Algebraic Expressions Test

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Algebraic Expressions Test - 1

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Question 1
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Which statement correctly represents the equation 2(x + 2) = x − 2?

A
Twice of x equals two more than x.

B
Two more than x equals two less than x.

C
The product of two and two more than x equals two less than x.

D
The product of two and two more than x equals two more than x.

Solution

The given equation is 2(x + 2) = x − 2.

The expression (x + 2) means two more than x.

Thus, 2(x + 2) means the product of two and two more than x.

The expression x − 2 means two less than x

Thus, 2(x + 2) = x − 2 means ‘the product of two and two more than x equals two less than x’.
Question 2
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If the width of a rectangular park is 9 m less than twice its length (l), then its width can be expressed as

A
(2l – 9) m

B
(2l + 9) m

C
(9l – 2) m

D
(9l + 2) m

Solution

Length of the rectangular park is l.

It is given that the width of the park is 9 m less than twice the length.

∴ Twice the length = 2 × l = 2l

⇒9 m less than twice the length = (2l– 9) m

Thus, the width of the park is (2l– 9) m.
Question 3
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Which of the following pair of terms are like terms?

A
x²y and 3xy²

B
x²y and 5y²x²

C
xyz and 7zxy

D
x³y and x²y

Solution

Terms having same algebraic factors are called like terms.

Terms having different algebraic factors are called unlike terms.

Let us consider the terms xyz and 7zxy.

Here, xyz has factors 1, x, y, and z.

7zxy has factors 7, x, y, and z.

Since xyz and 7zxy have the same algebraic factors x, y, and z, they are like terms.

Thus, the terms given in alternative C are like terms.
Question 4
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Which of the following polynomials is not cubic?

A
3y³ + 1

B
y³

C
y³ + 3y² + 3

D
3y + 3

Solution

A polynomial of degree 1 is known as linear polynomial.

A polynomial of degree 2 is known as quadratic polynomial.

A polynomial of degree 3 is known as cubic polynomial.

A polynomial of degree 0 is known as constant polynomial.

Number 0 is known as zero polynomial.

Since the degree of the polynomial 3y + 3 is 1, it is not a cubic polynomial. It is a linear polynomial.