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 6 of 9 pages

Question 51.

The area of a rectangle having length and width as $5 x y$ and $9 y$ respectively is $45 x y$ .

True
False
$5 q^{2} p$
$12 p q^{2}$

Discuss Question

Answer: Option B. -> False
:
B

Area of a rectangle = length × width

Area = $5 x y \times 9 y$

= $45 x y^{2}$

Hence the given statement is false.

Question 52.

Which of the following are like terms to $9 p q^{2}$ ?

$8 a b$
$5 b c$
$5 q^{2} p$
$12 p q^{2}$

Discuss Question

Answer: Option C. ->

5 q^{2} p

:
C and D

Like terms are terms with the same variables raised to the same power. Coefficients of like terms need not be the same.
$5 q^{2} p = 5 p q^{2}$ .
Hence $5 q^{2} p$ and $12 p q^{2}$ are both correct answers.

Question 53.

The product of $(t + s^{2})$ and $(t^{2} - s)$ is

$t^{3} + s^{2} t^{2} - s t - s^{3}$
$t^{3} + s^{2} t^{2} - s t - s^{2}$
$t^{3} + s^{2} t^{2} - 2 s t - s^{3}$
$t^{3} + t^{2} - s t - s^{3}$

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

:
A

$(t + s^{2}) (t^{2} - s) = [t (t^{2} - s) + s^{2} (t^{2} - s)]$
$= t^{3} - t s + s^{2} t^{2} - s^{3}$

$= t^{3} + s^{2} t^{2} - s t - s^{3}$

Question 54.

Add the following:
$a (a + b), b (b + c), c (a + c) a n d a^{2} + b^{2} + c^{2}$ [2 MARKS]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Concept: 1 Mark
Application: 1 Mark
$\Rightarrow a (a + b) + b (b + c) + c (a + c) + a^{2} + b^{2} + c^{2}$
$\Rightarrow a^{2} + a b + b^{2} + b c + c^{2} + c a + a^{2} + b^{2} + c^{2}$
$\Rightarrow 2 a^{2} + 2 b^{2} + 2 c^{2} + a b + b c + c a$

Question 55.

Subtract (ap+bq-cr) from (a+b+c)(p+q+r) . [1 MARK]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

:
Concept: 1 Mark
(a + b + c)(p + q + r) - (ap + bq - cr)
= (ap + aq + ar + bp + bq + br + cp + cq + cr) - (ap + bq - cr)
Now,
= ap + aq + ar + bp + bq + br + cp + cq + cr - ap - bq + cr
= aq + ar + bp + br + cp + cq + 2cr

Question 56.

Using the identities of algebraic expressions , find
$(i) 1002 \times 1003$
$(i i) 97 \times 103$ . [2 MARKS]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Application: 1 Mark each
$(i) 1002 \times 1003$
$= (1000 + 2) (1000 + 3) \Rightarrow 1000^{2} + (2 + 3) 1000 + (3) (2)$
$= 1000000 + 5000 + 6$
$= 1005006$
$(i i) 97 \times 103$
$= (100 - 3) (100 + 3)$
$= [{(100)}^{2} - {(3)}^{2}]$
$= [10000 - 9]$
$= 9991$

Question 57.

Find the volume of rectangular boxes with the following length, breadth and height respectively
$(i) (a^{2}, a^{3}, a^{4})$
$(i i) (x^{2} y^{2}, x z, z^{4})$ [2 MARKS]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Concept: 1 Mark
Application: 1 Mark
(i) Volume = $a^{2} \times a^{3} \times a^{4} = a^{9}$
(ii) Volume = $x^{2} y^{2} \times x z \times z^{4} = x^{3} y^{2} z^{5}$

Question 58.

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

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Concept: 1 Mark
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 59.

Simplify the following:
$(i) (1.5 x - 4 y) (1.5 x + 4 y + 3)$
$(i i) (x + y) (2 x + y) + (x + 2 y) (x - y)$
$(i i i) (a^{2} + 5) (b^{3} + 3) + 5$ [3 MARKS]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Application: 1 Mark each
$(i) (1.5 x - 4 y) (1.5 x + 4 y + 3)$
$2.25 x^{2} + 6 x y + 4.5 x - 6 x y - 16 y^{2} - 12 y$
$\Rightarrow 2.25 x^{2} - 16 y^{2} + 4.5 x - 12 y$
$(i i) (x + y) (2 x + y) + (x + 2 y) (x - y)$
$(2 x^{2} + x y + 2 x y + y^{2}) + (x^{2} + x y - 2 y^{2})$
$3 x^{2} + 4 x y - y^{2}$
$(i i i) (a^{2} + 5) (b^{3} + 3) + 5$
$a^{2} b^{3} + 3 a^{2} + 5 b^{3} + 15 + 5$
$\Rightarrow a^{2} b^{3} + 3 a^{2} + 5 b^{3} + 20$

Question 60.

Using the identities of algebraic expressions, Find :
$(i) 102^{2}$
$(i i) 53^{2}$
$(i i i) 1001^{2}$ [3 MARKS]

Discuss Question

Answer: Option A. ->

t^{3} + s^{2} t^{2} - s t - s^{3}

Application: 1 Mark each
Using the identity :
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
$(i) (102)^{2}$
$\Rightarrow (100 + 2)^{2}$
$\Rightarrow (100)^{2} + (2)^{2} + 2 (100) (2)$
$\Rightarrow 10000 + 4 + 400$
$\Rightarrow 10404$
$(i i) (53)^{2}$
$\Rightarrow (50 + 3)^{2}$
$\Rightarrow (50)^{2} + (3)^{2} + 2 (50) (3)$
$\Rightarrow 2500 + 9 + 300$
$\Rightarrow 2809$
$(i i i) (1001)^{2}$
$\Rightarrow (1000 + 1)^{2}$
$\Rightarrow (1000)^{2} + (1)^{2} + 2 (1000) (1)$
$\Rightarrow 1000000 + 1 + 2000$
$\Rightarrow 1002001$