Introduction of passport to algebra and geometry

Introduction of passport to algebra and geometry:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.

Concepts of Passport to Algebra and Geometry:

Algebra: The following are some of the concepts of passport to algebra.

Number theory : The number theory has a natural numbers and whole numbers which can show below. The counting of numbers 1, 2, 3, 4, 5…is known as natural numbers and the whole numbers have o along with the natural numbers.

Rational numbers : The rational number can be defined as the integer of values is not equal to 0 which is in the form m / n, where m, n is the integers and n ≠ 0. The rational number is said to be in a proper form.

Linear equation: It is an algebraic equation which has the term of constant and product of a constant in single variable. The values are not fixed it can be represented as p, q and r.

Geometry: The following are some of the concepts of passport to geometry.

Radius: A radius is the distance from center of a circle to any point on that circle's circumference.

Perimeter :  The perimeter is a path which can be surrounds an area and also used for path or length.

Circumference: A circumference is the distance around a circle.

Example of Passport to Algebra and Geometry Answers:

Ex 1: We can be obtained the natural number by subtracting of 1 from in the given numbers as shown.

Predecessor of 13 = 13 – 1 = 12

Predecessor of 43 = 43 – 1 = 42

Sol:  We can be obtained the natural number by adding of 1 from in the given numbers as shown.

Successor of 97 = 97 + 1 = 99

Successor of 18 = 18 + 1 = 19

EX 2:   Determine rational number represented as 65.0.

Sol :   Let x = 65.0. Then x = 0.656565…

 100 x = 65.656565…

 100 x − x = (65.656565…) − (0.656565…)

                = 65.0000…

 99x = 65

 x = 65 / 99

    = 13 / 33

Ex 3:  Solve the linear equation for a variable:      x + 7 = 19

Sol :  Take away 7 from the both sides using the property 1

x + 7 - 7 = 19 - 7

x = 12

Ex 4: Solve: y - 3 = 16

Sol :  Add 3 to both sides using property 2

y - 3 + 3 = 16 + 3

y = 19

Q 5 : Find the area and perimeter of rectangle with length 10cm, width 2 cm.

Sol :  Area of rectangle = Length x width

                            = 10 * 2

                            = 20cm^2

Perimeter of rectangle = 2 (Length + width)

                                   = 2 (10 + 2)

                      Answer = 24cm

Q 6:  Find the area and circumference of the circle when the radius is 5cm.
 

Sol : Circle Area= (r= 5) (Pi=3.14 constant)

                                  = 3.14 * 5 * 5

                                  = 78.5cm^2

       Circumference = 2* pi * r

                                 = 2 * 3.14 * 5

                  Answer = 31.4 cm