Algebraic Expressions(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

ALGEBRAIC EXPRESSIONS MCQs

Total Questions : 116 | Page 11 of 12 pages

Question 101.

Each symbol given below represents an algebraic expression: [4 MARKS]

Find the expression represented by the above symbols.

Discuss Question

Answer: Option A. ->
:

Visualizing the question and forming equation: 2 Marks
Steps: 1 Mark
Answer: 1 Mark
According to question:
$= [(2 x^{2} + 3 y) + (5 x^{2} + 3 x)] - (8 y^{2} + 3 x^{2} + 2 x + 3 y)$
$= [2 x^{2} + 3 y + 5 x^{2} + 3 x] - (8 y^{2} + 3 x^{2} + 2 x + 3 y)$
$= [7 x^{2} + 3 y + 3 x] - (8 y^{2} + 3 x^{2} + 2 x + 3 y)$
$= [7 x^{2} + 3 y + 3 x - 8 y^{2} - 3 x^{2} - 2 x - 3 y$
$= 4 x^{2} + x - 8 y^{2}$
Hence, the expression represented by the above symbols is $4 x^{2} + x - 8 y^{2}$ .

Question 102.

Sonu and Raju have to collect different kinds of leaves for a science project. They went to a park where Sonu collected 12 leaves and Raju collected $x$ leaves. After sometime Sonu lost 3 leaves and Raju collects $2 x$ leaves. Write an algebraic expression to find the total number of leaves collected by both of them. If they collected an equal number of leaves then find the value of $x$ . [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Final number of leaves by both: 2 Mark
Steps: 1 Mark
Answer: 1 mark
The first case, Sonu collected 12 leaves and Raju collected x leaves.
Sum of leaves collected by Sonu = 12
Sum of leaves collected by Raju = $x$
After some time, Sonu lost 3 leaves and Raju collected $2 x$ leaves.
Sum of leaves collected by Sonu = 12 - 3 = 9
Sum of leaves collected by Raju $= 2 x + x = 3 x$
Algebraic expression for the total number leaves collected by both $= 9 + 3 x$
It is given that, both of them collected equal number of leaves,
So, $3 x = 9$
Or $x = 9 \div 3 = 3$
Hence, the value of $x$ is $3$ .

Question 103.

Add
$t - t^{2} - 14$ , $15 t^{3} + 13 + 9 t - 8 t^{2}$ , $12 t^{2} - 19 - 24 t$ and $4 t - 9 t^{2} + 19 t^{3}$ .
If $t = - 1$ find the value of the expression. [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Forming equation: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Value: 1 Mark
Here while adding the algebraic expressions we need to know that we can only add the like terms.
Like terms are those terms which have the same algebraic factors.
Sum
$= (t - t^{2} - 14) + (15 t^{3} + 13 + 9 t - 8 t^{2}) + (12 t^{2} - 19 - 24 t) + (4 t - 9 t^{2} + 19 t^{3})$
$= t - t^{2} - 14 + 15 t^{3} + 13 + 9 t - 8 t^{2} + 12 t^{2} - 19 - 24 t + 4 t - 9 t^{2} + 19 t^{3}$
$= (t + 9 t - 24 t + 4 t) + (- t^{2} - 8 t^{2} + 12 t^{2} - 9 t^{2}) + (- 14 + 13 - 19) + (15 t^{3} + 19 t^{3})$
$= - 10 t - 6 t^{2} - 20 + 34 t^{3}$
Hence, the required expression is $- 10 t - 6 t^{2} - 20 + 34 t^{3}$ .
Given that:
$t = - 1$
On substituting the values we get:
$- 10 t - 6 t^{2} - 20 + 34 t^{3}$
$= - 10 \times (- 1) - 6 \times (- 1)^{2} - 20 + 34 \times (- 1)^{3}$
$= 10 - 6 - 20 - 34$
$= - 50$

Question 104.

Remit's mother gave him $R s . 3 x y^{2}$ and his father gave him $R s 5 (x y^{2} + 2)$ .Out of this total money, he spent $R s . (10 - 3 x y^{2})$ on his birthday party. How much money is left with him? If $x = 2 a n d y = 3$ find the total amount left with him. [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Forming the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark

As per the question,
The amount of money given by Remits' mother $R s 3 x y^{2}$ .
The amount of money given by Remits' father $R s 5 (x y^{2} + 2)$ .
Total amount $= 3 x y^{2} + 5 x y^{2} + 10 = 3 x y^{2} + 5 x y^{2} + 10 = 8 x y^{2} + 10$
Total amount Remit spent $= 10 - 3 x y^{2}$
Amount of money left $= (8 x y^{2} + 10) - (10 - 3 x y^{2}) = 8 x y^{2} + 10 - 10 + 3 x y^{2} = R s . 11 x y^{2}$
Now if $x = 2 a n d y = 3$ , then on substituting the values we get,
Amount of money left with
= $11 \times 2 \times \times 3 \times 3$ = $R s 198$
Hence, the amount of money left with Remit is $R s 198$ .

Question 105.

The sum of two consecutive numbers with a difference of 5 is 55. Find the numbers. [4 MARKS]

Discuss Question

Answer: Option A. ->
:
Forming the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Let the numbers be

x

and

x + 5

Therefore,

x + x + 5 = 55

\Rightarrow 2 x + 5 = 55

\Rightarrow 2 x = 55 - 5

\Rightarrow 2 x = 50

\Rightarrow x = \frac{50}{2}

\Rightarrow x = 25

Therefore, the requirednumbers are

x = 25, a n d x + 5 = 30

Therefore, the two numbers with a difference of 5 whose sum is 55 are 25 and 30.

Question 106.

A number is 12 more than the other if their sum is 48. What are the numbers? Also, find the product of these numbers. [4 MARKS]

Discuss Question

Answer: Option A. ->
:
Forming the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
Given that
A number is 12 more than the other number.
Let the number be

x

, then the other number will be

x + 12

.
As per question

x + (x + 12) = 48

\Rightarrow 2 x + 12 = 48

\Rightarrow 2 x = 48 - 12

\Rightarrow x = \frac{36}{2} = 18

Then, the other number is

x + 12 = 18 + 12 = 30

.
Therefore, the numbers are 18 and 30.
The product of these numbers

= 18 \times 30 = 540

Question 107.

The coefficient of x in '2x +5y' is __

Discuss Question

Answer: Option A. ->
:
Coefficient is defined as a number or symbol multiplied to a variable or an unknown quantity in an algebraic term. The coefficient of x in '2x + 5y' is 2.

Question 108.

On subtracting $(x + a)$ from $(4 x + 3 a)$ , the result obtained is_____.

$3 x + 2 a$
$9 x + 6 a$
$11 x + 2 a$
$3 x + 7 a$

Discuss Question

Answer: Option A. ->

3 x + 2 a

:
A

Arrange the polynomials with like terms one below the other. Change the sign of each term to be subtracted and then combine the like terms.

$\begin{matrix} 4 x + 3 a x + a (-) (-) 3 x + 2 a \end{matrix}$
$(4 x + 3 a) - (x + a) = 3 x + 2 a$

Question 109.

$25 x^{2} + 5 + 15$ is a binomial.

True
False

Discuss Question

Answer: Option B. -> False
:
B

A polynomial with two unlike terms is called a binomial and the one with three unlike terms is called a trinomial.
Hence, $25 x^{2} + 5 + 15$ is a trinomial.

Question 110.

The algebraic expression "x” does not contain any constant term.

True
False

Discuss Question

Answer: Option A. -> True
:
A

In the expression "x”, the variable is x and it does not have any constant term.
For example, in the expression 5 + 10y, the constant term is 5.
Hence, the statement is correct.