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# Important Questions for CBSE Class 7 Maths Chapter 10 - Algebraic Expressions

Last updated date: 13th Sep 2024
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## CBSE Class 7 Maths Chapter 10 Important Questions - Algebraic Expressions - (FREE PDF Download)

These questions are prepared for students to develop a better understanding of the topics. They also help students in the preparation and practice for their upcoming examinations. Class 7 Algebraic expression important questions are prepared in a way to help the learners acquire what kind of problems they can expect to answer in their exams.

Vedantu provides important questions of mathematics class 7 chapter 10. The topic of Chapter 10 of Mathematics is Algebraic Expression. The chapter Algebraic expression class 7 covers the basic terminologies of algebra, forming expressions, and solving expressions. Register Online for NCERT Solutions Class 7 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions ,they can download Class 7 Maths NCERT Solutions to help you to revise complete syllabus and score more marks in your examinations.

## Important Questions for CBSE Class 7 Maths Chapter 10 - Free PDF Download

1. Write an expression for a number $\mathbf{7}$ is subtracted from sum of x and $\mathbf{4}$.

Ans: According to the given statement the expression that is developed is given as $\left( x+4 \right)-7$

2. The difference of numbers p and q is subtracted from its product. Give equation.

Ans: According to the given statement the expression that is developed is given as$pq-\left( p-q \right)$

3. $-12x$, $\frac{3}{4}x$ is an example for ___

Ans: As we can see that by dividing the first term by 16 we get the second term. So, we can say that the given two terms are like Term

Ans:  Adding the coefficients of the given terms will give the sum of two terms that is,

\begin{align} & -12pq \\ & \underline{+\text{ }5pq} \\ & -\text{ }7pq \\ \end{align}

5. Subtract 12xy from -5xy.

Ans: Subtracting the coefficients of the given terms will give the difference of two terms that is,

\begin{align} & -\text{ }5xy \\ & \underline{-12xy} \\ & -17xy \\ \end{align}

6. Add $x+y-5$, $y-x+5$, $x-y+5$

Ans: Adding the coefficients of the similar terms will give the sum of three terms that is,

\begin{align} & +x+y-5 \\ & -x+y+5 \\ & \underline{+x-y+5} \\ & x+y+5 \\ \end{align}

7. Add $3{{a}^{2}}{{b}^{2}}-4ab+5,8{{a}^{2}}{{b}^{2}}+12ab-9,15-6ab-5{{a}^{2}}{{b}^{2}}$.

Ans: Adding the coefficients of the similar terms will give the sum of three terms that is,

\begin{align} & \text{ 3}{{a}^{2}}{{b}^{2}}-4ab+5 \\ & +8{{a}^{2}}{{b}^{2}}+12ab-9 \\ & \underline{-5{{a}^{2}}{{b}^{2}}-6ab+15} \\ & \text{ }6{{a}^{2}}{{b}^{2}}+2ab+11 \\ \end{align}

8. Subtract $\text{-}{{\text{x}}^{\text{2}}}\text{+6xy}$ from $\text{8}{{\text{x}}^{\text{2}}}\text{-4xy+12}$.

Ans: Subtracting the coefficients of the similar terms will give the difference of two terms that is,

\begin{align} & +8{{x}^{2}}-4xy+12 \\ & \text{ }-{{x}^{2}}+6xy \\ & \underline{\text{ + - }} \\ & \text{ 9}{{x}^{2}}+10xy+12 \\ \end{align}

9. Subtract ${{a}^{2}}-4{{b}^{2}}+3ab-20$ from $2{{a}^{2}}+6{{b}^{2}}+7ab+12$.

Ans: Subtracting the coefficients of the similar terms will give the difference of two terms that is,

\begin{align} & 2{{a}^{2}}+6{{b}^{2}}+7ab+12 \\ & \text{ }{{a}^{2}}-4{{b}^{2}}+3ab-20 \\ & \underline{-\text{ + }-\text{ + }} \\ & {{a}^{2}}+10{{b}^{2}}+4ab+32 \\ \end{align}

10. Find the value of the given equation $4{{x}^{2}}-3x+12$, if $x=-3$

Ans: We are given the quadratic equation of $\text{x}$ as,

$4{{x}^{2}}-3x+12$

Substituting the value $x=-3$,

\begin{align} & =4{{\left( -3 \right)}^{2}}-3\left( -3 \right)+12 \\ & =4\times 9+9+12 \\ & =36+9+12 \\ & =57 \\ \end{align}

11. Simplify $3\left( 2x+1 \right)+4x+15$ when $x=-1$.

Ans: We are given the quadratic equation of $\text{x}$ as,

$3\left( 2x+1 \right)+4x+15$

Substituting $x=-1$,

\begin{align} & =3\left[ 2\left( -1 \right)+1 \right]+4\left( -1 \right)+15 \\ & =3\left( -2+1 \right)-4+15 \\ & =-3-4+15 \\ & =-7+15 \\ & =8 \\ \end{align}

12. Find the value of ${{a}^{2}}-{{b}^{2}}$ for $a=-2$ and $b=3$.

Ans: We are given the quadratic equation of $\text{a,b}$ as,

${{a}^{2}}-{{b}^{2}}$

Substituting $a=-2$ and $b=3$,

### Types of Algebraic Expression

Based on the number of terms;

• Monomial Expression - Expression that has only one term. Example: 9xy, 3x², 22y

• Binomial Expression - Expression with only two terms. Example: xyz + 8y², x²y² + 9xy

• Trinomial Expression - Expression with more than two terms. Example: 65xyz + 10x²y + 31y²z + 42z²

### General Formulae for Solving Sums on Algebraic Expression

1. (a + b)² = a²+ 2ab + b²

2. (a – b) ² = a² – 2ab + b²

3. (a + b) (a – b) = a²– b²

4. (a + b)³ = a³ + b³+ 3ab (a + b)

5. (a – b) ³ = a³ – b³– 3ab (a – b)

6. x³ + y³ = (x + y) (x² – xy + y²)

7. x³ – y³ = (x – y) (x² + xy + y²)

Algebraic expressions can be used to find out the perimeter of various figures.

If l is considered to be the length of each side, then the perimeter of

1. Square= 4l

2. Equilateral Triangle= 3l

3. Regular Pentagon= 5l

4. Regular Hexagon= 6l, and so on

Algebraic expressions can also be used to find out the area of various figures.

Square: area= l² (l= length of each side)

Rectangle: area= l*b (l is the length and b is the breadth)

Triangle: area= (b*h)/2 (b and h are the base and height of the triangle respectively)

Diagonal: Number of diagonals drawn  by choosing one vertex of a polygon = n-3 (n = number of sides of the polygon)

### Some Important Questions from Algebraic Expression

1. Subtract 12xy from -5xy. ( 1 mark )

Solution:

-5xy

-12xy

-17xy

2. Subtract - x² + 6xy from 8x² - 4xy + 12 (2 marks)

Solution:

8x² - 4xy + 12

- x² + 6xy

+       -

9x² - 10xy + 12

3. Simplify 3(2x+1) + 4x + 15 When x=1 (2 marks)

Solution:

3(2x+1) + 4x + 15

= 3[2(-1) +1] + 4(-1) + 15

= -3-4+15

= -7+15

= 8

4. Find the Value of

a) 3p² + 4q² - 5 when p=3 and q= -2

b) x³ - 3x²y + 2xy² + 8xy + 9 when x= -3 and y= 1. (3 marks)

Solution:

a) 3p² + 4q² - 5

= 3(3)² + 4(-2)² - 5

= 3*9 + 16 – 5

= 38

b) x³ - 3x²y + 2xy² + 8xy + 9

= (-3)³ – 3(-3)²(1)+ 2(-3)(1)²+ 8(-3)(1)+ 9

= -27 – 27 – 6 – 24 + 9

= - 75

5. What should be the Value of ‘p’, 3m² + m + p= 12 When m= 0. (3 marks)

Solution:

3m² + m + p= 12

=˃ 3(0) + 0 + p = 12 [m=0]

=˃ p= 12

### Why Should I Study Class 7 Mathematics Chapter 10 (Algebraic Expression) from Vedantu?

In Vedantu, the notes, important questions, and solutions are prepared by the leading educators who have gained expertise in this field over the years. Vedantu is amongst the most reputed and trustworthy online coaching institutions in India.

The study material of Algebraic Expression by Vedantu covers all the topics that could be asked for in the course of the examination. Start preparing for the exam from Vedantu's Important Questions Class 7 Mathematics chapter 10 without any second thought. The step-by-step approach to any solution allows students to clear up their major doubts. The study material and solutions are prepared in compliance with the existing CBSE guidelines.

Vedantu enrolls students of all merit. After you register in Vedantu, it becomes our responsibility to improve your mathematics core to solve the most challenging problems. The regular classes offered by Vedantu helps them build an in-depth understanding of the key concepts. Vedantu offers the student the freedom to learn the concepts at their own pace.

The notes are written after very careful study so that students can understand the topic well enough to see successful outcomes in their examinations. Vedantu allows the student to see studying as a source of fun and not a burden.

Hence, this article has provided an outline of Chapter 10 (Algebraic Expression) and covered all the basic terminologies in Algebra with a few examples of the method of solving algebraic expressions. Some important questions with solutions are also provided which one can easily download.

## Conclusion

Algebraic Expressions is an integral part of Class 7 Maths and plays a crucial role from an examination perspective. The important questions for Class 7 Maths, as discussed by NCERT, cover a wide range of topics within the subject. They also provide a concise guide to critical points and details related to the topic.

A solid understanding of each section of Class 7 Maths is fundamental as it forms the basis for higher-level studies. However, this section primarily focuses on important questions within the context of Class 7 Maths.

## FAQs on Important Questions for CBSE Class 7 Maths Chapter 10 - Algebraic Expressions

1. Is 8 an Algebraic Expression?

According to the definition of algebraic expression, an algebraic expression is formed with the help of operators i.e. addition, subtraction, multiplications, and divisions. As we can see there aren’t any operators used in 8, therefore 8 is not an algebraic expression.

2. How Can the Concepts of Algebra be Used in Geometry?

Geometry is that branch of mathematics that deals with the dimensions, sizes, shapes, and angles of a figure. While solving sums of geometry, we are often asked to find the perimeter and area of a certain figure. We can solve this easily with the help of algebra.  We can find the perimeter using the following formulae:

( l is the length of each side)

Square= 4l

Equilateral Triangle= 3l

Regular Pentagon= 5l

Regular Hexagon= 6l

We can also find the area of the figures using the following formulae:

Square: area= l² (l= length of each side)

Rectangle: area= l*b (l is the length and b is the breadth)

Triangle: area= (b*h)/2 (b and h are the base and height of the triangle respectively)

3. How is Algebra Useful in Our Day to Day Life?

Without our understanding, we have used algebra in many different aspects of our lives. When you go to a store to buy a bunch of goods, you prefer to use algebra out of unconsciousness.

When cooking, we often use algebra since it requires the measurement of many ingredients. It is also used to resolve business solutions as well as to solve certain financial problems. The principles and skills that algebra develops significantly contribute to our higher education.

4. Who Coined the Term "Algebra"? Who Invented Algebra?

The word algebra originated from the Arabic word al-jabr, which has its roots in the title of a 9th-century manuscript written by the mathematician Al-Khwarizmi.

Algebra was invented in the 9th century by Muhammad al-Khwarizmi, a mathematician and an astronomer. Muhammad al-Khwarizmi is also known as the "Father of Algebra".

His work in this field contributed to the dilemma of land distributions, distributing salaries, and rules of inheritance. His works on developing the concept of algorithms are quite remarkable. Therefore, he is also known as the "grandfather of computer science".

5. What are the main topics that are covered in Chapter 10 of Class 7 Maths?

NCERT Chapter 10 of Class 7 Maths mainly explains algebraic expressions and how they are formed by performing various operations of expressions and constants. The value of expression depends on the variables used in the equation. This Chapter covers different algebraic expressions such as term, coefficient, monomial, binomial, trinomial, polynomial and also provides certain rules of mathematics to use proper techniques for specific types of questions to get correct answers.

6. Is it necessary to learn all the questions provided in Chapter 10 of Class 7 Maths?

Yes, It is essential to learn all the provided questions in Chapter 10 of Class 7 Maths as all these questions are framed in a way that each of them deals with a unique type of problem, and no two questions are of the same type. So by learning and solving all the questions, one can understand the concept of the Chapter clearly and easily solve the problems in this Chapter. The important questions for Chapter 10 of Class 7 Maths are available free of cost on the Vedantu website and the Vedantu app.

7. What are algebraic expressions and how are they formed, according to Chapter 10 of Class 7 Maths?

Algebraic expressions are the result of variables and constants. When a variable and constant are processed with certain algebraic operations like subtraction, addition, division, and multiplication, it gives the equation an algebraic expression. Variables are unknown values that are not fixed and are usually denoted with alphabets like X, Y, and Z, whereas constants are the known values that are fixed, for example: 6, 25, 89, etc.

8. What are the terms of algebraic expression, according to Chapter 10 of Class 7 Maths?

An algebraic expression is a complete equation, and terms are the components that make that equation complete. If we consider an equation (2x + 10y), here the complete equation represents an expression, and components of this expression 2X and 10Y are the terms of expression if we further separate them into 2, X, 10, and Y now each of these become factors of the term. Factors combine to make terms, and terms combined make expressions.

9. How many exercises are there in NCERT Chapter 10 of Class 7 Maths?

In NCERT Chapter 10 of Class 7 Maths:

• Exercise 10.1 has seven questions.

• Exercise 10.2 has six questions.

• Exercise 10.3 has 10 questions

• Exercise 10.4 has two questions.

Each of the questions given in the above-mentioned exercises is framed in a specific way to address different problems. Students should solve and practice all the questions in order to get a clear understanding of the concept and solve the question in the chapter