The following is the list of competitive exams for Class 9: NSTSE: The National Level Science Talent Search Exam encourages students to reason critically while solving problems. NSTSE question papers are scientifically designed to test concepts underlying the curriculum. CBSE Maths Lab Manual Class 9 Chapters wise Download here in pdf format. These Maths Lab Manual may be freely downloadable and used as a reference book. Learning does not mean only gaining knowledge about facts and principles rather it is a path which is informed by scientific truths, verified experimentally.
NCERT Class 9 Maths Lab Manual – Verify the Algebraic Identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca
OBJECTIVE
To verify the algebraic identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca .
Materials Required
- Hardboard
- Coloured papers
- Adhesive
- White paper
- Scissors
- Geometry Box
Prerequisite Knowledge
- Square and its area.
- Rectangle and its area.
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Theory
- For square and its area refer to Activity 3.
- For rectangle and its area refer to Activity 3.
Procedure
- Take a hardboard of suitable size and paste a white paper on it.
- From a coloured paper, cut out a square of side a units, (see Fig. 6.1)
- Further, cut out a square of sided units (b < a)from another coloured paper, (see Fig. 6.2)
- Also, cut out a square of sidec units (c < b)from different coloured paper.(see Fig. 6.3)
- Cut out two rectangles of dimensions b x a from different coloured paper, (see Fig. 6.4)
- Also, cut out two rectangles of dimensions c x b from different coloured paper, (see Fig. 6.5)
- Now further, cut out two rectangles of dimensions c x a from another coloured paper, (see Fig. 6.6)
- Paste the squares and rectangles on the hardboard as shown in Fig. 6.7.
Demonstration
From Fig. 6.7, it is clear that from the arrangement of sqaures and rectangle, square PQRS of side (a + b+c) units is obtained.
Area of square PQRS = (a + b +c)² [∴ area of square = (side)²] … (i)
Also, area of square PQRS = Sum of the areas of all the squares and rectangles, which are
used to make the square PQRS = a² + b² + c² + ab + ab + bc +bc +ca+ca = (a² + b² + c² + 2ab + 2bc + 2ca) …(ii)
From Eqs. (i) and (ii), we have
(a + b+c)² =(a² +b² +c² + 2ab + 2bc + 2ca) Here, area is in square units.
From Fig. 6.7, it is clear that from the arrangement of sqaures and rectangle, square PQRS of side (a + b+c) units is obtained.
Area of square PQRS = (a + b +c)² [∴ area of square = (side)²] … (i)
Also, area of square PQRS = Sum of the areas of all the squares and rectangles, which are
used to make the square PQRS = a² + b² + c² + ab + ab + bc +bc +ca+ca = (a² + b² + c² + 2ab + 2bc + 2ca) …(ii)
From Eqs. (i) and (ii), we have
(a + b+c)² =(a² +b² +c² + 2ab + 2bc + 2ca) Here, area is in square units.
Observation
On actual measurement, we get
a = ……. , b = ……. , c = ……. ,
So, a² = ……. , b² = ……. , c² = ……. ,
ab = ……. , bc = ……. , ca = ……. ,
2ab = ……. , 2bc = ……. , 2ca = ……. ,
a + b+c = ……. ,
and (a + b+c)² = ……. ,
Hence, (a + b+c)² = a² + b² + c² + 2ab + 2bc +2ca
On actual measurement, we get
a = ……. , b = ……. , c = ……. ,
So, a² = ……. , b² = ……. , c² = ……. ,
ab = ……. , bc = ……. , ca = ……. ,
2ab = ……. , 2bc = ……. , 2ca = ……. ,
a + b+c = ……. ,
and (a + b+c)² = ……. ,
Hence, (a + b+c)² = a² + b² + c² + 2ab + 2bc +2ca
Result
Identity (a + b+c)²= a² +b² +c² +2ab + 2bc + 2ca has been verified.
Identity (a + b+c)²= a² +b² +c² +2ab + 2bc + 2ca has been verified.
Application
This identity may be used for
This identity may be used for
- calculating the square of a number which can be expressed as a sum of three convenient numbers.
- simplification and factorisation of algebraic expressions.
Viva Voce
Question 1:
Is the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca, holds for all real values of a, b and c?
Answer:
Yes
Question 1:
Is the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca, holds for all real values of a, b and c?
Answer:
Yes
Question 2:
Which identity should be used to expand (3x -√y + z)² ?
Answer:
(a+b+c)² = a²+b²+c² + 2ab + 2bc + 2ca . Adobe muse mac torrent.
Which identity should be used to expand (3x -√y + z)² ?
Answer:
(a+b+c)² = a²+b²+c² + 2ab + 2bc + 2ca . Adobe muse mac torrent.
Question 3:
What do you mean by a polynomial?
Answer:
An algebraic expression, in which the variables involved have only non-negative integral power, is called a polynomial.
What do you mean by a polynomial?
Answer:
An algebraic expression, in which the variables involved have only non-negative integral power, is called a polynomial.
Question 4:
What do you mean by zeroes of a polynomial?
Answer:
If p(x) is a polynomial, then a real number k is said to be zero of the polynomial p(x), If p(k) = 0.
What do you mean by zeroes of a polynomial?
Answer:
If p(x) is a polynomial, then a real number k is said to be zero of the polynomial p(x), If p(k) = 0.
Question 5:
What do you mean by a trinomial?
Answer:
A polynomial with three terms is called a trinomial.
What do you mean by a trinomial?
Answer:
A polynomial with three terms is called a trinomial.
Convert wad to iso file. Question 6:
Is the expansion of (x + y + z)², trinomial?
Answer:
No, because on expanding (x + y + z)², we get six terms.
Is the expansion of (x + y + z)², trinomial?
Answer:
No, because on expanding (x + y + z)², we get six terms.
Question 7:
Write the condition that the three variables in identity
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca should be written in two variables form (x + y)² =x² + y² + 2xy.
Answer:
Anyone of the variable in the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca should be zero. Why is my signature double spaced in outlook for mac download.
Write the condition that the three variables in identity
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca should be written in two variables form (x + y)² =x² + y² + 2xy.
Answer:
Anyone of the variable in the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca should be zero. Why is my signature double spaced in outlook for mac download.
Question 8:
If we take all the variables are equal in the identity
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca, then it will give us a cube of one variable. What is the name of the solid figure in which it gives out a cube of one variable?
Answer:
Cubic solid figure
If we take all the variables are equal in the identity
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca, then it will give us a cube of one variable. What is the name of the solid figure in which it gives out a cube of one variable?
Answer:
Cubic solid figure
Suggested Activity
Verify the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca by taking different values of a,b,c.
Verify the identity (a+b+c)² = a²+b²+c²+2ab+2bc+2ca by taking different values of a,b,c.
CBSE Maths Lab Manual Class 9 Chapters wise Download here in pdf format. These Maths Lab Manual may be freely downloadable and used as a reference book. Learning does not mean only gaining knowledge about facts and principles rather it is a path which is informed by scientific truths, verified experimentally. Keeping these facts in mind, CBSE Maths lab manual for Class 9 have been planned, evaluated under subject Improvement Activities. Check our CBSE Maths lab manual for Class 9. We are grateful to the teachers for their constant support provided in the preparation of this CBSE Maths Lab Manual.
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The laboratory is important for making the study complete, especially for a subject like Science and Maths. CBSE has included the practicals in secondary class intending to make students familiarised with the basic tools and techniques used in the labs. With the help of this, they can successfully perform the experiments listed in the CBSE Maths Lab Manual.
CBSE Maths Lab Manual for Class 9 PDF Features:
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By performing the experiments, students will know the concept in a better way as they can now view the changes happening in front of their eyes. Their basics will become solid as they will learn by doing things. By doing this activity they will also get generated their interest in the subject. Students will develop questioning skills and start studying from a scientific perspective. Here we have given all the necessary details that a Class 9 student should know about CBSE Maths Lab Manual. From CBSE practical to Maths Lab manual, project work, important questions and CBSE Maths lab kit manual, all the information is given in the elaborated form further in this page for Class 9 students.
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- Basic concepts of every experiment have been covered for better understanding. The matter is presented in the simple and lucid language under main-headings and sub-headings.
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