The National Council of Education and Training sets the curriculum for all schools that follow the Central Board of Secondary Education (CBSE) across the nation. The important questions provided below will also make students familiar with the marking scheme and the difficulty level of the exam. The important questions for CBSE class 8 Maths are prepared by subject experts according to the latest syllabus of CBSE. Students are advised to solve these important questions which can make them more focused on their exam and also bring a sense of discipline and seriousness in their exam preparation.

The Central Board of Secondary Education (CBSE) is a prestigious educational board which comes under the Union Government of India. Here, you will get the clue that from where and how the questions are being framed from the chapter Algebraic Expressions and Identities for CBSE Class 8 Maths. These questions can provide students a chapter wise preparation strategy so that they can prepare for their exam more efficiently.

Creative questions were added in this question paper in order to enhance the student's knowledge and get the idea that how to answer strategic questions asked in the board exams. This question paper is designed based on the academic syllabus. Sample papers should be practiced in examination condition at home or school and also show it to your teachers for checking or compare with the answers provided.

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Questions:

Generic 2

5 x 2 = 10

Expand the following:
\(\left( \frac { 2x }{ 3 } +\frac { 2 }{ 3 } \right) \left( \frac { 2x }{ 3 } +\frac { 2a }{ 3 } \right) \)

Multiply:(x+ 2y)and (3x- 5x)

Find the value of the product
\(\left( -2{ a }^{ 2 }b \right) \times \left( -\frac { 2 }{ 3 } ab \right) \times 3for\ a=2and\ b=\frac { 1 }{ 2 } \)

Find the product of the following pairs of monomials.
-4p,7-pq

Add 7x² - 4x+ 5, -3X² + 2x- 1and 5x² - x+ 9.

Generic 3

5 x 3 = 15

Complete the table for area of a rectangle with given length and breadth

	Length	Breadth	Area
(i)	3x	5y	___
(ii)	9y	4y²	___
(iii)	4ab	5bc	___
(iv)	2l²m	3lm	___

Multiply (x - xy - x²y) by (y - xy - y²x).

Solve \(\left( \frac { 3 }{ 4 } x+\frac { 4 }{ 3 } y \right) \times \left( \frac { 3 }{ 4 } x+\frac { 3 }{ 4 } z \right) \)

Subtract -3p2+3pq+3px from 3p(-p-a-r)

10.

Subtract 4a - 7ab + 3b + 12 from 12a- 9ab+ 5b- 3.

Generic 5

2 x 5 = 10

11.

One day, Sahil went to playa cricket tournament (organised in a sports complex) along with his two friends Rahul and Sunil. Someone stole Sahil's bicycle but Rahul and Sunil helped him to buy a new one bicycle contributing rs(2x +80) and rs (8x + 20), respectively, If the bicycle costs rs. 2100,
(a) what were the amount given by Rahul and Sunil to Sahil?
(b) what are the values depicted by Rahul and Sunil here?

12.

Simplify each of the following expressions.
\(\frac { 1 }{ 2 } { a }^{ 2 }\left( { a }^{ 2 }-2 \right) +\frac { 1 }{ 4 } { a }^{ 2 }\left( 2a+{ a }^{ 2 } \right) -\frac { 3 }{ 8 } a\left( a+1 \right) \)

Multiple Choice Question

11 x 1 = 11

13.

The product of x², - x³, - x⁴ is

(a)

x⁹

(b)

x⁵

(c)

x⁷

(d)

x⁶

14.

The result of subtraction of 3x from -4x is

(a)

-7x

(b)

(c)

(d)

-x

15.

The coefficient of x²y in -15 x²y is

(a)

(b)

-15

(c)

(d)

16.

The like terms of the following are

(a)

2x², 9x²

(b)

y², xy

(c)

xy, 9x²

(d)

y², 9x²

17.

How many terms are there In the expression 4a - 7ab + 3b + 12?

(a)

(b)

(c)

(d)

18.

Which of the following is a monomial?

(a)

4x²

(b)

a + b

(c)

a+b+c

(d)

a+b+c+d.

19.

The expression 4xy + 7 is in

(a)

one variable

(b)

two variables

(c)

no variable

(d)

none of these

20.

Which of the following is the value of 5x²⁵-3x³²+2x-12 at x =1 ?

(a)

(b)

(c)

(d)

none of these

21.

What kind of polynomial is p q r?

(a)

monomial

(b)

binomial

(c)

trimonial

(d)

none of these

22.

Product of the monomials, -15p, -13q², pq is

(a)

-165p²q³

(b)

195p²q³

(c)

195p³q²

(d)

-195p³q²

23.

Which is the like term as 36 abc²?

(a)

\(2\times18\times a\times a \times b \times c \times\)

(b)

\(3\times13\times a \times b \times c \times c \times c\)

(c)

\(3 \times17\times a\times c \times b \times c\)

(d)

\(4 \times 5 \times b \times c \times c \times a \times a\)

Fill up / 1 Marks

1 x 1 = 1

24.

The product of two terms with like signs is a__________term

True or False

1 x 1 = 1

25.

Like term as 15a³b² is 25a³b²c.

(a)

True

(b)

False

1 Marks

2 x 1 = 2

26.

Why are 7x and 5x² not like?

27.

Find the value of \({ x }^{ 2 }-\frac { 1 }{ 5 } \) at x= -1

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Answers Key:

Generic 2

5 x 2 = 10

\(\frac { { 4x }^{ 2 } }{ 9 } +\frac { 4x+4ax }{ 9 } +\frac { 4a }{ 9 } \)

We have, (x + 2y) x (3x - 5x) = x x (3x - 5x) + 2y x (3x - 5x) = (x x 3x) - (x x 5x) + (2y x 3x) + (2y x (-5)x)
= 3x² - 5x² + 6xy - 10xy = - 2x² - 4xy

we have,-4p,7pq
(-4p) x (7pq) = {(-4)ｘ7} x (p x p x q)
= (-28) x (p²q) = - 28p²q

(7x² - 4x + 5)+(-3x² + 2x-1) + (5x² -x + 9)
=7x² - 3x² +5x² -4x + 2x - x + 5 - 1 + 9 =(7 - 3 + 5) x² + (-4 + 2 - 1)x + (5 - 1 + 9)
=9x² - 3x + 13

Generic 3

5 x 3 = 15

(i) 3x\(\times\)5y = 15xy
(ii) 9y\(\times\)4y²= 36y3
(iii) 4ab\(\times\)5bc= 20ab²c
(iv) 2l²m x 3lm² = 6l²m³

x³y³+ x²y³+ x³y²- x²y²- x²y - xy²+ xy

We know that, (x + a)(x + b) = x² + (a + b) x + ab,
\(\left( \frac { 3 }{ 4 } x+\frac { 4 }{ 3 } y \right) \left( \frac { 3 }{ 4 } x\frac { 3 }{ 4 } z \right) \)
\(=\left( \frac { 3 }{ 4 } x \right) ^{ 2 }+\left( \frac { 4 }{ 3 } y+\frac { 3 }{ 4 } z \right) \frac { 3 }{ 4 } x+\frac { 4 }{ 3 } y\times \frac { 3 }{ 4 } z\)
\(\left[ x=\frac { 3 }{ 4 } x,a=\frac { 4 }{ 3 } y,b=\frac { 3 }{ 4 } z \right] \)
\(=\frac { 9 }{ 16 } { x }^{ 2 }+\frac { 4 }{ 3 } y\times \frac { 3 }{ 4 } x+\frac { 3 }{ 4 } z\times \frac { 3 }{ 4 } x+yz\)
\(=\frac { 9 }{ 16 } { x }^{ 2 }+xy+\frac { 9 }{ 16 } zx+yz\)

Given, 3p(-p - a - r) = -(3p²+ 3ap + 3pr)
(-3p² - 3ap - 3pr) - (-3p² + 3pq + 3px)
= -3p² - 3ap - 3pr + 3p² - 3pq - 3px
= -3ap - 3pr - 3pq - 3px

10.

For subtraction, write the like terms one below the other, we get
12a -9ab +5b -3
+4a - 7ab + 3b + 12
(-) (+) (-) (-)
_________________
8a - 2ab + 2b -15
_________________
Thus, the required answer is 8a - 2ab + 2b - 15.

Generic 5

2 x 5 = 10

11.

(a) Rahul contributed =rs(2x + 80)
Sunil contributed = rs(8x + 20)
The total amount=rs[(2x+80)+(8x+20)]
=2100
2x + 8x + 80+ 20 = 2100
10x=2000
x=200
Thus, Rahul's contribution
= 2x + 80= 2 x 200 + 80
= 400 + 80= rs480
and Sunil's contributuib
= 8x + 20 = 8 x 200 + 20
= 1600 + 20 = rs1620
Thus, Rahul's and Sunil contributed rs480 and rs1620 respectively
(b) Rahul and Sunil are very cooperative by nature and they literally proved that "A friend in need is a friend indeed".

12.

\(\frac { 3 }{ 4 } { a }^{ 4 }+\frac { 1 }{ 2 } { a }^{ 3 }-\frac { 11 }{ 8 } { a }^{ 2 }-\frac { 3 }{ 8 } { a }\)

Multiple Choice Question

11 x 1 = 11

13.

Product = (x²) (- x³)(- x⁴) = x⁹

14.

- 4x - 3x = -7x.

15.

(b)
-15

16.

(a)
2x², 9x²

17.

4a, - 7ab, 3b, 12.

18.

4x² contains only one term.

19.

There are two variables x and y.

20.

21.

(a)
monomial

22.

(b)
195p²q³

23.

Fill up / 1 Marks

1 x 1 = 1

24.

()
(-a)\(\times \)(-a)²=a3 and (ab)\(\times \)(b²)=ab³

True or False

1 x 1 = 1

25.

(b)
False

1 Marks

2 x 1 = 2

26.

()
7x and 5x² are not like because they have different powers of the variable x.

27.

()
\(\frac { 4 }{ 5 } \)

Important Questions from Algebraic Expressions and Identities - 8th Maths

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