Algebraic Expressions and Their Uses: MCQ test, Set 7

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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.

How many constants are there in the list $m, b, -7, 0, a, 3, 10$ ?
A $4$ B $3$ C $2$ D $7$

Answer and solution

Answer: (A) $4$

The constants are the fixed numbers $3$ , $-7$ , $0$ , $10$ (0 and negative numbers are constants too).

So there are $4$ constants.
" $8$ more than one-third of $p$ " in symbolic form is
A $\displaystyle \frac{p}{3} + 8$ B $3p + 8$ C $\displaystyle \frac{p + 8}{3}$ D $\displaystyle \frac{p}{3} - 8$

Answer and solution

Answer: (A) $\displaystyle \frac{p}{3} + 8$

One-third of $p$ is $\displaystyle \frac{p}{3}$ ; $8$ more means add $8$ .

So it is $\displaystyle \frac{p}{3} + 8$ .
The number of terms in $\displaystyle 6n^2 + 7n + \frac{2m^2}{3}$ is
A $5$ B $4$ C $3$ D $2$

Answer and solution

Answer: (C) $3$

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

The terms are $6n^2$ , $7n$ , $\displaystyle \frac{2m^2}{3}$ .

So there are $3$ terms.
$8xz^2$ written as a product of its factors is
A $8 \times x \times z$ B $8 + x + z + z$ C $8 \times x \times z \times z$ D $8 \times x \times z \times 2$

Answer and solution

Answer: (C) $8 \times x \times z \times z$

$z^2$ means $z$ multiplied $2$ times.

$8xz^2 = 8 \times x \times z \times z$
The co-efficient of $pt^3$ in $4pqt^3$ is
A $4$ B $-4q$ C $q$ D $4q$

Answer and solution

Answer: (D) $4q$

$4pqt^3 = \left(4q\right) \times pt^3$

So the co-efficient of $pt^3$ is $4q$ .
Which of the following is a like term of $9m^2t$ ?
A $9bt$ B $9mt^2$ C $-7tm^2$ D $9m^2$

Answer and solution

Answer: (C) $-7tm^2$

Like terms have the same literal factors.

$-7tm^2$ has the literal factors $tm^2 = m^2t$ , the same as $9m^2t$ .
$8a + 4a + 7a =$
A $19a^2$ B $19a$ C $19$ D $19a^3$

Answer and solution

Answer: (B) $19a$

$8a + 4a + 7a$

$= (8 + 4 + 7)a$

$= 19a$
$2y - 6y =$
A $8y$ B $-4y$ C $4y$ D $-8y$

Answer and solution

Answer: (B) $-4y$

$2y - 6y$

$= (2 - 6)y$

$= -4y$
Which of the following expressions has exactly two monomials?
A $-6a^2 - 5ac^2$ B $2a^2c$ C $-7a^2c^2 - 6a^2c + 3c^2 - 4c$ D $4a - 3c^3 - 5c^2$

Answer and solution

Answer: (A) $-6a^2 - 5ac^2$

A binomial has two monomials.

$-6a^2 - 5ac^2$ has two terms.
Which of the following statements is false?
A Every polynomial is a multinomial. B Every multinomial is a polynomial. C $\displaystyle \frac{5}{4}x^2$ is a monomial. D $\displaystyle x + \frac{4}{x}$ is a multinomial.

Answer and solution

Answer: (B) Every multinomial is a polynomial.

A multinomial such as $\displaystyle x + \frac{4}{x}$ need not be a polynomial.

So 'every multinomial is a polynomial' is false.
The degree of $\displaystyle \frac{4}{3}a^2b^5m^2$ is
A $10$ B $5$ C $9$ D $3$

Answer and solution

Answer: (C) $9$

Add the powers of the variables:

$2 + 5 + 2 = 9$
The degree of $-8 + 9t^3 + 7m^3t^3 + 3m^4t^4$ is
A $4$ B $17$ C $8$ D $0$

Answer and solution

Answer: (C) $8$

Degrees of the terms are $0, 3, 6, 8$ .

The greatest is $8$ .
The value of $-2a^2b$ when $a = -3$ and $b = 3$ is
A $-54$ B $36$ C $108$ D $54$

Answer and solution

Answer: (A) $-54$

Put $a = -3$ and $b = 3$ :

$-2(-3)^2(3)$

$= -54$
The value of $7 - 4a$ when $a = -4$ is
A $-23$ B $-9$ C $-12$ D $23$

Answer and solution

Answer: (D) $23$

Put $a = -4$ :

$7 - 4(-4)$

$= 7 + 16$

$= 23$
The sum of $6p^2 - 5r^2 + 8pr$ and $3p^2 - 6r^2 - pr$ is
A $9p^2 - 11r^2 - 7pr$ B $3p^2 + r^2 + 9pr$ C $9p^2 - 11r^2 + 7pr$ D $9p^2 - 11r^2 + 9pr$

Answer and solution

Answer: (C) $9p^2 - 11r^2 + 7pr$

$6p^2 - 5r^2 + 8pr + 3p^2 - 6r^2 - pr$

$= (6 + 3)p^2 + (-5 - 6)r^2 + (8 - 1)pr$

$= 9p^2 - 11r^2 + 7pr$
The sum of $2a + 3m$ , $6a + b$ and $3b - 8m$ is
A $8a - 11m + 4b$ B $8a + 5m + 4b$ C $8a - 5m + 4b$ D $8a + 11m - 2b$

Answer and solution

Answer: (C) $8a - 5m + 4b$

Add the like terms column by column:

$\begin{array}{rrr} 2a & +3m & \\ 6a & & +b \\ & -8m & +3b \\ \hline 8a & -5m & +4b \end{array}$
Subtract $-5p$ from $9p$ .
A $-14p$ B $-4p$ C $4p$ D $14p$

Answer and solution

Answer: (D) $14p$

$(9p) - (-5p)$

$= 9p + 5p$

$= (9 + 5)p$

$= 14p$
If $A = 6q^2 - 7q + 6$ and $B = 6q^2 - 6q - 9$ , then $A - 3B =$
A $-12q^2 - 25q - 21$ B $-12q^2 + 11q + 33$ C $-12q^2 - q + 15$ D $24q^2 - 25q - 21$

Answer and solution

Answer: (B) $-12q^2 + 11q + 33$

$(6q^2 - 7q + 6) - 3(6q^2 - 6q - 9)$

$= 6q^2 - 7q + 6 - 18q^2 + 18q + 27$

$= (6 - 18)q^2 + (-7 + 18)q + (6 + 27)$

$= -12q^2 + 11q + 33$
Subtract $2p^2 + 2pq + 1$ from $5p^2 + 3$ .
A $3p^2 + 4 + 2pq$ B $-3p^2 + 2pq - 2$ C $7p^2 + 4 + 2pq$ D $3p^2 + 2 - 2pq$

Answer and solution

Answer: (D) $3p^2 + 2 - 2pq$

Change the signs of $2p^2 + 2pq + 1$ and add:

$\begin{array}{rrr} 5p^2 & +3 & \\ 2p^2 & +1 & +2pq \\ (-) & (-) & (-) \\ \hline 3p^2 & +2 & -2pq \end{array}$

$= 3p^2 + 2 - 2pq$
$3x^3y^2 \times (-4xy) \times 6x^3y^3 =$
A $-72x^7y^6$ B $5x^7y^6$ C $-72x^9y^6$ D $72x^7y^6$

Answer and solution

Answer: (A) $-72x^7y^6$

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

$= (3 \times (-4) \times 6)(x^3 \times x \times x^3)(y^2 \times y \times y^3)$

$= -72x^7y^6$
$5b(6bc + 7 + 8b) =$
A $30b^2c + 35b + 40b^2$ B $30b^2c + 7 + 8b$ C $30bc + 35b + 40b^2$ D $30b^2c + 35b - 40b^2$

Answer and solution

Answer: (A) $30b^2c + 35b + 40b^2$

Multiply $5b$ with every term inside the bracket:

$= (5b)(6bc) + (5b)(7) + (5b)(8b)$

$= 30b^2c + 35b + 40b^2$
$(2x + 5)(x - 3) =$
A $2x^2 - 15$ B $2x^2 - x - 15$ C $2x^2 - x + 15$ D $2x^2 + x - 15$

Answer and solution

Answer: (B) $2x^2 - x - 15$

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

$= 2x^2 - 6x + 5x - 15$

$= 2x^2 - x - 15$
$(2x + 3y)(3x - 6y) =$
A $6x^2 + 3xy - 18y^2$ B $6x^2 - 3xy - 18y^2$ C $6x^2 - 18y^2$ D $6x^2 - 3xy + 18y^2$

Answer and solution

Answer: (B) $6x^2 - 3xy - 18y^2$

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

$= 6x^2 - 12xy + 9xy - 18y^2$

$= 6x^2 - 3xy - 18y^2$
$4x(4x + 5z) - 4z(x + 4z) =$
A $16x^2 + 24xz + 16z^2$ B $-16x^2 - 16xz + 16z^2$ C $16x^2 + 16xz + 16z^2$ D $16x^2 + 16xz - 16z^2$

Answer and solution

Answer: (D) $16x^2 + 16xz - 16z^2$

Multiply out each bracket and add like terms:

$= 16x^2 + 20xz - 4xz - 16z^2$

$= 16x^2 + (20 - 4)xz - 16z^2$

$= 16x^2 + 16xz - 16z^2$
$6x - \{3z + (5x + 5z)\} =$
A $x + 2z$ B $11x + 8z$ C $11x + 2z$ D $x - 8z$

Answer and solution

Answer: (D) $x - 8z$

Remove the round brackets first, then the curly brackets:

$= 6x - \{3z + 5x + 5z\}$

$= 6x - \{8z + 5x\}$

$= 6x - 8z - 5x$

$= x - 8z$

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MCQ test, Set 7