Algebraic Expressions And Identities(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

ALGEBRAIC EXPRESSIONS AND IDENTITIES MCQs

Total Questions : 88 | Page 2 of 9 pages

Question 11. Classify the following polynomials as monomials, binomials, trinomials.

(i) 4 x^{2}

(i i) 5 x y^{2} + 6 x y z

(i i i) 5 x y z

(i v) a + b + c

(v) 5 x^{2} + 6 x + 25

(v i) x + y

[4 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 0.5Mark each
Monomials -:

4 x^{2}, 5 x y z

Binomials -:

5 x y^{2} + 6 x y z, x + y

Trinomials -:

a + b + c, 5 x^{2} + 6 x + 25

Question 12. Write the algebraic expression for:
(i) The volume of cube if its side(a) is reduced by 5.
(ii) Simple interest if time is reduced by 2 years and rate is increased by

5 %

.
(iii) Distance travelled if speed is increased by 5 units and time by 10 units. [3 MARKS]

Discuss Question

:
Concept: 1Mark each
(i) Volume

= (a - 5)^{3}

Here a is the initial length of the side of the cube.
(ii) Simple interest

= \frac{[P \times (R + 5) \times (T - 2)]}{100}

P=Principal Amount
R=rate
T=Time
(iii) Distance = (s+5) (t+10)
s=speed
t=time

Question 13. Sandeep wants to buy 5 chocolates of Rs 10 each. He has to pay Rs 20 for parking also. If the price of chocolate is increased by Rs x, he decides to buy y less chocolates and he has to pay Rs z less for the parking. Write the arithmatic expression of the money spent by Sandeep. [2 MARKS]

Discuss Question

:
Concept: 1Mark
Application: 1 Mark
Price of chocolate = (10 + x)
No. of chocolates = (5 – y)
Parking fees = (20 – z)
Total money spent = (10 + x) (5 – y) + (20 – z)

Question 14.

5 x \times (- 4 y z) \times 3 x z

= ___

60xyz
15x2z2−4yz
−60xyz
−60x2yz2

Discuss Question

Answer: Option D. -> −60x2yz2
:
D
On multiplying

x

with

x

, its power is raised to 2 i.e.,

x \times x = x^{2}

On multiplying

z

with

z

its power is also raised to 2 .
i.e.,

z \times z = z^{2}

Multiply all the coefficients to get

5 \times (- 4) \times 3 = - 60

Therefore, the answer is

- 60 x^{2} y z^{2}

Question 15. Simplify:

{(x y + y z)}^{2} - {(x y - y z)}^{2}

4xy2
4xy2z
4xz
−4xy2z

Discuss Question

Answer: Option B. -> 4xy2z
:
B
Usingthe identity,

{(a + b)}^{2} = a^{2} + b^{2} + 2 a b,

we get,

{(x y + y z)}^{2} = x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2} . . . (1)

Using the identity,

{(a - b)}^{2} = a^{2} + b^{2} - 2 a b

we get,

{(x y - y z)}^{2} = x^{2} y^{2} + y^{2} z^{2} - 2 x z y^{2} . . . (2)

Subtracting (2) from (1), we get

(x^{2} y^{2} + y^{2} z^{2} + 2 x z y^{2}) - (x^{2} y^{2} + y^{2} z^{2} - 2 x z y^{2})

= 2 x z y^{2} + 2 x z y^{2}

= 4 x y^{2} z

Question 16.

Find the sum of

(11 x^{2} - 8 x + 4) and (6 x^{2} + 7 x - 10) .

17x2−x−6
17x2−x+6
17x2+x−6
18x2−x−6

Discuss Question

Answer: Option A. -> 17x2−x−6
:
A

To find : Sum of (11 x^{2} - 8 x + 4) and (6 x^{2} + 7 x - 10)

On adding the like terms together, we get,

11 x^{2} - 8 x + 4

+ 6 x^{2} + 7 x - 10 - ---------------- -

17 x^{2} - x - 6

Question 17. What must be subtracted from

(4 x^{3} - 3 x + 5)

to get

(2 x^{2} - 3 x^{3} + 5 x - 2)

x3−2x2−8x+7
7x3+2x2−8x+7
7x3−2x2−8x+3
7x3−2x2−8x+7

Discuss Question

Answer: Option D. -> 7x3−2x2−8x+7
:
D

4 x^{3} - 3 x + 5

- 3 x^{3} + 5 x - 2 + 2 x^{2}

(+) (-) (+) (-)

________________________

7 x^{3} - 8 x + 7 - 2 x^{2}

= 7 x^{3} - 2 x^{2} - 8 x + 7

Question 18. When

7 x y + 5 y z - 3 z x,

4 y z + 9 z x - 4 y

and

- 3 x z + 5 x - 2 x y

are added, we get ___.

5xy+9yz+3zx+5x−4y
5xy+9yz+15zx+5x−4y
5xy+9yz−3zx+5x−4y
5xy+9yz+3zx−5x−4y

Discuss Question

Answer: Option A. -> 5xy+9yz+3zx+5x−4y
:
A

7 x y + 5 y z - 3 z x

4 y z + 9 z x - 4 y

- 2 x y - 3 x z + 5 x

________________________

5 x y + 9 y z + 3 z x - 4 y + 5 x

Question 19. The numerical factor of a term is known as

Expression
Coefficient
Variable
Equation

Discuss Question

Answer: Option B. -> Coefficient
:
B
The numerical factor of a term is known as coefficient.

Question 20. Simplify

(3 x^{2} + 5 y^{2}) (4 x y - 5 y)

(6x3y−15xy+20xy3−5y3)
(12x3y−5x2y+10xy3+25y3)
(12x3y−15x2y+20xy3−25y3)
(6x3y−15x2y+10xy3−5y3)

Discuss Question

Answer: Option C. -> (12x3y−15x2y+20xy3−25y3)
:
C
Given:

(3 x^{2} + 5 y^{2}) (4 x y - 5 y)

= 3 x^{2} (4 x y - 5 y) + 5 y^{2} (4 x y - 5 y)

= 12 x^{3} y - 15 x^{2} y + 20 x y^{3} - 25 y^{3}

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