Algebraic Expressions and Their Uses: MCQ test, Set 9

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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 NOT a constant?
A $\displaystyle -\frac{1}{3}$ B $7$ C $0$ D $q$

Answer and solution

Answer: (D) $q$

$0$ , $\displaystyle -\frac{1}{3}$ and $7$ have fixed values.

$q$ can take various values, so it is not a constant.
"The sum of $p$ and $3$ " in symbolic form is
A $p - 3$ B $3p$ C $p + 3$ D $3 - p$

Answer and solution

Answer: (C) $p + 3$

Sum means add.

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

Answer and solution

Answer: (B) $5$

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

The terms are $\displaystyle -\frac{x^2z}{2}$ , $-4xz^2$ , $-7$ , $8x^2$ , $-7x^3$ .

So there are $5$ terms.
$4yz^3$ written as a product of its factors is
A $4 \times y \times z \times 3$ B $4 \times y \times z$ C $4 + y + z + z + z$ D $4 \times y \times z \times z \times z$

Answer and solution

Answer: (D) $4 \times y \times z \times z \times z$

$z^3$ means $z$ multiplied $3$ times.

$4yz^3 = 4 \times y \times z \times z \times z$
The co-efficient of $a^3$ in $\displaystyle -\frac{3}{2}a^3bc^3$ is
A $\displaystyle -\frac{3}{2}$ B $\displaystyle -\frac{3}{2}bc^3$ C $\displaystyle \frac{3}{2}bc^3$ D $bc^3$

Answer and solution

Answer: (B) $\displaystyle -\frac{3}{2}bc^3$

$\displaystyle -\frac{3}{2}a^3bc^3 = \left(-\frac{3}{2}bc^3\right) \times a^3$

So the co-efficient of $a^3$ is $\displaystyle -\frac{3}{2}bc^3$ .
Which of the following is a like term of $-9pr^3$ ?
A $-9p$ B $-9p^3r$ C $2r^3p$ D $-9mr^3$

Answer and solution

Answer: (C) $2r^3p$

Like terms have the same literal factors.

$2r^3p$ has the literal factors $r^3p = pr^3$ , the same as $-9pr^3$ .
$9m + 3t + 9m + t =$
A $18m + 4t$ B $18m + 3t$ C $22mt$ D $4m + 18t$

Answer and solution

Answer: (A) $18m + 4t$

$9m + 3t + 9m + t$

$= (9 + 9)m + (3 + 1)t$

$= 18m + 4t$
$4t - 14t =$
A $-10t$ B $-18t$ C $10t$ D $18t$

Answer and solution

Answer: (A) $-10t$

$4t - 14t$

$= (4 - 14)t$

$= -10t$
Which of the following expressions contains three monomials?
A $6t^3 + 3mt^2$ B $5t^2 - 3m^2t^2 + 7mt^2 - 8m^2t$ C $7m^2t + 4t^3 + 7m^2$ D $8m$

Answer and solution

Answer: (C) $7m^2t + 4t^3 + 7m^2$

A trinomial has three monomials.

$7m^2t + 4t^3 + 7m^2$ has three terms.
Every polynomial is also a
A binomial B trinomial C multinomial D monomial

Answer and solution

Answer: (C) multinomial

A polynomial has one or more monomials, and each monomial is a term.

So every polynomial is a multinomial (an expression of one or more terms).
The degree of $9x^3y^4$ is
A $2$ B $9$ C $4$ D $7$

Answer and solution

Answer: (D) $7$

Add the powers of the variables:

$3 + 4 = 7$
The degree of $6c^3 + 7c - a^5c^2 + 8a^2c^4$ is
A $7$ B $3$ C $5$ D $4$

Answer and solution

Answer: (A) $7$

Degrees of the terms are $3, 1, 7, 6$ .

The greatest is $7$ .
The value of $6 - 5x$ when $x = -4$ is
A $-26$ B $26$ C $-14$ D $-4$

Answer and solution

Answer: (B) $26$

Put $x = -4$ :

$6 - 5(-4)$

$= 6 + 20$

$= 26$
The value of $-3x^2 + x - 9$ when $x = -2$ is
A $25$ B $-23$ C $-14$ D $1$

Answer and solution

Answer: (B) $-23$

Put $x = -2$ :

$-3(-2)^2 + (-2) - 9$

$= -12 - 2 - 9$

$= -23$
The sum of $2a^2 + 7b^2 + 5ab$ and $-5a^2 + 7b^2 - ab$ is
A $3a^2 + 14b^2 + 4ab$ B $7a^2 + 6ab$ C $-3a^2 + 14b^2 + 4ab$ D $-7a^2 + 14b^2 + 4ab$

Answer and solution

Answer: (C) $-3a^2 + 14b^2 + 4ab$

$2a^2 + 7b^2 + 5ab - 5a^2 + 7b^2 - ab$

$= (2 - 5)a^2 + (7 + 7)b^2 + (5 - 1)ab$

$= -3a^2 + 14b^2 + 4ab$
The sum of $8b + 8c$ , $8b + 9z$ and $4c - 2z$ is
A $16b + 12c - 7z$ B $16b + 12c + 7z$ C $16b + 12c + 11z$ D $16b + 4c + 11z$

Answer and solution

Answer: (B) $16b + 12c + 7z$

Add the like terms column by column:

$\begin{array}{rrr} 8b & +8c & \\ 8b & & +9z \\ & 4c & -2z \\ \hline 16b & +12c & +7z \end{array}$
Subtract $-8y$ from $12y$ .
A $20y$ B $-20y$ C $4y$ D $-4y$

Answer and solution

Answer: (A) $20y$

$(12y) - (-8y)$

$= 12y + 8y$

$= (12 + 8)y$

$= 20y$
If $A = 4a^2 + 4a - 2$ and $B = a^2 + 7a - 4$ , then $2A - 3B =$
A $5a^2 + 29a - 16$ B $5a^2 + a$ C $11a^2 + 29a - 16$ D $5a^2 - 13a + 8$

Answer and solution

Answer: (D) $5a^2 - 13a + 8$

$2(4a^2 + 4a - 2) - 3(a^2 + 7a - 4)$

$= 8a^2 + 8a - 4 - 3a^2 - 21a + 12$

$= (8 - 3)a^2 + (8 - 21)a + (-4 + 12)$

$= 5a^2 - 13a + 8$
Subtract $3b^2 - 6bc + 8$ from $7b^2 - 6$ .
A $-4b^2 - 6bc + 14$ B $4b^2 - 14 + 6bc$ C $10b^2 + 2 - 6bc$ D $4b^2 + 2 - 6bc$

Answer and solution

Answer: (B) $4b^2 - 14 + 6bc$

Change the signs of $3b^2 - 6bc + 8$ and add:

$\begin{array}{rrr} 7b^2 & -6 & \\ 3b^2 & +8 & -6bc \\ (-) & (-) & (+) \\ \hline 4b^2 & -14 & +6bc \end{array}$

$= 4b^2 - 14 + 6bc$
$6xy \times (-3xy) \times 6x^2y =$
A $-108x^4y^3$ B $9x^4y^3$ C $108x^4y^3$ D $-108x^2y$

Answer and solution

Answer: (A) $-108x^4y^3$

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

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

$= -108x^4y^3$
$6x^2y(6xy + 8tx - 2) =$
A $36x^2y + 48tx^3y - 12x^2y$ B $36x^3y^2 + 8tx - 2$ C $36x^3y^2 + 48tx^3y + 12x^2y$ D $36x^3y^2 + 48tx^3y - 12x^2y$

Answer and solution

Answer: (D) $36x^3y^2 + 48tx^3y - 12x^2y$

Multiply $6x^2y$ with every term inside the bracket:

$= (6x^2y)(6xy) + (6x^2y)(8tx) + (6x^2y)(-2)$

$= 36x^3y^2 + 48tx^3y - 12x^2y$
$(3x - 5)(x - 9) =$
A $3x^2 - 32x + 45$ B $3x^2 + 32x + 45$ C $3x^2 - 32x - 45$ D $3x^2 + 45$

Answer and solution

Answer: (A) $3x^2 - 32x + 45$

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

$= 3x^2 - 27x - 5x + 45$

$= 3x^2 - 32x + 45$
$(2m + 4n)(m - 3n) =$
A $2m^2 - 2mn + 12n^2$ B $2m^2 - 2mn - 12n^2$ C $2m^2 + 2mn - 12n^2$ D $2m^2 - 12n^2$

Answer and solution

Answer: (B) $2m^2 - 2mn - 12n^2$

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

$= 2m^2 - 6mn + 4mn - 12n^2$

$= 2m^2 - 2mn - 12n^2$
$3x(3x - y) - 2y(4x + y) =$
A $9x^2 - 11xy + 2y^2$ B $-9x^2 + 11xy + 2y^2$ C $9x^2 + 5xy + 2y^2$ D $9x^2 - 11xy - 2y^2$

Answer and solution

Answer: (D) $9x^2 - 11xy - 2y^2$

Multiply out each bracket and add like terms:

$= 9x^2 - 3xy - 8xy - 2y^2$

$= 9x^2 + (-3 - 8)xy - 2y^2$

$= 9x^2 - 11xy - 2y^2$
$6y - \{2z - (6y - 5z)\} =$
A $12y + 3z$ B $7z$ C $12y - 7z$ D $3z$

Answer and solution

Answer: (C) $12y - 7z$

Remove the round brackets first, then the curly brackets:

$= 6y - \{2z - 6y + 5z\}$

$= 6y - \{7z - 6y\}$

$= 6y - 7z + 6y$

$= 12y - 7z$

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MCQ test, Set 9