# Free Algebraic Expressions Subjective Test 02 Practice Test - 7th grade

Simplify: 2(3y+6)  [1 MARK]

#### SOLUTION

Solution :

2(3y+6)=(2×3y)+(2×6)

=6y+(12)

=6y12

Which type of expression does (3x8y+4)(xy) give after simplification?  [2 MARKS]

#### SOLUTION

Solution :

Simplified equation: 1 Mark
Name of expression: 1 Mark

The given equation is:
(3x8y+4)(xy)

=3x8y+4x+y

=2x7y+4

where 2x, 7y and 4 are the three terms.
So, the simplified equation is a trinomial.

What will be the sum of the numerical coefficients in the below expression:  [2 MARKS]
4x2+12xy5y211y

#### SOLUTION

Solution : Numerical Coefficients: 1 Mark
Sum: 1 Mark

The numerical coefficient of 4x2 = 4
The numerical coefficient of 12xy = 12
The numerical coefficient of 5y2 = -5
The numerical coefficient of 11y = -11

Sum of the coefficients = 4 + 12 - 5 - 11 = 0
Hence, the sum of all the numerical coefficients in the above expression is zero.

Find the value of the polynomial a3+3a2b+2abb2 at a=2 and b=3.  [2 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark

The value of the polynomial a3+3a2b+2abb2 at  a = -2 and b = 3

a3+3a2b+2abb2
On substituting the values of a and b in the above expression we get:

=(2)3+3×(2)2×3+2×(2)×332

=8+36129=7

So, the value of the polynomial a3+3a2b+2abb2 at a=2 and b=3 is 7.

The number 5 is added to three times the product of two numbers, m, and n. What is the expression formed? What is the value of the expression if m is 4 and n is 5?  [2 MARKS]

#### SOLUTION

Solution :

Forming the expression: 1 Mark
Value of expression: 1 Mark

The product of two numbers, m, and n is
m×n.

Three times the product is 3mn.

Adding 5 to three times the product
= 5 + 3mn

The expression formed is 5 + 3mn

The value of the product at m = 4 and n = 5
=5+3×4×5=65

Hence, the value of the expression if m = 4 and n = 5 is 65.

(i) Will the value of 2x2+12x+3 for x = - 4 be greater than or less than 15?

(ii) If x2 is added to 2x2+12x+3 and 15 is subtracted from it then evaluate its value at x = -4?  [3 MARKS]

#### SOLUTION

Solution :

Each part: 1.5 Marks

(i) Value of the expression for x=4

2x2+12x+3

2(4)2+12(4)+3

2(16)48+3

3248+3=15

Hence, the value of expression 2x2+12x+3 at x=4 is lesser than 15.

(ii) As per question

x2 is added to 2x2+12x+3 and 15 is subtracted from it

So, the final expression is:

2x2+12x+3+x215

3x2+12x12

On putting x = -4 in the above equation we get:

3×(4)2+12×(4)12

=484812

=12

From the sum of 3x - y + 11 and  - y - 11,  subtract  3x – y – 11. Write the algebraic expression.  [3 MARKS]

#### SOLUTION

Solution : Forming the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark

According to question,

= (3x - y + 11) + (- y - 11) - (3x - y - 11)

= 3x - y + 11 - y - 11 - 3x + y + 11

= 3x - 3x - y - y + y + 11 - 11 + 11

= (3 - 3)x - (1 + 1 - 1)y + 11 + 11 -11

= 0x - y + 11

= -y +11
The required expression is -y +11.

Write the steps which should be followed to check if two terms are like or unlike.  Are x2y and xy like terms? [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

Steps to be followed to decide whether the given terms are like or not are as followed:
i) Ignore the numerical coefficients.
ii) Check the variables in the terms. They must be same otherwise they are unlike terms.
iii) Next, check the powers of each variable in the terms. They should be the same and if they are not then they are not like terms.

We have to check if x2 and xy are like terms.

The variables in both these expressions are x and y.

The power of y is equal in both the expressions.

But the power of x in the term x2y is 2, while in the term xy it is one.

The terms are not like.

Two adjacent sides of a rectangle are 5x23y2 and x22xy. Find its perimeter.  [3 MARKS]

#### SOLUTION

Solution :

Formula: 1 Mark
Steps: 1 Mark

Given that:
Two adjacent sides of a rectangle are 5x23y2 and x22xy.

The perimeter of a rectangle is given by:

Perimeter of a rectangle = 2 (Length + Breadth)

=2[(5x23y2)+(x22xy)]

=[10x26y2)+(2x24xy)]

=12x26y24xy

So, the perimeter of the rectangle is 12x26y24xy.

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

Find the expression represented by the above symbols.

#### SOLUTION

Solution :

Visualizing the question and forming equation: 2 Marks
Steps: 1 Mark

According to question:

=[(2x2+3y)+(5x2+3x)](8y2+3x2+2x+3y)

=[2x2+3y+5x2+3x](8y2+3x2+2x+3y)

=[7x2+3y+3x](8y2+3x2+2x+3y)

=[7x2+3y+3x8y23x22x3y

=4x2+x8y2

Hence, the expression represented by the above symbols is 4x2+x8y2.

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 2x 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]

#### SOLUTION

Solution :

Final number of leaves by both: 2 Mark
Steps: 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 2x leaves.

Sum of leaves collected by Sonu = 12 - 3 = 9

Sum of leaves collected by Raju =2x+x=3x

Algebraic expression for the total number leaves collected by both =9+3x

It is given that, both of them collected equal number of leaves,
So, 3x=9
Or x=9÷3=3
Hence, the value of x is 3.

tt214, 15t3+13+9t8t2, 12t21924t and 4t9t2+19t3.

If t=1 find the value of the expression.  [4 MARKS]

#### SOLUTION

Solution :

Forming equation: 1 Mark
Steps: 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

=(tt214)+(15t3+13+9t8t2)+(12t21924t)+(4t9t2+19t3)
=tt214+15t3+13+9t8t2+12t21924t+4t9t2+19t3
=(t+9t24t+4t)+(t28t2+12t29t2)+(14+1319)+(15t3+19t3)
=10t6t220+34t3

Hence, the required expression is  10t6t220+34t3.

Given that:
t=1
On substituting the values we get:
10t6t220+34t3
=10×(1)6×(1)220+34×(1)3
=1062034
=50

Remit's mother gave him Rs. 3xy2 and his father gave him Rs 5(xy2+2).Out of this total money, he spent Rs.(103xy2) on his birthday party. How much money is left with him? If x=2 and y=3 find the total amount left with him. [4 MARKS]

#### SOLUTION

Solution :

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

As per the question,

The amount of money given by Remits' motherRs 3xy2.

The amount of money given by Remits' father Rs 5(xy2+2).

Total amount =3xy2+5xy2+10=3xy2+5xy2+10=8xy2+10

Total amount Remit spent =103xy2

Amount of money left =(8xy2+10)(103xy2)=8xy2+1010+3xy2=Rs.11xy2

Now if  x=2 and y=3, then on substituting the values we get,
Amount of money left with
= 11×2××3×3 = Rs 198

Hence, the amount of money left with Remit is Rs 198.

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]

#### SOLUTION

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

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

2x+12=48

2x=4812

x=362=18

Then, the other number is x+12=18+12=30.

Therefore, the numbers are 18 and 30.
The product of these numbers =18×30=540.

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

#### SOLUTION

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

Let the numbers be x and x+5

Therefore, x+x+5=55

2x+5=55

2x=555

2x=50

x=502

x=25

Therefore, the requirednumbers are x=25,and x+5=30

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