Chapter 1 Types of algebra, mapping, function, and Straight line equality Matematika SMP Kelas 2....

Chapter 1Types of algebra, mapping, function, and

Straight line equality

Matematika SMP Kelas 2 .

(1. Factor of algebra)

A. Calculate operation of algebra

1. The sum and subtraction of algebra

a. Commutative characteristica + b = b + a, with a and b are real numbers

b. Associative characteristics(a + b) + c = a + (b +c), with a, b, and c are real numbers

c. Distributive characteristicsa (b + c) = ab + ac, with a, b, and c are real numbers

2. Multiplication of algebra

a. Multiplication of term one and term twob. Multiplication of term two and term twoc. Division of algebrad. The power of algebra


B. Factorial of algebra1. Factorial by distributive characteristic

a. Commutative characteristicsa + b = b + a, with a and b are real numbers

b. Associative characteristics(a + b) + c = a + (b +c), with a, b, and c are real number

c. Distributive characteristicsa (b + c) = ab + ac, with a, b, and c real numbers

2. Subtraction of two quadrats


3. Factorial of quadrat

a. Factorial of ax2 + bx + c with a = 1b. Factorial of ax2+bx+c with a 1

C. Fraction on algebra1. The sum and subtraction of algebra

2. Multiplication and division on fraction of algebra


3. The power of fraction of algebra

e.g. :

a. Multiplication

b. Division

C. Fraction on algebra1. The sum and subtraction on fraction of algebra

2. Multiplication and division on fraction of algebra


3. The power of fraction of algebra

e.g. :

a. Multiplication

b. Division


4. Simplifying on fraction of algebra

e.g. :Simplify the following fraction! :

Answer:

(2. Mapping)

A. Definition of Mapping

1. Diagram of arrow


B. Declaring a Mapping

2. Sets of sequence pairs

e.g. :There are two set of numbers P = {0, 2, 4, 6, 8} and Q = {0, 1, 2, 3, 4, 5}. If the relation of set P to set Q are “two times of", determine the set of sequence pairs for the relation.

Answer:0 ∈ A is paired with 0 ∈ B because 0 = 0 × 2, written as(0, 0)2 ∈ A paired with 1 ∈ B because 2 = 1 × 2, written as (2, 1)4 ∈ A paired with 2 ∈ B because 4 = 2 × 2, written as (4, 2)6 ∈ A paired with 3 ∈ B because 6 = 3 × 2, written as (6, 3)8 ∈ A paired with 4 ∈ B because 8 = 4 × 2, written as (8, 4)

Therefore, The sets of sequence pairs for relation “two times of“ is {(0, 0), (2, 1), (4, 2), (6, 3), (8, 4)}



C. Cartesian diagram

A. Definition of function or cartography


The arrow diagram shows the function of set P to set Q with relation “two times of". Determine the domain, cod domain, and it s function range.answer:

a. The domain (Df) is P = {4, 6, 8, 10}

b. The cod domain is Q = {1, 2, 3, 4, 5}c. The range (Rf) is {2, 3, 4, 5}

(3. Function)

B. Domain, Cod domain and Range function

C. Function graphic


D. Calculating the value of function1. Notation of function

2. Calculating the value of function

3. Determining the formula of function


(4. The equality of line)

A. Definition of equality of line

1. Cartesian coordinate

a. Drawing points on Cartesian coordinate

b. Drawing lines on Cartesian coordinate

2. Drawing equality of line


B. Gradient

1. Definition of gradien

Gradient is a level of line’s declivity.

2. Calculation of gradient

a. Calculating gradient on equality of line y=mxb. Calculating Gradient on equality of line y = mx + cc. Calculating Gradient on equality of line ax + by + c = 0d. Calculating gradient on the line that pass two points

3. Characteristics of gradient

a. Gradient of line that parallel with axis –x b. Gradient of line that parallel with axis –yc. Gradient of two parallel linesd. Gradient of perpendiculars on two lines


C. Determining the equality of line

1. Determining the equality of line on gradient and coordinate point

General form of line’s equality :

Formula:

2. Determining the equality of line that pass two points

Formula:

3. Determining the coordinate of meet point on two lines


4. The Application of line equality

e.g. :A car moves in constant speed of 15 km/hour. After 3 hours, the car take on 45 km. How long it needs to take on 90 km?Answer:Look at the picture.The picture is the illustration of the question about the providing speed and distance. Point coordinate of A (15, 1) is the speed of the car, that is 15 km/hour . Point coordinate of B (45, 3) is the distance and the time to take on that is 45 km in 3 hours. By the point of A and B can be pulled a line so that gain the solving that in taking on 90 km, the car need 6 hours.

Chapter 1 Types of algebra, mapping, function, and Straight line equality Matematika SMP Kelas 2....

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