Algebraic Expressions and Their Uses: MCQ test, Set 1

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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.

Which of the following is a constant?
A $2a$ B $a$ C $a + 2$ D $-13$

Answer and solution

Answer: (D) $-13$

A constant has a fixed value.

$-13$ is a fixed number; the others contain the variable $a$ .
" $8$ divided by $m$ " in symbolic form is
A $\displaystyle \frac{8}{m}$ B $8 - m$ C $8m$ D $\displaystyle \frac{m}{8}$

Answer and solution

Answer: (A) $\displaystyle \frac{8}{m}$

$8$ divided by $m$ is written $\displaystyle \frac{8}{m}$ .

So it is $\displaystyle \frac{8}{m}$ .
The number of terms in $\displaystyle 6 - \frac{3b^3}{4} - 5a^3$ is
A $2$ B $3$ C $4$ D $5$

Answer and solution

Answer: (B) $3$

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

The terms are $6$ , $\displaystyle -\frac{3b^3}{4}$ , $-5a^3$ .

So there are $3$ terms.
$5mn^2$ written as a product of its factors is
A $5 \times m \times n \times 2$ B $5 + m + n + n$ C $5 \times m \times n \times n$ D $5 \times m \times n$

Answer and solution

Answer: (C) $5 \times m \times n \times n$

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

$5mn^2 = 5 \times m \times n \times n$
The co-efficient of $xz^2$ in $\displaystyle \frac{1}{6}xy^2z^2$ is
A $\displaystyle \frac{1}{6}y^2$ B $\displaystyle \frac{1}{6}$ C $\displaystyle -\frac{1}{6}y^2$ D $y^2$

Answer and solution

Answer: (A) $\displaystyle \frac{1}{6}y^2$

$\displaystyle \frac{1}{6}xy^2z^2 = \left(\frac{1}{6}y^2\right) \times xz^2$

So the co-efficient of $xz^2$ is $\displaystyle \frac{1}{6}y^2$ .
Which of the following is a like term of $-6a^2b$ ?
A $-6a^2$ B $9ba^2$ C $-6bt$ D $-6ab^2$

Answer and solution

Answer: (B) $9ba^2$

Like terms have the same literal factors.

$9ba^2$ has the literal factors $ba^2 = a^2b$ , the same as $-6a^2b$ .
$9m + 3 + 9m + 7 =$
A $18m^2 + 10$ B $28m$ C $18m + 10$ D $28$

Answer and solution

Answer: (C) $18m + 10$

$9m + 3 + 9m + 7$

$= (9 + 9)m + (3 + 7)$

$= 18m + 10$
$2y - 13y =$
A $-11y$ B $-15y$ C $15y$ D $11y$

Answer and solution

Answer: (A) $-11y$

$2y - 13y$

$= (2 - 13)y$

$= -11y$
Which of the following is a trinomial?
A $5b^2c^2 + 4bc^2$ B $7b^2c^2 - 9c^2 + 3b^2c - 2c$ C $-4c^2 + 3b^2 - 4b^3$ D $2bc$

Answer and solution

Answer: (C) $-4c^2 + 3b^2 - 4b^3$

A trinomial has three monomials.

$-4c^2 + 3b^2 - 4b^3$ has three terms.
Which of the following is a multinomial but not a polynomial?
A $\displaystyle 3 + \frac{4}{t}$ B $\displaystyle \frac{4}{3}t + 1$ C $4t^2 + 3$ D $t^2 - 3t + 4$

Answer and solution

Answer: (A) $\displaystyle 3 + \frac{4}{t}$

$\displaystyle \frac{4}{t} = 4t^{-1}$ has the power $-1$ , so it is not a monomial.

So $\displaystyle 3 + \frac{4}{t}$ is a multinomial but not a polynomial.
The degree of $-2p^2q^5t^3$ is
A $3$ B $2$ C $5$ D $10$

Answer and solution

Answer: (D) $10$

Add the powers of the variables:

$2 + 5 + 3 = 10$
The degree of $3m^2 + 4m^3n^3 - 2m^5n^3$ is
A $5$ B $8$ C $3$ D $2$

Answer and solution

Answer: (B) $8$

Degrees of the terms are $2, 6, 8$ .

The greatest is $8$ .
The value of $4b - 2c - 5$ when $b = -5$ and $c = -2$ is
A $19$ B $21$ C $-16$ D $-21$

Answer and solution

Answer: (D) $-21$

Put $b = -5$ and $c = -2$ :

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

$= -20 + 4 - 5$

$= -21$
The value of $x^2 + 3xz - 2z^2$ when $x = 2$ and $z = -1$ is
A $0$ B $8$ C $2$ D $-4$

Answer and solution

Answer: (D) $-4$

Put $x = 2$ and $z = -1$ :

$(2)^2 + 3(2)(-1) - 2(-1)^2$

$= 4 - 6 - 2$

$= -4$
The sum of $3n^2 - 3t^2 + 5nt$ and $7n^2 + 6t^2 + 8nt$ is
A $-4n^2 - 9t^2 - 3nt$ B $10n^2 + 3t^2 + 13nt$ C $10n^2 - 3t^2 + 13nt$ D $10n^2 + 9t^2 + 13nt$

Answer and solution

Answer: (B) $10n^2 + 3t^2 + 13nt$

$3n^2 - 3t^2 + 5nt + 7n^2 + 6t^2 + 8nt$

$= (3 + 7)n^2 + (-3 + 6)t^2 + (5 + 8)nt$

$= 10n^2 + 3t^2 + 13nt$
The sum of $7a - 5b$ , $3b - 9m$ and $8a + 5m$ is
A $15a + 2b - 4m$ B $-a - 2b - 14m$ C $15a - 8b - 4m$ D $15a - 2b - 4m$

Answer and solution

Answer: (D) $15a - 2b - 4m$

Add the like terms column by column:

$\begin{array}{rrr} 7a & -5b & \\ & 3b & -9m \\ 8a & & +5m \\ \hline 15a & -2b & -4m \end{array}$
Subtract $-9m$ from $8m$ .
A $-m$ B $-17m$ C $m$ D $17m$

Answer and solution

Answer: (D) $17m$

$(8m) - (-9m)$

$= 8m + 9m$

$= (8 + 9)m$

$= 17m$
If $A = 6p^2 - 4p + 5$ and $B = 2p^2 + 7p + 9$ , then $A - 2B =$
A $2p^2 - 11p - 4$ B $2p^2 - 18p - 13$ C $10p^2 + 10p + 23$ D $2p^2 + 10p + 23$

Answer and solution

Answer: (B) $2p^2 - 18p - 13$

$(6p^2 - 4p + 5) - 2(2p^2 + 7p + 9)$

$= 6p^2 - 4p + 5 - 4p^2 - 14p - 18$

$= (6 - 4)p^2 + (-4 - 14)p + (5 - 18)$

$= 2p^2 - 18p - 13$
Subtract $5a^2 - 2ac - 7$ from $6a^2 - 1$ .
A $11a^2 - 8 - 2ac$ B $a^2 - 8 - 2ac$ C $a^2 + 6 + 2ac$ D $-a^2 - 2ac - 6$

Answer and solution

Answer: (C) $a^2 + 6 + 2ac$

Change the signs of $5a^2 - 2ac - 7$ and add:

$\begin{array}{rrr} 6a^2 & -1 & \\ 5a^2 & -7 & -2ac \\ (-) & (+) & (+) \\ \hline a^2 & +6 & +2ac \end{array}$

$= a^2 + 6 + 2ac$
$5p^3q \times 2p^3q \times 3p^2q =$
A $10p^8q^3$ B $30p^8q^3$ C $30p^{18}q$ D $30p^8q$

Answer and solution

Answer: (B) $30p^8q^3$

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

$= (5 \times 2 \times 3)(p^3 \times p^3 \times p^2)(q \times q \times q)$

$= 30p^8q^3$
$-4m^2(7mp + 3m^2n - 4m) =$
A $-28m^3p - 12m^4n - 16m^3$ B $-28m^3p + 3m^2n - 4m$ C $-28m^2p - 12m^4n + 16m^3$ D $-28m^3p - 12m^4n + 16m^3$

Answer and solution

Answer: (D) $-28m^3p - 12m^4n + 16m^3$

Multiply $-4m^2$ with every term inside the bracket:

$= (-4m^2)(7mp) + (-4m^2)(3m^2n) + (-4m^2)(-4m)$

$= -28m^3p - 12m^4n + 16m^3$
$(4q - 8)(2q - 6) =$
A $8q^2 + 48$ B $8q^2 - 40q - 48$ C $8q^2 - 40q + 48$ D $8q^2 + 40q + 48$

Answer and solution

Answer: (C) $8q^2 - 40q + 48$

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

$= 8q^2 - 24q - 16q + 48$

$= 8q^2 - 40q + 48$
$(4y + z)(y - z) =$
A $4y^2 - z^2$ B $4y^2 - 3yz + z^2$ C $4y^2 - 3yz - z^2$ D $4y^2 + 3yz - z^2$

Answer and solution

Answer: (C) $4y^2 - 3yz - z^2$

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

$= 4y^2 - 4yz + yz - z^2$

$= 4y^2 - 3yz - z^2$
$6n(4n + t) - 4t(3n + t) =$
A $24n^2 - 6nt - 4t^2$ B $24n^2 + 18nt + 4t^2$ C $-24n^2 + 6nt + 4t^2$ D $24n^2 - 6nt + 4t^2$

Answer and solution

Answer: (A) $24n^2 - 6nt - 4t^2$

Multiply out each bracket and add like terms:

$= 24n^2 + 6nt - 12nt - 4t^2$

$= 24n^2 + (6 - 12)nt - 4t^2$

$= 24n^2 - 6nt - 4t^2$
$y - \{5y - (2z - 7z)\} =$
A $-4y - 5z$ B $-4y + 9z$ C $6y + 5z$ D $-4y + 5z$

Answer and solution

Answer: (A) $-4y - 5z$

Remove the round brackets first, then the curly brackets:

$= y - \{5y - 2z + 7z\}$

$= y - \{5y + 5z\}$

$= y - 5y - 5z$

$= -4y - 5z$

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MCQ test, Set 1