# Free Algebra 01 Practice Test - 6th grade

The branch of mathematics in which we study the use of letters to write rules and formulae in a general way is known as _______.

A.

Arithmetic

B.

Algebra

C.

Statistics

D.

Geometry

#### SOLUTION

Solution : B

Algebra is the branch of mathematics in which we study the use of letters to represent numbers/quantities.

For example, ram bought mangoes, but we don't know the number of mangoes he bought. So, let's say he bought x number of mangoes.

Here x is an alphabet but represents the number of mangoes.

All integers are constants not variables.

A. True
B. False

#### SOLUTION

Solution : A

All integers are constants since they have a fixed value which will not change with time.

Example: 5,6, -7,....

35xy + 45x + 5y2 + 25xyz is a

A.

Monomial

B.

Binomial

C.

Trinomial

D.

Polynomial

#### SOLUTION

Solution : D

35xy, 45x, 5y2 and 25xyz are unlike terms.

Therefore, there are 4 unlike terms. So it is a polynomial.

Rahul's dad's age is 4 more than 3 times of his present age. If Rahul is 11 years old, then his dad is _____.

A.

35 years old

B.

36 years old

C.

34 years old

D.

37 years old

#### SOLUTION

Solution : D

Rahul's dad's age is 4 more than 3 times of his age.
Let Rahul's present age be x years.
Then his dad's age = (3x + 4) years.
Given that Rahul's present age is 11, x = 11.

Hence, his dad's present age = (3 × 11) + 4 = 37 years.

If x3=9, then x is equal to

A.

9

B.

6

C.

12

D.

0

#### SOLUTION

Solution : C

Distance between Mumbai and Pune is (2y2+y+2). There are two routes to travel from Mumbai to Pune as shown in the figure. What is the difference between the distances of the two routes?

A. 32 units
B. 23 units
C. 57 units
D. 34 units

#### SOLUTION

Solution : D

When y=5
Distance=(2y2+y+2)=2×52+5+2=50+5+2=57 units
When y =3,
Distance =(2y2+y+2)=2×32+3+2=18+3+2=23 units
Required difference = 57 – 23 = 34 units.

Identify the pair(s) of like terms among the given options.

A.

3yx,8x2

B.

4xy,3yx

C.

4xy,8x2

D.

All terms are unlike

#### SOLUTION

Solution : B

Like terms are terms that contain the same variables with the same power.

Here, 3yx and 4xy are like terms,

3yx and 8x2 are unlike terms,

4xy and 8x2 are unlike terms.

The pattern formed by all odd numbers is correctly represented by the expression

A. 2n+1
B. 2(n+1)
C. 2n
D. None of above

#### SOLUTION

Solution : A

Even numbers are divisible by 2.
So, all even numbers can be represented by 2 × n; where n represents whole numbers 0, 1, 2....
All, even number are succeeded by an odd number.
2n+1 gives the pattern formed by odd numbers.
For n=0, 2n+1 = 2 × 0 + 1 = 1
For n=1, 2n+1 = 2 × 1 + 1 = 3
For n=2, 2n+1 = 2 × 2 + 5 = 5.
So, it is clear that A is the correct option.

Autos in Bangalore have a fixed charge of ₹ 25 for first 2 km and variable charge of ₹ 13 per additional km. If x represents the total distance travelled, then what is the expression for the total charge?

A. ₹ (13x + 1)
B. ₹ (13x - 1)
C. ₹ (25+13x)
D. 13x

#### SOLUTION

Solution : B

Total distance travelled = x km
So, the distance applicable for additional charge is (x2) km.

Total charge = Fixed charge + Additional charge
=13(x2)+25
=13x26+25
=(13x -1)

Expression for total charge is (13x -1).

Sum of the expressions 3x+4y and 2y+7x is _____.

A.

5x+11y

B.

11x+5y

C.

10x+6y

D.

6x+10y

#### SOLUTION

Solution : C

Adding the coefficients of x and y, we get

3x+4y   +
7x+2y
_______
10x+6y

3x+4y+2y+7x=10x+6y