# Free Algebraic Expressions 01 Practice Test - 7th grade

If 5 is added to three times the product of two numbers m and n, then the expression will be _______.

A.

5+mn

B.

5+3mn

C.

m+3n+5

D.

(mn+5)×3

#### SOLUTION

Solution : B

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators. According to the given question,
Three times the product of two numbers m and n is 3mn.
5 is added to three times the product of two numbers m and n.
The equation that represents this statement is 5+3mn.

What is the coefficient of term xy3 in the expression 5x3+10xy3 ?

A.

10x

B.

10

C.

-10

D.

-1

#### SOLUTION

Solution : B

The coefficient of term xy3 in the expression 5x3+10xy3 is 10.

A coefficient may be either a numerical factor (like 5, -3, 25...) or an algebraic factor (like x,y,x3y...) or a product of two or more factors (like 3xy,5x2z...) in a term of an algebraic expression.

The coefficient of xy3 in the expression 5x3+10xy3 is 10

Choose the option that contains like terms from the following terms.

12x, 12a, 25p, 25q, x and 12y.

A.

12x,x

B.

12a,12x

C.

25p,25q

D.

12a,25q

#### SOLUTION

Solution : A

The terms which have the same variable raised to the same power but may only differ in numerical coefficient are called like terms.

For example:

(i) 3m and 7m are like terms.

(ii)z and 32z are like terms.

So, among the given set of terms,
12x and x are like terms.

Observe the pattern given below. What is the general expression for this pattern?

A.

n(n+1)2

B.

n(n1)2

C.

n(n1)

D.

n2

#### SOLUTION

Solution : A So the general expression for this pattern is n(n+1)2, where n is the next term and n = 1, 2, 3, 4....

[Alternatively, eliminate the options to figure out the correct answer. This is a good method while attending competitive exams where time plays a crucial role.]

Find the value of expression:
2a - 2b - 10 + 4a + b, if a = 5 and b = 1.

A.

-1

B.

19

C.

-19

D.

20

#### SOLUTION

Solution : B

Simplify the expression:2a2b10+4a+b
=(2a+4a)+(2b+b)10=6ab10

Substituting  a=5 and b=1 in the above expression,

6ab10
=(6×5)110
=3011
=19

5ab3 + 22abc + 10bc is a ____________.

A.

monomial

B.

binomial

C.

trinomial

D.

term

#### SOLUTION

Solution : C

A trinomial is defined as a polynomial which contains three unlike terms. The expression 5ab3 + 22abc + 10bc has three unlike terms and hence, it is a trinomial.

2+3x is an algebraic expression.

A.

True

B.

False

#### SOLUTION

Solution : A

An algebraic expression is a mathematical phrase that contains numbers, variables (represented by lower case letters of the English alphabet) and operators (such as addition, subtraction, multiplication  and division).

Here are some examples of algebraic expressions:
a+1, ab,  3x, 43, etc.

Hence, 2+3x is an algebraic expression.

What should be the value of a, if the value of 2x2+6a5x+10 is 25, when x = 1?

A.

6

B.

3

C.

-3

D.

-6

#### SOLUTION

Solution : B

Given, 2x2+6a5x+10=25

Substituting the value of x = 1 in the above equation, we get,

2(1)2+6a5(1)+10=25

2 + 6a - 5 + 10 = 25

6a  + 7 = 25

6a = 25 - 7 = 18

a = 3

Find the sum of
2mn+11x and 22x+4mn.

A.

6mn+33x

B.

33mnx

C.

5mn+22x

D.

29mnx

#### SOLUTION

Solution : A

In order to find the sum of 2mn+11x and 22x+4mn, we need to group the like terms first (we can add only the like terms).

(2mn+11x)+(22x+4mn)
=2mn+11x+22x+4mn
=(2mn+4mn)+(11x+22x)
=6mn+33x

Hence, the sum is
6mn+33x.

An expression 5x2 5x + 5 is a binomial.

A.

True

B.

False

#### SOLUTION

Solution : B

An algebraic expression which contains two unlike terms is called a binomial. For example, 8 + x, xy - 4 are binomials.

An algebraic expression which contains three unlike terms is called trinomial. For example, 8 + x + y, xy - 4x + y, etc.

So, the expression, 5x2 + 5x + 5, is a trinomial as this expression contains three unlike terms, which are, 5x2, 5x and 5.

Hence the given statement is false.