2 Marks Questions

Question 12 Marks

Factorise $15 x^2 y+6 x^4 y^2-9 x y$ and find its irreducible form.

Answer

We can write
$
\begin{aligned}
15 x^2 y & =3 \times 5 \times x \times x \times y \\
6 x^4 y^2 & =2 \times 3 \times x \times x \times x \times x \times y \times y \\
9 x y & =3 \times 3 \times x \times y
\end{aligned}
$
Here, $3 \times x \times y$ is common in these terms.
$
\begin{aligned}
\therefore 15 x^2 y+ & 6 x^4 y^2-9 x y \\
& =3 \times 5 \times x \times x \times y+2 \times 3 \times x \times x \times x \times x \times y \times y \\
& \quad-3 \times 3 \times x \times y \\
& =3 \times x \times y[5 \times x+2 \times x \times x \times x \times y-3 \times 1] \\
& =3 x y\left(5 x+2 x^3 y-3\right)
\end{aligned}
$

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Question 22 Marks

Build a square garden. Divide the square garden into four rectangular flower beds in such a way that each flower bed is as long as one side of the square. The perimeter of each flower bed is 40 m .
(i) Draw a diagram to represent the above information.
(ii) Mention the expression for perimeter of the entire garden.

Answer

Self

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Question 32 Marks

Algebraic Tiles
(i) Cut the following tiles from a graph sheet. Now, colour the tiles as per the colour code. Arrange these algebraic tiles to form a square.

Find the length of the side of the square so formed. Also find the area of the square. Using the above result factorise $x^2+4 x+4$.
(ii)

Find the length of the side of the rectangle so formed. Also, find the area of the rectangle. Using the above result factorise $x^2+5 x+4$.
Now, choose and cut more algebraic tiles from the graph sheet. Create your own colour code and colour the tiles. Arrange them to form square/rectangle. Find the area of the figure so formed using it to factorise
(a) $x^2+4 x+3$ $\qquad$ (b) $x^2+9 x+18$
(iii) Build a square garden. Divide the square garden into four rectangular flower beds in such a way that each flower bed is as long as one side of the square. The perimeter of each flower bed is 40 m .
(a) Draw a diagram to represent the above information.
(b) Mention the expression for perimeter of the entire garden.

Answer

Self

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Question 42 Marks

Divide $\left(-27 x^2 y\right)+(-3 x y)$.

Answer

Firstly, factorise both terms,
$
\text { } \begin{aligned}
-27 x^2 y & =-3 \times 3 \times 3 \times x \times x \times y \\
and \qquad -3 x y & =-3 \times x \times y \\
\therefore-27 x^2 y ÷ (-3 x y) & =\frac{-27 x^2 y}{-3 x y} \\
& =\frac{-3 \times 3 \times 3 \times x \times x \times y}{-3 \times x \times y}
=3 \times 3 \times x=9 x
\end{aligned}
$

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Question 52 Marks

Divide $\left(-121 p^3 q^3 r^3\right)$ by $\left(-11 x y^2 z^3\right)$.

Answer

We have.
$
\begin{array}{l}
\left(-121 p^{3} q^{3} r^3\right)+\left(-11 \times y^2 z^3\right) \\
=\frac{-121 p^{3} q^{3} r^{3}}{-11 \times y^2 z^3} \\
=\frac{-11 \times 11 \times p \times p \times p \times q \times q \times q \times r \times+\times r}{-11 \times x \times y \times y \times z \times z \times z} \\
=\frac{11 \times p \times p \times p \times q \times q \times q \times r \times r \times r}{x \times y \times y \times z \times z \times z} \\
=\frac{11 p^3 q^3 r^3}{x y^2 z^3} .
\end{array}
$

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MATHS 2 Marks Questions

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