Test: Algebraic Expressions And Identities- 1


10 Questions MCQ Test NCERT Mathematics for CAT Preparation | Test: Algebraic Expressions And Identities- 1


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Attempt Test: Algebraic Expressions And Identities- 1 | 10 questions in 10 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study NCERT Mathematics for CAT Preparation for Class 8 Exam | Download free PDF with solutions
QUESTION: 1

Which of the following is an expression?

Solution:

An algebraic expression include constants, variables and coefficients, so answer is 4x+7

QUESTION: 2

Which of the following is a binomial?

Solution:

A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial. Binomials are used in algebra.

For option a) there are three terms in the expression i.e. 7, 3x and 4

For option c) there are three terms as well i.e. 4x, y and 2.

For option d) there is only one term i.e. 3x

For option b) there are two terms i.e 2x and 7. Therefore it is a binomial.

Notice Bi means 2 so a binomial has 2 terms.

QUESTION: 3

Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xz + 5x – 2xy.

Solution:

Writing the three expressions in separate rows, with like terms one below the other, we have

7xy + 5yz    – 3zx

+        4yz   + 9zx        – 4y

+ –2xy        – 3zx  + 5x         

-----------------------------------------

= 5xy + 9yz + 3zx  + 5x – 4y

 

Thus, the sum of the expressions is 5xy + 9yz + 3zx + 5x – 4y. Note how the terms, – 4y

in the second expression and 5x in the third expression, are carried over as they are, since

they have no like terms in the other expressions.

QUESTION: 4

Expression that contains only one term is called a __________.

Solution:
QUESTION: 5

Simplify: (xy + yz)2− (xy − yz)2

Solution:

(xy+yz)²-(xy-yz)²

xy² +yz² +2.xy.yz -(xy²+yz²-2xy.yz)

(xy)² +(yz)² +2xy²z -[(xy)² +(yz)² -2xy²z

(xy)² +(yz)² +2xy²z -(xy²)-(yz)² + 2xy²z


Cancelled (xy)² +(yz)² and -(xy²)-(yz)².

2xy²z+ 2xy²z

=> 4xy²z


Hence, Value of (xy + yz)² – (xy – yz)² => 4xy²z


Note;-

(a+b)²-(a-b)² = 4ab

QUESTION: 6

Simplify(xy + yz)2− 2x2y2z. Find the value when x = -1, y = 1 and z = 2.

Solution:
QUESTION: 7

Using identity (x - a) (x + a) = x2 - a2 find 5− 42.

Solution:

x2 - a2 = ( x + a) (x - a) using this equation.

52 - 42 = ( 5 + 4) ( 5 - 4 )= ( 9 ) (1 )= 9 

QUESTION: 8

Using identity (x − a) (x + a) = x− a2 find 6− 52

Solution:

To find: 62 - 52:

Putting x = 6 and a = 5 in identity x2 - a2 = (x - a)(x+a);

⇒ 62- 52 = (6 - 5)(6 + 5) = 11.

QUESTION: 9

Terms are added to form ___________.

Solution:

Terms include variables,constants and coefficients which when added forms an expression.

QUESTION: 10

Which of the following is like term as 7xy?

Solution: 9xy is the like term of 7xy as ...9xy and 7xy contains the same variable (xy).. if we have to find like terms then.. we we should see that they both contains same variable ..numbers doesn't matter ..they can be sake itlr different.. therefore 9xy is the like term of 7xy and visa versa..
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