Math Algebra Practicals (10th)-I,II,III

Practical No.1

Aim:

On a graph paper, draw a line parallel to the $X$- axis or $Y$- axis. Write coordinates of any four points on the line. Write how the equation of the line can be obtained from the coordinates. [Instead of parallel lines, lines passing through the origin or intersecting the $X$ or $Y$- axis can also be considered]

Requirement:

Graph paper,scale, eraser,pen,pencil

Procedure:

1]A line equation $y=2$ is also written as $0x+y=2$,The graph of this line is parallel to $x$-axis;as for any value of $x,y$ is always.
2] Similarity equation $x=2$ is written as $x+0y=2$ and its graph is parallel to $y$-axis.

$x$	1	4	-3
$y$	2	2	2
$(x,y)$	(1,2)	(4,2)	(-3,2)

Conclusion:

In this activity we have observed that x-axis and y-axis are parallel to each other

Graph:

Practical No.2

Aim:

Bear a two- digit number in mind. Without disclosing it, cunstruct a puzzle. Create two algebraic relations between the two digits of the number and solve the puzzle. [The above practical can be extended to a three-digit number also.]

Puzzle:

I am a number, tell my identity, three times of me, add fifty. You still need forty to have a triple century.

Puzzle

\[Let \ the \ number \ be \ x\] \[(3x+50)+40=300\] \[⇒3x=300-90\] \[⇒3x=210\] \[⇒x=70\]

Practical No.3

Aim:

Write $ α = 6$ on one side of a card sheet and $α = -6$ on its backside. Similarly, write $β = -3$ on one side of another card sheet and $β = 7$ on its backside. From these values, form different values of $(α+β)$ and $(αβ)$; using these values form quadratic equations.

Procedure:

\[α = 6 \ on \ one \ side (α1)\] \[α =-6 \ on \ its \ backside \ (α2)\] \[β =-3 \ on \ one \ side \ (β1)\] \[β = 7 \ on \ its \ backside \ (β2)\] \[from \ the \ above \ values\] \[i] (α1+β1)=(6)+(-3)= 3\] \[(α1β1)=(6)×(-3)= -18\] \[to \ form \ a \ quadratic \ equation:\] \[x²-(α+β)x+(αβ)=0\] \[x²-3x-18=0\] \[ii] (α2+β2)=(-6)+(7)= 1\] \[(α2β2)=(-6)×(7)= -42\] \[to \ form \ a \ quadratic \ equation:\] \[x²-(α+β)x+(αβ)=0\] \[x²-x-42=0\]

Conclusion:

In this activity we observed that by putting different values of $α$ and $β$ we would get different values of $(α+β)$ and $(αβ)$