Algebraic Expressions and Their Uses: MCQ test, Set 5

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

In $7 + y$ , the constant is
A $y$ B $7$ C $7 + y$ D $7y$

Answer and solution

Answer: (B) $7$

$7$ has a fixed value; $y$ can take various values.

So the constant is $7$ .
" $11$ less than the product of $x$ and $z$ " in symbolic form is
A $11 - xz$ B $xz - 11$ C $x + z - 11$ D $xz + 11$

Answer and solution

Answer: (B) $xz - 11$

The product of $x$ and $z$ is $xz$ ; $11$ less means subtract $11$ .

So it is $xz - 11$ .
The number of terms in $\displaystyle -7m^2 + \frac{5n^3}{4} + 7 + 3m^3$ is
A $5$ B $3$ C $6$ D $4$

Answer and solution

Answer: (D) $4$

Terms are separated by $+$ and $-$ signs.

The terms are $-7m^2$ , $\displaystyle \frac{5n^3}{4}$ , $7$ , $3m^3$ .

So there are $4$ terms.
$6mn^2$ written as a product of its factors is
A $6 \times m \times n \times n$ B $6 \times m \times n \times 2$ C $6 \times m \times n$ D $6 + m + n + n$

Answer and solution

Answer: (A) $6 \times m \times n \times n$

$n^2$ means $n$ multiplied $2$ times.

$6mn^2 = 6 \times m \times n \times n$
The co-efficient of $z^2$ in $\displaystyle \frac{5}{2}xy^3z^2$ is
A $xy^3$ B $\displaystyle \frac{5}{2}$ C $\displaystyle \frac{5}{2}xy^3$ D $\displaystyle -\frac{5}{2}xy^3$

Answer and solution

Answer: (C) $\displaystyle \frac{5}{2}xy^3$

$\displaystyle \frac{5}{2}xy^3z^2 = \left(\frac{5}{2}xy^3\right) \times z^2$

So the co-efficient of $z^2$ is $\displaystyle \frac{5}{2}xy^3$ .
Which of the following is a like term of $2b^3c$ ?
A $2cn$ B $2bc^3$ C $2b^3$ D $-5cb^3$

Answer and solution

Answer: (D) $-5cb^3$

Like terms have the same literal factors.

$-5cb^3$ has the literal factors $cb^3 = b^3c$ , the same as $2b^3c$ .
$x + x + x + x + x + x =$
A $5x$ B $6 + x$ C $x^6$ D $6x$

Answer and solution

Answer: (D) $6x$

$x$ is added $6$ times, so the sum is $6x$ .
$8m - 9m =$
A $-17m$ B $17m$ C $-m$ D $m$

Answer and solution

Answer: (C) $-m$

$8m - 9m$

$= (8 - 9)m$

$= -m$
Which of the following is a monomial?
A $\displaystyle \frac{7}{6}c$ B $6c^3 + 4c$ C $4b - 5bc^2 - 8c - 4b^2c$ D $-4b^2 - 2b^2c^2 - 9c^2$

Answer and solution

Answer: (A) $\displaystyle \frac{7}{6}c$

A monomial has one monomial.

$\displaystyle \frac{7}{6}c$ has one term.
Which of the following is NOT a polynomial?
A $\displaystyle \frac{2}{5}p^2 + p$ B $\displaystyle \frac{p}{2} - 5$ C $\sqrt{p} - 5$ D $5p^3$

Answer and solution

Answer: (C) $\sqrt{p} - 5$

$\displaystyle \sqrt{p} = p^{\frac{1}{2}}$ ; the power is not a whole number.

Fraction co-efficients such as $\displaystyle \frac{2}{5}$ are allowed in a polynomial.
The degree of $5a^3bm^3$ is
A $7$ B $3$ C $5$ D $6$

Answer and solution

Answer: (A) $7$

Add the powers of the variables:

$3 + 1 + 3 = 7$
The degree of $-6b^3 + 5b^3c^4 + 5bc^3$ is
A $14$ B $4$ C $3$ D $7$

Answer and solution

Answer: (D) $7$

Degrees of the terms are $3, 7, 4$ .

The greatest is $7$ .
The value of $8 - 4x$ when $x = -4$ is
A $-16$ B $24$ C $-8$ D $-24$

Answer and solution

Answer: (B) $24$

Put $x = -4$ :

$8 - 4(-4)$

$= 8 + 16$

$= 24$
The value of $4x - 7y - 2$ when $x = -5$ and $y = 5$ is
A $-57$ B $-55$ C $57$ D $-17$

Answer and solution

Answer: (A) $-57$

Put $x = -5$ and $y = 5$ :

$4(-5) - 7(5) - 2$

$= -20 - 35 - 2$

$= -57$
The sum of $6x^2 + z^2 + 8xz$ and $-7x^2 - 2z^2 - 6xz$ is
A $-13x^2 - z^2 + 2xz$ B $x^2 - z^2 + 2xz$ C $-x^2 - z^2 + 2xz$ D $13x^2 + 3z^2 + 14xz$

Answer and solution

Answer: (C) $-x^2 - z^2 + 2xz$

$6x^2 + z^2 + 8xz - 7x^2 - 2z^2 - 6xz$

$= (6 - 7)x^2 + (1 - 2)z^2 + (8 - 6)xz$

$= -x^2 - z^2 + 2xz$
The sum of $-7m + 6p$ , $6m - 6n$ and $2n - 8p$ is
A $-m + 14p - 8n$ B $m - 2p - 4n$ C $-13m - 2p - 4n$ D $-m - 2p - 4n$

Answer and solution

Answer: (D) $-m - 2p - 4n$

Add the like terms column by column:

$\begin{array}{rrr} -7m & +6p & \\ 6m & & -6n \\ & -8p & +2n \\ \hline -m & -2p & -4n \end{array}$
Subtract $-7y$ from $4y$ .
A $11y$ B $-3y$ C $3y$ D $-11y$

Answer and solution

Answer: (A) $11y$

$(4y) - (-7y)$

$= 4y + 7y$

$= (4 + 7)y$

$= 11y$
If $A = x^2 - 4x + 2$ and $B = 3x^2 + 5x - 9$ , then $3A - B =$
A $-7x - 3$ B $-17x + 15$ C $-2x^2 - 9x + 11$ D $6x^2 - 7x - 3$

Answer and solution

Answer: (B) $-17x + 15$

$3(x^2 - 4x + 2) - (3x^2 + 5x - 9)$

$= 3x^2 - 12x + 6 - 3x^2 - 5x + 9$

$= (3 - 3)x^2 + (-12 - 5)x + (6 + 9)$

$= -17x + 15$
Subtract $4b^2 - bc - 8$ from $2b^2 + 8$ .
A $6b^2 - bc$ B $2b^2 - bc - 16$ C $-2b^2 + 16 + bc$ D $-2b^2 - bc$

Answer and solution

Answer: (C) $-2b^2 + 16 + bc$

Change the signs of $4b^2 - bc - 8$ and add:

$\begin{array}{rrr} 2b^2 & +8 & \\ 4b^2 & -8 & -bc \\ (-) & (+) & (+) \\ \hline -2b^2 & +16 & +bc \end{array}$

$= -2b^2 + 16 + bc$
$4b^2c^2 \times 3b^3c^3 \times 2b^2c^2 =$
A $24b^7c^3$ B $24b^{12}c^{12}$ C $9b^7c^7$ D $24b^7c^7$

Answer and solution

Answer: (D) $24b^7c^7$

Multiply the numbers and add the powers of the same letters:

$= (4 \times 3 \times 2)(b^2 \times b^3 \times b^2)(c^2 \times c^3 \times c^2)$

$= 24b^7c^7$
$2m^2(-8m + 2 - 5mn) =$
A $-16m^2 + 4m^2 - 10m^3n$ B $-16m^3 + 4m^2 + 10m^3n$ C $-16m^3 + 4m^2 - 10m^3n$ D $-16m^3 + 2 - 5mn$

Answer and solution

Answer: (C) $-16m^3 + 4m^2 - 10m^3n$

Multiply $2m^2$ with every term inside the bracket:

$= (2m^2)(-8m) + (2m^2)(2) + (2m^2)(-5mn)$

$= -16m^3 + 4m^2 - 10m^3n$
$(3x - 2)(2x + 8) =$
A $6x^2 + 20x + 16$ B $6x^2 + 20x - 16$ C $6x^2 - 20x - 16$ D $6x^2 - 16$

Answer and solution

Answer: (B) $6x^2 + 20x - 16$

$(a + b)(c + d) = ac + ad + bc + bd$

$= 6x^2 + 24x - 4x - 16$

$= 6x^2 + 20x - 16$
$(2n - t)(4n - t) =$
A $8n^2 + t^2$ B $8n^2 - 6nt + t^2$ C $8n^2 + 6nt + t^2$ D $8n^2 - 6nt - t^2$

Answer and solution

Answer: (B) $8n^2 - 6nt + t^2$

$(a + b)(c + d) = ac + ad + bc + bd$

$= 8n^2 - 2nt - 4nt + t^2$

$= 8n^2 - 6nt + t^2$
$2m(3m + t) - 5t(3m + t) =$
A $6m^2 - 13mt - 5t^2$ B $6m^2 - 13mt + 5t^2$ C $6m^2 + 17mt + 5t^2$ D $-6m^2 + 13mt + 5t^2$

Answer and solution

Answer: (A) $6m^2 - 13mt - 5t^2$

Multiply out each bracket and add like terms:

$= 6m^2 + 2mt - 15mt - 5t^2$

$= 6m^2 + (2 - 15)mt - 5t^2$

$= 6m^2 - 13mt - 5t^2$
$2a + \{b - (6b + a)\} =$
A $3a - 5b$ B $3a + 7b$ C $a - 5b$ D $3a + 5b$

Answer and solution

Answer: (C) $a - 5b$

Remove the round brackets first, then the curly brackets:

$= 2a + \{b - 6b - a\}$

$= 2a + \{-5b - a\}$

$= 2a - 5b - a$

$= a - 5b$

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MCQ test, Set 5