# Free Algebra 02 Practice Test - 6th grade

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

A.

True

B.

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.

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)

A. 2r+5b=160
B. 3r+5b=160
C. r+5b=80
D. 2r5b=160

#### 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

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

A. True
B. False

#### SOLUTION

Solution : A

2x2, 3xy, 4xy2 and 5z are terms and they are combined using the operator "+”.
Therefore, it is an algebraic expression.

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

A. 8 years
B. 9 years
C. 27 years
D. 32 years

#### 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.

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

A. 2 × 8 + 9
B. 2x + 3
C. 215 + 8
D. 5x × 12

#### 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.

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

A. 3n+1
B. 3n+2
C. 3n-2
D. 3n

#### 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.

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 ________.

A. 2x
B. 2x + 5
C. 5x+2
D. 2x5

#### 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.

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

A. 3x+2y2x+7y
B. 4x+4y, 5x+y
C. 3x+7y, 6x2y
D. 3x+3y, 4x+7y

#### SOLUTION

Solution : B and C

3x+2y + 2x+7y =5x+9y 9x+5y
4x+4y + 5x+y =9x+5y =9x+5y
3x+7y + 6x2y =9x+5y =9x+5y
3x+3y + 4x+7y =7x+10y 9x+5y

If 3x2=13, then x is

A. 2
B. 3
C. 4
D. 5

#### SOLUTION

Solution : D

Given, 3x2=13
3x=13+2      [Transposing 2 to the other side]
3x=15
x=153   [Transposing 3 to the other side]
x=5

Solve the equation 5x312=1.

A. 2
B. 3
C. 4
D. -3

#### SOLUTION

Solution : B

5x312=15x3=1×125x3=125x=12+35x=15x=155x=3