Algebra: Overview, Questions, Preparation

Algebra is a broad part of mathematics, together with number systems, geometry. Algebra is the study of mathematical symbols and the rules for handling these symbols. The use of letters in algebra allows us to write formulas in a general manner for particular problems as numbers can be inserted in the place of letters, and thus, we can get solutions to multiple similar type questions with an algebraic expression. 

Definition of a Variable

A variable is a symbol that has no fixed value in any particular expression. It can be represented as many different elements like x,y,l,m,n, a, etc.    

Operations with a variable

Numbers can be added, subtracted, multiplied, and divided with any variable.
Suppose a variable is ‘x.’

Add 10 : x+10

Subtract 10: x-10

Multiply by 10: x*10 

(can also be written as 10x)
Divide by 10: x/10

Rules of Geometry

The perimeter of a Square: Suppose a square has sides ABCD. We know that all sides of a square are identical. Therefore,                  
AB=BC
BC=CD
CD=AD

Let AB = s
Perimeter= Sum of all the sides
     = AB+AD+CD+BC
     = s+s+s+s
     = 4s.

The perimeter of a Rectangle: Suppose a rectangle has sides ABCD. We know that the opposite sides of a rectangle are equal. Therefore,

AB=CD
AD=BC

Let the length AB= l, 
The breadth AD= b 
Perimeter = Sum of all sides
     = AB+BC+CD+AD
     = l+b+l+h
     = 2l + 2b
    = 2(l+b)

Rules of Arithmetic

1. Commutativity of addition of two numbers: a+b=b+a
2. Commutativity of Multiplication of two numbers: a*b=b*a
3. Distributivity of two numbers: a*(b+c)=a*b+a*c

The chapter is taught in class 6th. This chapter carries 6-8 marks.

1. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.) 

Solution.

The total number of boxes = b
Number of mangoes in 1 box = 50
Therefore,
Number of mangoes in b boxes = 50*b = 50b

2. A cube is a three-dimensional figure, as shown in the figure given below. It has six faces, and all of them are identical squares. The length of each side is denoted by s. What will be the total length of edges of the cube?

Solution.

We know that a cube has 12 edges.
Length of each edge of the cube = s

No. of edges of a cube = 12

The total length of the edges of the cube = 12s.

3. Meena, Beena, and Leena are climbing the steps to the hilltop. Meena is at step s, Beena is 8 steps ahead, and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hilltop is 10 less than 4 times what Meena has reached. Express the total number of steps using s.

Solution.

According to the question,
Steps of Meena = s
Steps of Beena = Meena’s steps +8
                            = s+8
Steps of Clay = Meena’s steps-7
                        = s-7

Also,
    The total number of steps = 4s-10.

Q: Who is known as the father of algebra?

Q: What is a simple linear equation?

Q: Can the value of variables be negative or zero?

Q: What are constants?

Q: Can an algebraic expression have two or more than two variables?