebra Questions from the NCERT Class 6 Maths Solutions. This fear can lead to anxiety and stress level, this can be eliminated by completing the Class 6 Maths Chapter 11 Algebra concepts in a proper way. 
• Lack of Organisation: Students may face difficulty in solving Chapter 11 Algebra Questions from the NCERT Class 6 Maths Solutions if they are not organised in a proper way.

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What is Algebra? We all have been listening to this word from our childhood and somehow we are really afraid of this. But let me tell you Algebra is nothing but a study of mathematical symbols and here we are going to learn about the algebraic expressions and properties. And it’s so easy to understand that after learning you are going to love it. Let us learn more about Algebra.

Algebra is the study of mathematical symbols and the rules for manipulating these symbols to obtain the desired results.

• In the most basic way Algebra is the branch of mathematics in which we study about the use of letters in mathematics.
• Use of letters will allow us to write rules and formulas in a general way.

A variable is any symbol basically letter only, which has no definite value. In different cases the value of the variable changes.

• It is strictly to be remembered the value of the variable is never fixed.

Example 1 : Find the value of the variable p if p is natural number.

Solution : p is natural number which means it can take any value 1, 2, 3, 4, 5…………. And hence we cannot predict any fixed value of the variable p.

  Let us now understand why and how do we use variables

Suppose Aman has 5 pencils and Raju has 10 pencils. When Aman has 10 pencils, Raju has 15 pencils. When Aman has 15 pencils, Raju has 20 pencils and so on.

The above case can be written in an expression form as:

Pencils of Raju are always 5 more than that of Aman.

Pencils of Raju = Pencils of Aman + 5

If we assume the number of pencils of Aman to be x.

 We can write the expression and find out the pencil of Raju

Pencils of Raju = x + 5.

Here the variable x is the number of pencils of Aman and hence can take nay value from 1, 2, 3, 4, 5………….

This is the beauty of algebra in mathematics; it reduces the complexities of algebraic expressions.

Example 2 : Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows).

Solution : Let us assume that number of rows is n and hence n can take any value from 1, 2, 3, 4……….

If there are 5 cadets in 1 row,

Therefore if number of rows is n then number of cadets will be

Use of Variables

• Perimeter of Square

We all know that perimeter of Square = Sum of all sides

Perimeter = a + a + a + a = 4 a.

Here the variable a helps us to make a generalize rule or formula for finding the perimeter of a square with side a and here a is a variable so it can take any value from 1, 2, 3, 4……….

• Perimeter of Rectangle

We all know that perimeter = Sum of all sides

Perimeter = l + b + l + b = 2(l + b).

Here the variable l and b are the length and breadth of the rectangle.

Here, both l and b are variables. They take on values independent of each other that is the value one variable takes does not depend on what value the other variable has taken .

Rules from Arithmetic

1) Commutativity of Addition

Commutativity means to interchange and according to this property

a + b = b + a

Here a and b are the variables.

Example 3 : Examine the rule of commutativity of addition for two numbers 3 and 4.

Solution : Here we get that a =3 and b= 4

a + b = 3 + 4 = 7.

b +a = 4 + 3 = 7.

Since a + b = b + a

Hence the rule is verified.

2) Commutativity of Multiplication

  Using variables a and b as in the case of addition, we can express the commutativity of multiplication of two numbers as

a × b = b × a

• Distributivity of numbers

Let a , b and c be three variables, each of which can take any number. Then the following expression shows the distributive property:

a × (b + c) = a × b + a × c

Expression with Variables

At our initial stages we all have formed certain expressions with numbers for the addition, multiplication, subtraction or division. Here we will learn how to make and deal with the expressions with variables.

• We know that variables can take different values; they have no fixed value. But they are numbers. That is why as in the case of numbers, operations of addition, subtraction, multiplication and division can be done on them .

We can make unlimited expression with the help of variables and can perform any arithmetic operations in it and on assigning certain values to the variables we can find out the value of the expression also.

Example 4 : Form any expression using the variable x and find the value of the expression at x=5.

Solution : We can make any expression and let it be

4x – 15 = 0.

Hence on putting the value x = 5, get the value of expression as

4 x 5 – 15 = 20 – 15 = 5.

Any equation is a condition on a variable and is satisfied only for a definite value of the variable.

An equation has an equal sign (=) between its two sides. The equation says that the value of the left hand side (LHS) is equal to the value of the right hand side (RHS). If the LHS is not equal to the RHS, we do not get an equation.

For example the expression 2n is greater than 10, i.e. 2 n > 10 is not an equation, it is a statement.

Also, the expressions ( x – 8) > 15 or ( x + 3) < 11 are not equations, they are just statements.

Now, let us consider 9 – 2 = 7

There is an equal sign between the LHS and RHS and neither of the two sides contains a variable. Both contain numbers. We may call this a numerical equation. Usually, the word equation is used only for equations with one or more variables.

The value of the variable in an equation which satisfies the equation is called a solution to the equation.

Here we are going to use trial and error method to find the solution of an equation as shown in the example.

Example 5 : Find the solution of the equations:

• a) m - 5 =2
• b) p – 3 = 5

Solution : m - 5 = 2 is an equation in the variable m.

On randomly putting some values in m like m = 9, m = 7,

We get 9 – 5 = 4 which is not equal to 2.

On putting m = 7 we get 7 – 5 = 2 and hence we get that m = 7.

Similarly we can find p = 8 for the second equation.

Practice Questions on Algebra

Q1) Which of the following is an equation?

• a) 17 = x + 7 b) ( t – 7) > 5
• c) (7 × 3) – 19 = 8 d) 5 × 4 – 8 = 2 x

Q2) The length of a rectangular hall is 4 mete less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?

Q3) A bus travels at v km per hour. It is going from Delhi to Agra. After the bus has travelled 5 hours, Agra is still 50 km away. What is the distance from Delhi to Agra? Express it using v .

Q4) The side of an equilateral triangle is shown by l . Express the perimeter of the equilateral triangle using l .

• A variable takes on different values; its value is not fixed. The length of a square can have any value. It is a variable. But the number of angles of a triangle has a fixed value 3. It is not a variable.
• A variable allows us to express relations in any practical situation.
• An equation is a condition on a variable. It is expressed by saying that an expression with a variable is equal to a fixed number, e.g. x – 3 = 10.
• An equation has two sides, LHS and RHS, between them is the equal (=) sign.
• The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation. That definite value of the variable satisfies the equation. This value itself is called the solution of the equation.

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6th Class Mathematics Algebra Question Bank

Done algebra total questions - 40.

question_answer 1) \[{{a}^{2}}{{b}^{3}}\times 2a{{b}^{3}}\times 3{{a}^{2}}{{b}^{2}}\]is equal to

A) \[6{{a}^{5}}{{b}^{7}}\]                          done clear

B)  \[7{{a}^{2}}{{b}^{2}}\] done clear

C) \[8{{a}^{2}}{{b}^{2}}\]                          done clear

D)  \[6a\,\,{{b}^{2}}\] done clear

question_answer 2) 9 taken away from the sum of \[x\]and \[y\]is

A) \[x+y-9\]                      done clear

B) \[9-(x+y)\]     done clear

C) \[xy-4\]             done clear

D)  \[xy+4\] done clear

question_answer 3) The product of x and y is decreased by 4, is written as

A) \[4-xy\]             done clear

B)  \[x(y-4)\] done clear

C) \[xy-4\]             done clear

D)  \[~xy+4\] done clear

question_answer 4) The population of a dragonfly is x now. It becomes y times itself after one week. What will be its population after 2 weeks.

A)  \[{{y}^{2}}x\]                     done clear

B)  \[{{x}^{2}}{{y}^{2}}\] done clear

C) \[x{{y}^{3}}\]                                  done clear

D)  \[{{x}^{3}}y\] done clear

question_answer 5) The method of finding solution by trying out various values for the variable is called

A)  Error method                     done clear

B)  Trial and error method done clear

C)  Testing method                  done clear

D)  Checking method done clear

question_answer 6) If \[\frac{x}{2}-\frac{x}{3}=5,\]then\[x=\]?

A)  8                                 done clear

B)  16            done clear

C)  24                   done clear

D)  30 done clear

question_answer 7) If the sum of a number and its two fifth is 70. The number is

A)  20                               done clear

B)  50            done clear

C)  60                   done clear

D)  80 done clear

question_answer 8) \[0.3x+0.4=0.28x+1.16\] find \[x=?\]

A)  38                               done clear

B)  40             done clear

C)  60                   done clear

D)  70 done clear

question_answer 9) For which equation, is \[x=-3\] a solution?

A) \[3x-5=10\]     done clear

B) \[7=-10+x\] done clear

C) \[\frac{x}{3}+3=2\]              done clear

D) \[~3x=9\] done clear

question_answer 10) Find the value of \[2x-y+z,\] when \[x=1,\] \[y=-2,\] \[z=-1\]

A)  3                                 done clear

B)  5             done clear

C)  6                                 done clear

D)  7 done clear

A) \[100{}^\circ ,\,\,80{}^\circ \]          done clear

B) \[60{}^\circ ,\,\,\text{7}0{}^\circ \] done clear

C) \[40{}^\circ ,\,\,140{}^\circ \]                      done clear

D) \[50{}^\circ ,\,\,130{}^\circ \] done clear

question_answer 12) Simplify: \[15a-\left[ 8{{a}^{3}}+3{{a}^{2}}-\left\{ 8{{a}^{2}} \right. \right.\left. \left. \left( 4-2a-{{a}^{2}} \right)-5{{a}^{3}} \right\} \right]\]

A)  \[-12{{a}^{3}}+5{{a}^{2}}+19a-4\] done clear

B)  \[3{{a}^{2}}{{b}^{2}}+5a\] done clear

C) \[5{{a}^{2}}+6{{a}^{2}}+2a+3\]                 done clear

D) \[3{{x}^{2}}z-3yz+3xy+7z\] done clear

question_answer 13) What should be added to \[xy+yz+zx\] to get\[-xy-yz-zx\]?

A) \[-2xy-2yz-2zx\] done clear

B)  \[-3xy-yz-zx\] done clear

C) \[-3xy-3yz-3zx\] done clear

D) \[-3xy-yz\] done clear

question_answer 14) Solve\[\frac{12}{7}(x-5)=24+8x\]

A) \[\frac{-57}{11}\]                               done clear

B)  \[\frac{57}{11}\] done clear

C) \[\frac{67}{11}\]                     done clear

D)  \[\frac{-67}{11}\] done clear

question_answer 15) The sum of two consecutive even numbers is 86. Find the greatest number

A)  42 done clear

B)  44 done clear

C)  40 done clear

D)  45 done clear

question_answer 16) If \[(3x-4)(5x+7)=15{{x}^{2}}-ax-28a\] then\[a=\]?

A)  1 done clear

B)  \[-1\] done clear

C) \[-3\] done clear

D)  4 done clear

question_answer 17) If\[A=\frac{9{{x}^{4}}-3{{x}^{3}}-6{{x}^{2}}-9x}{3x},\] \[B=\frac{18{{x}^{4}}+12{{x}^{3}}+6{{x}^{2}}+9x}{3x}\]then \[B-A\] is

A)  \[3{{x}^{2}}-5{{x}^{2}}-4x+6\]            done clear

B)  \[3{{x}^{3}}+5{{x}^{2}}+4x+6\] done clear

C)  \[3{{x}^{3}}-5{{x}^{2}}-4x-6\]  done clear

D) \[3{{x}^{3}}+5{{x}^{2}}-4x-6\] done clear

question_answer 18) The value of\[\left( {{a}^{3}}-2{{a}^{2}}+4a-5 \right)-\left( {{a}^{2}}+2{{a}^{2}}-8a+5 \right)\]

A)  \[2{{a}^{3}}-4{{a}^{2}}+12a-10\] done clear

B)  \[2{{a}^{3}}-4{{a}^{2}}-12a+10\] done clear

C)  \[2{{a}^{3}}+4{{a}^{2}}+12a+10\] done clear

D)  \[2{{a}^{3}}-4{{a}^{2}}+12a+10\] done clear

question_answer 19) Additive inverse\[{{x}^{2}}-x+2\]

A) \[-{{x}^{2}}+x-2\]               done clear

B)  \[{{x}^{2}}+x+2\] done clear

C) \[-{{x}^{2}}-x+2\]               done clear

D)  \[-{{x}^{2}}+x+2\] done clear

question_answer 20) If \[x=2,\] \[y=3\] and \[z=-5\] then \[{{x}^{3}}+\]\[{{y}^{3}}+\]\[{{z}^{3}}=?\]

A)  90                               done clear

B)  \[-90\] done clear

C)  0                                 done clear

D)  \[-90xyz\] done clear

question_answer 21) If \[\left( x+\frac{1}{x} \right)=\frac{10}{3},\] then \[{{\left( x-\frac{1}{x} \right)}^{2}}\] is

A) \[{{\left( \frac{7}{3} \right)}^{2}}\]             done clear

B)  \[{{\left( \frac{8}{3} \right)}^{2}}\] done clear

C) \[{{\left( \frac{10}{3} \right)}^{2}}\]                       done clear

D)  \[{{\left( \frac{5}{3} \right)}^{2}}\] done clear

question_answer 22) If \[9{{x}^{2}}+48+p\] to be a perfect square , then the value of \[p\] is

A)  81                               done clear

B)  64 done clear

C)  36                               done clear

D)  16 done clear

question_answer 23) Solve:  \[\frac{3}{4}\left( 7x-1 \right)-\left( 2x-\frac{1-x}{2} \right)\] \[=x+\frac{3}{2}\] then \[x=?\]

A)  1                                 done clear

B)  2 done clear

C)  3                                 done clear

question_answer 24) Kajal's father is thrice as old as Kajal. After 12 year he will be just twice his daughter. Find their present ages.

A)  12 years, 36 years done clear

B)  15 years, 45 years done clear

C)  40 years, 20 years                   done clear

D)  10 years, 12 years done clear

question_answer 25) If \[4{{x}^{2}}+{{y}^{2}}=40\] and \[xy=6,\]find the value of \[2x+y=?\]

A) \[\pm 8\]                       done clear

B)  \[\pm 6\] done clear

C) \[\pm 7\]                       done clear

D) \[\pm 5\] done clear

question_answer 26) If \[x-\frac{1}{x}=9,\] find the value of\[a{{x}^{2}}+\frac{1}{{{x}^{2}}}=\]?

A)  83 done clear

B)  84 done clear

C)  85 done clear

D)  86 done clear

question_answer 27) A number is 56 greater then the average of its third, quarter and one twelfth. Find it.

A)  53 done clear

B)  72 done clear

question_answer 28) After 12 years I shall be 3 times as old as I was 4 years ago. Find my present age.

A)  12 years          done clear

B)  13 years        done clear

C)  14 years                      done clear

D)  18 years done clear

question_answer 29) Three prizes are to be distributed in a Mental Ability quiz contest. The value of the second prize is five-sixths the value of the first prize and the value of the third prize is four-fifths that of the second prize. If the total value of three prizes is Rs. 150, find the value of third prize.

A)  Rs. 40             done clear

B)  Rs. 50 done clear

C)  Rs. 60                         done clear

D)  Rs. 120 done clear

question_answer 30) For her mobile phone service, Sachi pays Rs. 145 per month and 75 paise for each extra minute. She talks over the allowed number of minutes in the monthly plan. She received a bill of Rs.178 last month. How many extra minutes did she use her phone beyond the allowed time.

A)  46 min                        done clear

B)  44 min   done clear

C)  55 min           done clear

D)  48 min done clear

question_answer 31) \[x+\frac{1}{x}=1\]then find \[{{x}^{30}}+{{x}^{27}}+{{x}^{36}}+{{x}^{33}}-1\]

A)  2 done clear

B)  6 done clear

C)  3 done clear

D)  8 done clear

question_answer 32) \[y+\frac{1}{y}=0\]then find\[{{y}^{1001}}+{{y}^{999}}+1\]

A)  1                                 done clear

B)  2              done clear

C)  3                                 done clear

D)  None of these done clear

question_answer 33) \[{{\left( a+b \right)}^{2}}-{{\left( a-b \right)}^{2}}+\left( a-b \right)\left( a+b \right)-4ab=?\]

A) \[{{a}^{2}}-{{b}^{2}}\]               done clear

B)  \[{{b}^{2}}+{{c}^{2}}\] done clear

C) \[{{c}^{2}}+{{d}^{2}}\]c                       done clear

D)  None done clear

question_answer 34) \[\frac{x}{1-x}+\] \[\frac{y}{1-y}+\] \[\frac{z}{1-z}=1\]then, find \[\frac{1}{1-x}+\]\[\frac{1}{1-y}+\]\[\frac{1}{1-z}=?\]

A)  1                                 done clear

question_answer 35) If \[\frac{1}{a+1}+\] \[\frac{2}{b+2}+\] \[\frac{1001}{c+1001}=1\] then find \[\frac{a}{a+1}+\] \[\frac{b}{b+2}+\] \[\frac{c}{c+1001}=?\]

A) \[-1\] done clear

C)  4                                 done clear

D)  \[-3\] done clear

question_answer 36) If \[x+\frac{1}{x}=1,\] then find\[{{x}^{6}}=?\]

A)  \[1\]                             done clear

B)  2             done clear

C)  3                                 done clear

question_answer 37) If \[a+\frac{4}{a}=4\] (Here\[a\ne 0\]) then find\[{{a}^{2}}+\frac{1}{{{a}^{3}}}=\]?

A)  \[2\frac{1}{8}\]                                  done clear

B)  \[3\frac{1}{8}\] done clear

C)  \[4\frac{1}{8}\]                      done clear

D) \[5\frac{1}{8}\] done clear

question_answer 38) If \[x=y=z\] then find \[\frac{{{\left( x+y+z \right)}^{2}}}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}\]

A)  9                                 done clear

B)  3 done clear

C)  4                                 done clear

D)  1 done clear

question_answer 39) If \[x+\frac{1}{x}=5\] (where\[x\ne 0\]) then find \[\frac{2x}{3{{x}^{2}}-5x+3}=?\]

A) \[\frac{1}{2}\]                         done clear

B)  \[\frac{1}{3}\] done clear

C) \[\frac{1}{4}\]                         done clear

D) \[\frac{1}{5}\] done clear

question_answer 40) If \[{{x}^{2}}+{{y}^{2}}+2y+4x+5=0\] then find\[\frac{x-y}{x+y}=?\]

A)  3                                 done clear

B)  \[-3\] done clear

C) \[\frac{1}{3}\]                         done clear

D)  \[\frac{-1}{3}\] done clear

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Case Study Questions for Class 6 Maths Chapter 1 Knowing Our Numbers

• Last modified on: 10 months ago
• Reading Time: 10 Minutes

Here in this article, we are providing case study questions for class 6 maths. Here you will find case study questions for Class 6 Maths Chapter 1 Chapter 1 Knowing Our Numbers.

Knowing Our Numbers Case Study Questions

Case Study Question 1:

The population of Delhi in 2017 was 19072564 and it increased to 25704625 in 2021.

(i) Write the population of 2021 in words. (a) two crore fifty seven lakh four thousand six hundred twenty five (b) twenty five lakh seventy thousand six hundred twenty five (c) two hundred fifty seven thousand four hundred twenty five. (d) twenty five crore seventy lakh forty six thousand and twenty five.

(ii) The successor of 19072564 is. (a) 19072563 (b) 19072565 (c) 29072564 (d) 19072574

(iii) What is the place value of ‘ 7 ‘ in 19072564 (a) 7 (b) 70000 (c) 7000 (d) 700

(iv) Write the population of 2017 in words according to International system of numeration.

(v) Write the population of 2021 in expanded form.

Maths Class 6 Chapter List

Latest chapter list (2023-24).

Chapter 1 Knowing Our Numbers Case Study Questions Chapter 2 Whole Numbers Case Study Questions Chapter 3 Playing with Numbers Case Study Questions Chapter 4 Basic Geometrical Ideas Case Study Questions Chapter 5 Understanding Elementary Shape Case Study Questions Chapter 6 Integers Case Study Questions Chapter 7 Fractions Case Study Questions Chapter 8 Decimals Case Study Questions Chapter 9 Data Handling Case Study Questions Chapter 10 Mensuration Case Study Questions Chapter 11 Algebra Case Study Questions Chapter 12 Ratio and Proportion Case Study Questions

Old Chapter List

Chapter 1 Knowing Our Numbers Chapter 2 Whole Numbers Chapter 3 Playing with Numbers Chapter 4 Basic Geometrical Ideas Chapter 5 Understanding Elementary Shape Chapter 6 Integers Chapter 7 Fractions Chapter 8 Decimals Chapter 9 Data Handling Chapter 10 Mensuration Chapter 11 Algebra Chapter 12 Ratio and Proportion Chapter 13 Symmetry Chapter 14 Practical Geometry

Deleted Chapter:

Tips for Answering Case Study Questions for Class 6 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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