# Free Algebra 02 Practice Test - 6th grade

### Question 1

The equation 5t - 4 = 1 is satisfied when the value of t = 1.

True

False

#### SOLUTION

Solution :A

In order to check whether the above equation 5t-4 =1 is satisfied for t =1, we simply put 1 in place of t, So substituting t = 1 in the equation , we get

LHS = 5× (1) - 4 =1 and RHS = 1.

Since, LHS=RHS, t =1 satisfies the equation 5t-4 =1.

### Question 2

The cost of two red balls and five blue balls is ₹160. Then the correct equation for this situation among the given options is _______.

(r:price of one red ball)

(b:price of one blue ball)

#### SOLUTION

Solution :A

Let the cost of one Red ball be r.

Let the cost of one Blue ball be b.

So, the algebraic equation will be 2r+5b=₹160

### Question 3

(2x2+3xy+4xy2+5z) is an algebraic expression.

#### SOLUTION

Solution :A

2x^{2}, 3xy, 4xy^{2 }and 5z are terms and they are combined using the operator "+”.

Therefore, it is an algebraic expression.

### Question 4

Tulika is 3 times as old as her cousin. The sum of their ages is 36 years. How old is Tulika?

#### SOLUTION

Solution :C

Let Tulika’s cousin's age be x.

Then Tulika’s age will be 3x.

Given that the sum of their ages is 36.

∴x+3x=36

⇒4x=36

⇒x=364=9

⇒Tulika's age=3x=3×9=27 years.

### Question 5

Which of the following is/are algebraic expression/s?

#### SOLUTION

Solution :B and D

An algebraic expression should have numbers or constants, variables or unknowns (usually represented by alphabets) and mathematical operation like multiplication, addition etc.

Hence from the given option 2x+3 and 5x×12 are algebraic expressions.

### Question 6

Which of the given expressions represent/s the pattern 1, 4, 7, 10, 13..... ?

#### SOLUTION

Solution :A and C

On careful observation, you can see that each term in the pattern is one more than multiples of three.

Since the multiples of 3 can be represented by 3n, the pattern can be represented by 3n+1 (where n is 0, 1, 2...)

But each term can also be thought of two less than multiples of 3.

So, the pattern can also be represented by 3n-2 (where n is 1, 2, 3....)

Hence 3n + 1 and 3n -2 are the correct options.

### Question 7

Raju's age is 5 more than twice of Ram's age. If Ram's age is represented by x, then the expression which represents Raju's age is ________.

#### SOLUTION

Solution :B

Given Ram's age is x.

Twice of Ram's age is 2x.

∴ 5 more than twice Ram's age is 2x+5 which gives Raju's age.

### Question 8

Which of the pairs given in options will add up to give (9x+5y)?

#### SOLUTION

Solution :B and C

3x+2y + 2x+7y =5x+9y ≠9x+5y

4x+4y + 5x+y =9x+5y =9x+5y

3x+7y + 6x−2y =9x+5y =9x+5y

3x+3y + 4x+7y =7x+10y ≠9x+5y

### Question 9

If 3x−2=13, then x is

#### SOLUTION

Solution :D

Given, 3x−2=13

⇒3x=13+2 [Transposing 2 to the other side]

⇒3x=15

⇒x=153 [Transposing 3 to the other side]

⇒x=5

### Question 10

Solve the equation 5x−312=1.

#### SOLUTION

Solution :B

5x−312=1⇒5x−3=1×12⇒5x−3=12⇒5x=12+3⇒5x=15⇒x=155⇒x=3