1 Marks Question

Question 11 Mark

Subtract:
$4 a^2+5 b^2-6 c^2+8$ from $2 a^2-3 b^2-4 c^2-5$

Answer

$ 2 a^2-3 b^2-4 c^2-5-\left(4 a^2+5 b^2 2-6 c^2+8\right)$
$=2 a^2-3 b^2-4 c^2-5-4 a^2-5 b^2+6 c^2-8 $
$ =2 a^2-4 a^2-3 b^2-5 b^2-4 c^2+6 c^2-5-8$
$=-2 a^2-8 b^2+2 c^2-13$

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Question 21 Mark

Write $'T'$ for true and $'F'$ for false of the following: $\frac{\text{x}}{4}+\frac{\text{x}}{6}-\frac{\text{x}}{2}=\frac{3}{4}\Rightarrow\text{x}=-9$

Answer

$\frac{\text{x}}{4}+\frac{\text{x}}{6}-\frac{\text{x}}{2}=\frac{3}{4}$
$\Rightarrow\frac{3\text{x}+2\text{x}-6\text{x}}{12}=\frac{3}{4}$
$\Rightarrow\frac{-\text{x}}{12}=\frac{3}{4}$
$\Rightarrow-4\text{x}=36$
$\Rightarrow\text{x}=-\frac{36}{4}$
$\Rightarrow\text{x}=-9$

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Question 31 Mark

Write $'T'$ for true and $'F'$ for false of the following: $(5a - 9b) - (-6a + 2b) = (-a - 7b)$

Answer

$L.H.S. = (5a - 9b) - (-6a + 2b)$
$= 5a - 9b + 6a - 2b = (-a - 7b)$
$= 5a + 6a - 9b - 2b = (-a - 7b)$
$= (11a - 11b)$
This is not equal to $(-a - 7b).$
Thus, the $L.H.S.$ is not equal to the $R.H.S.$

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Question 41 Mark

Fill in the blanks.
$x^2-18 x+81=(\_\_\_\_)$

Answer

$x^2-18 x+81=(x-9)^2$
Solution:
$ x^2-18 x+81 $
$=x^2-2 \times x \times 9+9^2 $
$=(x-9)^2$

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Question 51 Mark

Write $'T'$ for true and $'F'$ for false of the following: $2\text{x}-5=0\Rightarrow\text{x}=\frac{2}{5}$

Answer

$2\text{x} - 5 = 0$
$\Rightarrow 2\text{x}= 5$
$\Rightarrow\text{x} = \frac{5}{2}$

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Question 61 Mark

Write $'T'$ for true and $'F'$ for false of the following: $-8$ is a monomial.

Answer

Any expression that contains only one term is called a monomial. It can either be a constant or a variable.

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Question 71 Mark

Fill in the blanks. $abc - ab - c + 1 = ($_____$)($_____$)$

Answer

$abc - ab - c + 1$
$= ab(c - 1) - 1(c - 1)$
$= (c - 1)(ab - 1)$

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MCQ 81 Mark

Mark $(\checkmark)$ against the correct answer: $8x^3 - 2x = ?$

A
$(4 x-1)(2 x-1) x$
B
$\left(2 x^2+1\right)(2 x-1)$
✓
$2 x(2 x-1)(2 x+1)$
D
None of these

Answer

Correct option: C.

$2 x(2 x-1)(2 x+1)$

$ 8 x^3-2 x $
$ =2 x\left(4 x^2-1\right) $
$ =2 x\left((2 x)^2-1^2\right)$
$ =2 x(2 x-1)(2 x+1)$

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Question 91 Mark

Fill in the blanks.
$4 - 36x^2= ($_____$)($_____$)($_____$)$

Answer

$ 4-36 x^2$
$ =4\left(1-9 x^2\right)$
$ =4\left(12-(3 x)^2\right) $
$ =(4)(1-3 x)(1+3 x)$

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Question 101 Mark

Fill in the blanks.
$x^2 - 14x + 13 = (\_\_\_\_\_)(\_\_\_\_\_)$

Answer

$(x - 13)(x - 1)$
Solution:
$x^2-14 x+13$
$ =x^2-13 x-x+13$
$=x(x-13)-1(x-13) $
$=(x-13)(x-1)$

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MCQ 111 Mark

Mark $(\checkmark)$ against the correct answer: $\frac{\text{x}+5}{2}+\frac{\text{x}-5}{3}=\frac{25}{6}$ gives:

A
$x = 3$
✓
$x = 4$
C
$x = 5$
D
$x = 2$

Answer

Correct option: B.

$x = 4$

$\frac{\text{x}+5}{2}+\frac{\text{x}-5}{3}=\frac{25}{6}($because $\text{L.C.M.}$ of $2$ and $3$ is $6)$
$\Rightarrow\frac{3(\text{x}+5)+2(\text{x}-5)}{6}=\frac{25}{6}$
$\Rightarrow\frac{3\text{x}+15+2\text{x}-10}{6}=\frac{25}{6}$
$\Rightarrow\frac{5\text{x}+5}{6}=\frac{25}{6}$
$\Rightarrow5\text{x}+5=25 ($cancelling $6$ from the denominator on both the sides$)$
$\Rightarrow5\text{x}=25-5$
$\Rightarrow\text{5x}=20$
$\Rightarrow\text{x}=\frac{20}{5}$
$\Rightarrow\text{x}=4$

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Question 121 Mark

Fill in the blanks.
$9 z^2-x^2-4 y^2+4 x y$=(_______)(_______)

Answer

$(3z + x - 2y)(3z - x + 2y)$
Solution:
$ 9 z^2-x^2-4 y^2+4 x y $
$ =9 z^2-\left(x^2-4 x y+4 y^2\right) $
$=9 z^2-\left(x^2-2 \times x \times 2 y+(2 y)^2\right)$
$ =9 z^2-(x-2 y)^2$
$ =(3 z)^2-(x-2 y)^2$
$=(3 z+(x-2 y))(3 z-(x-2 y))$
$ =(3 z+x-2 y)(3 z-x+2 y)$

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Question 131 Mark

Write $'T'$ for true and $'F'$ for false of the following: When $x = 2$ and $y = 1,$ the value of $\frac{-8}{7}\text{x}^3\text{y}^4\text{ is }\frac{-64}{7}$

Answer

$x = 2$
$y = 2$ Give expression $=\frac{-8}{7}(2)^3(1)^4$
$=\frac{-8}{7}\times8\times1$
$=\frac{-64}{7}$

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Question 141 Mark

Write $'T'$ for true and $'F'$ for false for the following:
$(5 - 3x^2)$ is a binomial.

Answer

Binomial expression is an expression that shows the sum or the difference of two unlike terms. The above expression has two unlike terms, i.e. $5$ and $3x^2$.

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