Algebraic Expressions and Their Uses: MCQ test, Set 6

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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 $6a - 11$ , the variable is
A $6a$ B $a$ C $6$ D $-11$

Answer and solution

Answer: (B) $a$

$6$ and $-11$ are fixed numbers.

Only $a$ can take various values, so $a$ is the variable.
" $7$ times $p$ subtracted from $4$ times $q$ " in symbolic form is
A $4q + 7p$ B $7p - 4q$ C $4q - 7p$ D $4p - 7q$

Answer and solution

Answer: (C) $4q - 7p$

Start with $4q$ and take away $7p$ .

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

Answer and solution

Answer: (B) $5$

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

The terms are $8$ , $5a^3$ , $3a^2b$ , $\displaystyle \frac{5ab}{4}$ , $-2a$ .

So there are $5$ terms.
The numerical factor of $\displaystyle -\frac{8}{3}pr^2$ is
A $\displaystyle \frac{8}{3}$ B $-8$ C $2$ D $\displaystyle -\frac{8}{3}$

Answer and solution

Answer: (D) $\displaystyle -\frac{8}{3}$

$\displaystyle -\frac{8}{3}pr^2 = \left(-\frac{8}{3}\right) \times pr^2$

The numerical factor is $\displaystyle -\frac{8}{3}$ .
The co-efficient of $x^2$ in $\displaystyle \frac{5}{2}x^2y^2z$ is
A $y^2z$ B $\displaystyle \frac{5}{2}y^2z$ C $\displaystyle -\frac{5}{2}y^2z$ D $\displaystyle \frac{5}{2}$

Answer and solution

Answer: (B) $\displaystyle \frac{5}{2}y^2z$

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

So the co-efficient of $x^2$ is $\displaystyle \frac{5}{2}y^2z$ .
Which of the following is a like term of $6p^3q^2$ ?
A $\displaystyle -\frac{q^2p^3}{2}$ B $6p^2q^3$ C $6p^3$ D $6mq^2$

Answer and solution

Answer: (A) $\displaystyle -\frac{q^2p^3}{2}$

Like terms have the same literal factors.

$\displaystyle -\frac{q^2p^3}{2}$ has the literal factors $q^2p^3 = p^3q^2$ , the same as $6p^3q^2$ .
$x + x + x + x + x + x + x + x + x =$
A $9x$ B $8x$ C $9 + x$ D $x^9$

Answer and solution

Answer: (A) $9x$

$x$ is added $9$ times, so the sum is $9x$ .
$4z + z - 10z - 5 =$
A $-5z + 5$ B $5z - 5$ C $-6z - 5$ D $-5z - 5$

Answer and solution

Answer: (D) $-5z - 5$

$4z + z - 10z - 5$

$= (4 + 1 - 10)z - 5$

$= -5z - 5$
$\displaystyle \frac{7}{x}$ is
A a binomial B a term but not a monomial C a constant D a monomial

Answer and solution

Answer: (B) a term but not a monomial

$\displaystyle \frac{7}{x} = 7x^{-1}$ is one term.

The power $-1$ is not a whole number, so it is not a monomial.
$\displaystyle \frac{2}{5}p^3 - p + 7$ is
A a polynomial B a binomial C a multinomial but not a polynomial D not an algebraic expression

Answer and solution

Answer: (A) a polynomial

The powers of $p$ are $3$ , $1$ , $0$ : all whole numbers.

The fraction $\displaystyle \frac{2}{5}$ is only a co-efficient, so this is a polynomial (of three terms).
The degree of $4m^2n^4$ is
A $7$ B $4$ C $2$ D $6$

Answer and solution

Answer: (D) $6$

Add the powers of the variables:

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

Answer and solution

Answer: (A) $6$

Degrees of the terms are $4, 6, 2$ .

The greatest is $6$ .
The value of $6p - 7r - 6$ when $p = -2$ and $r = -3$ is
A $3$ B $-3$ C $27$ D $9$

Answer and solution

Answer: (A) $3$

Put $p = -2$ and $r = -3$ :

$6(-2) - 7(-3) - 6$

$= -12 + 21 - 6$

$= 3$
The value of $3a^2 + 4ab - 3b^2$ when $a = 1$ and $b = -3$ is
A $12$ B $-12$ C $-36$ D $18$

Answer and solution

Answer: (C) $-36$

Put $a = 1$ and $b = -3$ :

$3(1)^2 + 4(1)(-3) - 3(-3)^2$

$= 3 - 12 - 27$

$= -36$
The sum of $2b^2 - 4c^2 + 4bc$ and $2b^2 - 6c^2 - 3bc$ is
A $2c^2 + 7bc$ B $4b^2 - 10c^2 - bc$ C $4b^2 - 10c^2 + 7bc$ D $4b^2 - 10c^2 + bc$

Answer and solution

Answer: (D) $4b^2 - 10c^2 + bc$

$2b^2 - 4c^2 + 4bc + 2b^2 - 6c^2 - 3bc$

$= (2 + 2)b^2 + (-4 - 6)c^2 + (4 - 3)bc$

$= 4b^2 - 10c^2 + bc$
The sum of $-5x + 2y$ , $3y + 2t$ and $6x + 5t$ is
A $x + 5y + 7t$ B $-x + 5y + 7t$ C $11x + 5y + 7t$ D $-11x + 5y - 3t$

Answer and solution

Answer: (A) $x + 5y + 7t$

Add the like terms column by column:

$\begin{array}{rrr} -5x & +2y & \\ & 3y & +2t \\ 6x & & +5t \\ \hline x & +5y & +7t \end{array}$
Subtract $6x + z$ from $2x + 6z$ .
A $-4x + 7z$ B $4x - 5z$ C $-4x + 5z$ D $8x + 7z$

Answer and solution

Answer: (C) $-4x + 5z$

$(2x + 6z) - (6x + z)$

$= 2x + 6z - 6x - z$

$= (2 - 6)x + (6 - 1)z$

$= -4x + 5z$
If $A = 2a - 4b - 6$ and $B = 3a + 2b - 7$ , then $3A - B =$
A $9a - 10b - 25$ B $3a - 14b - 11$ C $-a - 6b + 1$ D $3a - 10b - 25$

Answer and solution

Answer: (B) $3a - 14b - 11$

$3(2a - 4b - 6) - (3a + 2b - 7)$

$= 6a - 12b - 18 - 3a - 2b + 7$

$= (6 - 3)a + (-12 - 2)b + (-18 + 7)$

$= 3a - 14b - 11$
Subtract $3a^2 - 3ac - 2$ from $4a^2 - c^2 + 4$ .
A $a^2 - c^2 + 6 + 3ac$ B $a^2 - c^2 + 2 - 3ac$ C $-a^2 - 3ac - 6 + c^2$ D $7a^2 - c^2 + 2 - 3ac$

Answer and solution

Answer: (A) $a^2 - c^2 + 6 + 3ac$

Change the signs of $3a^2 - 3ac - 2$ and add:

$\begin{array}{rrrr} 4a^2 & -c^2 & +4 & \\ 3a^2 & & -2 & -3ac \\ (-) & & (+) & (+) \\ \hline a^2 & -c^2 & +6 & +3ac \end{array}$

$= a^2 - c^2 + 6 + 3ac$
$3x^2y^2 \times (-5x^3yz) =$
A $15x^5y^3z$ B $-15x^6y^2z$ C $-2x^5y^3z$ D $-15x^5y^3z$

Answer and solution

Answer: (D) $-15x^5y^3z$

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

$= (3 \times (-5))(x^2 \times x^3)(y^2 \times y)z$

$= -15x^5y^3z$
$2a(-2ac + 8a) =$
A $-4ac + 16a^2$ B $-4a^2c + 8a$ C $-4a^2c + 16a^2$ D $-4a^2c - 16a^2$

Answer and solution

Answer: (C) $-4a^2c + 16a^2$

Multiply $2a$ with every term inside the bracket:

$= (2a)(-2ac) + (2a)(8a)$

$= -4a^2c + 16a^2$
$(3m - 6)(3m - 7) =$
A $9m^2 + 39m + 42$ B $9m^2 + 42$ C $9m^2 - 39m + 42$ D $9m^2 - 39m - 42$

Answer and solution

Answer: (C) $9m^2 - 39m + 42$

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

$= 9m^2 - 21m - 18m + 42$

$= 9m^2 - 39m + 42$
$(x + 3z)(x - 6z) =$
A $x^2 - 3xz + 18z^2$ B $x^2 + 3xz - 18z^2$ C $x^2 - 18z^2$ D $x^2 - 3xz - 18z^2$

Answer and solution

Answer: (D) $x^2 - 3xz - 18z^2$

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

$= x^2 - 6xz + 3xz - 18z^2$

$= x^2 - 3xz - 18z^2$
$3p(p - r) + 2r(3p - 4r) =$
A $3p^2 - r + 6pr - 8r^2$ B $3p^2 + 3pr - 8r^2$ C $3p^2 + 3pr - 4r$ D $3p^2 - 9pr + 8r^2$

Answer and solution

Answer: (B) $3p^2 + 3pr - 8r^2$

Multiply out each bracket and add like terms:

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

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

$= 3p^2 + 3pr - 8r^2$
$6y - \{2y - (4z + 7z)\} =$
A $8y - 11z$ B $4y - 3z$ C $4y + 11z$ D $4y - 11z$

Answer and solution

Answer: (C) $4y + 11z$

Remove the round brackets first, then the curly brackets:

$= 6y - \{2y - 4z - 7z\}$

$= 6y - \{2y - 11z\}$

$= 6y - 2y + 11z$

$= 4y + 11z$

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MCQ test, Set 6