DEVELOPMENT P & L EDUCATION

Lesson Plan

COMPILED BY :

Maria Priscillya PasaribuIDN : 4103312018

BILINGUAL MATHEMATICS 2012

STATE UNIVERSITY OF MEDAN

LESSON PLAN

School Name : SMA ...

Subject : Polynomial

Class / Semester: XI IPA / 2 (even)

Allocation of Time   : 8 hours of lessons (4 meetings)

A. Competency Standards : 4.   Using rules of polynomial in problem solving.

B. Basic Competency : 4.1.   Using polynomial division algorithm to determine the

outcome for the rest of the division.

C. Indicator   :

1. Determine the degree and coefficients - coefficient of each tribe of polynomial and

identify the mathematical form is polynomial. 2. Determining the value of a polynomial using direct substitution method and schemes.

3. Complete interoperability between polynomial which includes addition, subtraction, and multiplication polynomial.

4. Determine the coefficient of the unknown value of the two polynomial same. 5. Determine the quotient and remainder of the division polynomial by linear or

quadratic shape and determine the degree of the quotient and the remainder of the

division by using the division and synthetic polynomial long form (Horner). D. Learning Objectives :

1. Learners can determine the degree and coefficients - coefficient of each tribe of

polynomial and identify the mathematical form is polynomial. 2. Learners can determine the value of a polynomial using direct substitution method

and schemes. 3. Learners can determine the value of a polynomial using direct substitution method

and schemes. 4. Learners can determine the coefficient of the unknown value of the two polynomial

same. 5. Learners can determine the quotient and remainder of the division polynomial by

linear or quadratic shape and determine the degree of the quotient and the remainder

of the division by division polynomial use the long form and the synthetic (Horner). E. Teaching Materials :

The general form

By:

coefficient , coefficient , and so on

called a fixed rate

natural numbers which indicate the degree polynomial.

LESSON PLAN Page 1

Polinormal in variable x of degree r

Addition, Measurement, Multiplication of Polynomial

Two tribes can be aggregated or much reduced by adding or reducing the tribes the same degree.

To multiply by multiplying term by term.

Value of Polynomial

Many tribes in x is often written in the function f (x).

When the value of x is replaced by a constant k, then f (k) is called the value of polynomial.

To determine the value of polynomial can be many ways:

1. Direct substitution

2. Horner

Example:

Determine the value of f (x) = 2x7 + 5x6 - 5x4 + 7x3 – 5

For x = - 2

First way → direct substitutionf (-2) = 2 (-2)7 + 5 (-2)6 – 5 (-2)4 + 7 (-2)3 – 5

= -256 + 320 – 80 – 56 – 5

= -77

Second way → horner

Similarity of Polynomial

Two forms of the same algebra for any value of x is said to identical or similar. Symbols are identical:

(Equivalent).

Example:

Determine the value of p, q, r with the following equation:

Answer:

LESSON PLAN Page 2

p + q + r = 6 …. (1)

-q – 3r = -7 … (2)

-p – 2q + 2r = -1 … (3)

(1) & (3) (1) & (2)

Polynomial Division

Which is divided = divider. quotient + remainder

f (x) = (xa). h (x) + reminder

f (a) = remainder

If the divisor of function x is n degree, then the remainder of the highest rank is (n-1)

Remainder theorem and the factor

If polynomial f (x) of degree and divided (x - k) then the remainder of s = f (k).

Example:

Polynomial of f (x) divided by (x - 2) the remaining 8, when divided by (x + 3) the remaining 7, how

the remainder of f (k) when divided by x 2 + x - 6?

Answer:

Which is divided = divider. quotient + remainderf (x) = (x – 2) . H (x) + 8

f (x) = 8

f (x) = (x + 3) . H (x) + (-7)

f (-3) = -7

f (x) = (x2 + x – 6) . H (x) + (ax + b)

f (x) = (x + 3) (x – 2) . H (x) + (ax + b)

f (-3) = a (-3) + b → -3 a + b = -7

f (-2) = a . 2 + b → 2 a + b = 8 -

- 5 a = -15

a = 3

b = 2

Factoring Polynomial

Steps:

LESSON PLAN Page 3

… (4)

q =1.5 p = 3

If the number of coefficients of polynomial including the constant is 0, then 1 is a root / completion of

polynomial.

If an even number of coefficients = number of coefficients, the degree is odd, then -1 is a root /

completion of polynomial.

If steps 1 and 2 are not satisfied, then try to the constant factor divided by the coefficient factor of the

highest degree.

Polynomial with degree of 3 and 4 Degree of 3

ax3 + bx2 + cx + d = 0

x1 + x2 + x3 =

x1x2 + x2x3 + x1x3 =

x1x2x3 =

Degree of 4ax4 + bx3 + cx2 + dx1 + e = 0

x1 + x2 + x3 + x4 =

x1x2 + x1x3 + x1x4 + x2x3 + x2x4 + x3x4 =

x1x2x3 + x1x2x4 + x1x3x4 + x2x3x4 =

x1 x2 x3 x4 =

Model and Learning Method

a. Learning Model   :   Direct Teaching Model (MPL), Cooperative Learning Model Learning Circle and NHT (Numbered Head Together).

b. Methods of Learning   :   lectures, discussions, question and answer

H. Scenario Learning

First Meeting

Indicators:

1. Determine the degree and the coefficients of each tribe of polynomial and identify the mathematical form is polynomial.

2. Determining the value of a polynomial using direct substitution method and schemes.

Topic:

1. Understanding Polynomial

LESSON PLAN Page 4-2

2

2 1 -1 9 -18 36 -77

-4 -2 4 2 -18 36 -72

-2 F (-2)

5 0 -5 7 0 0 -5 Koefisien suku banyak dengan pangkat turun

-2

2

2 1 -1 9 -18 36 -77

-4 -2 4 2 -18 36 -72

-2 F (-2)

5 0 -5 7 0 0 -5 Koefisien suku banyak dengan pangkat turun

The general form of a polynomial in x polynomial or degree n that

By:

coefficient , coefficient , and so on

called a fixed rate

natural numbers which indicate the degree polynomial.

2. Value Polynomial (Substitution Method and Method Chart).

Many tribes in x is often written in the function f (x).

When the value of x is replaced by a constant k, then f (k) is called the value of polynomial.

To determine the value of polynomial can be many ways:

1. Direct substitution

2. Scheme Method

3. Horner

a. Substitution Method

Thus the value of f(x) = for x = 1 is???????

b. Scheme MethodWill be found the value of f(x) = for x = 1

First Step : write the coefficient of each tribex = 1 1 3 -1 5

1 4 3 + 1 4 3 8

So f (x) = f (1) = 8

c. Horner

Example : Determine the value of f (x) = 2x7 + 5x6 - 5x4 + 7x3 – 5

For x = - 2

Model and Method of Learning:

LESSON PLAN Page 5

Value of

for x = k ( k ) represented:

a. Learning Model : Direct Learning Model b. Methods of Learning : Lecture, discussion, question and answer

Scenario of Learning

Preliminary

Motivation: If you success share with others, if you fail ask to yourself why you fail Apersepsi: - Looking back on a quadratic function

Example: f (x) = 5x 2 + 4x -3 Learners communicate coefficients of each tribe

Core activities

a. Learners are given a stimulus materials by teachers about:

Understanding of polynomial

The general form of a polynomial in x polynomial or degree n that

By:

coefficient , coefficient , and so on

called a fixed rate

natural numbers which indicate the degree polynomial.

b. Learners are given a student worksheet. c. Learners communicate orally will answer student worksheets on determining the degree and

the coefficients of each tribe of polynomial and determining what type of mathematics that is polynomial.

d. Teachers demonstrate how to determine the value polynomial substitution and schemes / charts.

Value of PolynomialPolynomial in x of degree-n can be written in the following functions:

Usually known as polynomial functions. Polynomial value of f (x) for x = k is f (k) Search strategy values of f (k) is 2:

a. Substitution Method

Thus the value of f(x) = for x = 1 is???????

LESSON PLAN Page 6

Value of

for x = k ( k ) represented:

b. Scheme MethodWill be found the value of f(x) = for x = 1

First Step : write the coefficient of each tribex = 1 1 3 -1 5

1 4 3 + 1 4 3 8

So f (x) = f (1) = 8

e. Learners work on some exercises given by the teacher. f. Learners and teachers together to discuss answers to the questions given.

Cover

a. Learners and teachers to reflect on and concluded the material. b. Learners are given homework related to polynomial understanding, identifying the

mathematical form is polynomial, and the determination of the value of polynomial by direct substitution and schemes.

c. Students are reminded about the interoperability between the pretest and the similarity polynomial polynomial.

Second Meeting

Indicators:

3. Solving interoperability between polynomial which includes addition, subtraction, and multiplication polynomial.

4. determine the coefficient of the unknown value of the two polynomial same.

Topics:

1. Operating between polynomial (addition, subtraction, and multiplication polynomial).2. Similarity of polynomial.

Model and Method of Learning:

a. Learning Model :   Direct Learning Model

b. Methods of Learning :   Lectures, discussions, question and answer

Scenario of Learning

Preliminary

Motivation: We can not be successed if we said we would fail

Apersepsi: - reminding on form and value polynomial polynomial.

- Discuss homework

Core Activities

LESSON PLAN Page 7

a. Learners working on the pretest. b. Demonstration of the operation and the similarity between polynomial polynomial.

Interagency Operations Polynomial

f (x) + g (x) =? (addition)

f (x) - g (x) =? (subtraction)

f (x). g (x) =? (Multiplication)

Conclusion:

For polynomial f (x) of degree m and g (x) of degree n, then:

f(x) g(x) is the maximum degree polynomial of m or n

f (x). g (x) is polynomial of degree (m + n)

Polynomial similarity

c. Learners work on practice questions given by the teacher. d. Learners and teachers together to discuss answers to practice questions.

Cover

a. Learners and teachers to reflect. b. Students are given homework on algebraic operations and similarities polynomial.

Third Meeting

Indicator :

5. Determine the quotient and remainder of the division polynomial by linear or quadratic shape and determine the degree of the quotient and the remainder of the division by using the division and synthetic polynomial long form (Horner).

Topic:

1. Relationships divisor, the quotient and remainder (division polynomial by linear (x-k) and (ax + b).

LESSON PLAN Page 8

Theorem :

Suppose that

if f(x) g(x) then it be

Model and Method of Learning:

a. Learning Model    :   Model Cooperative Learning Circle Learning / Learning together b. Methods of Learning   :   Lectures, discussions, question and answer

Scenario Learning

Preliminary

Motivation: Success is not measured by what you accomplish, but the failures you have faced, and the courage that keeps you battling a barrage of obstacles

Apersepsi: - Discussing homework

Core Activities

a. Learners are given a stimulus materials by teachers about the division polynomial.

Relationships divisor, the quotient and remainder

a. Polynomial division by (x-k)

Example:

Determine the distribution of the remaining proceeds and f (x) = by (x-2)!

Answer:   

How schematic

(x-2)

How Horner

x = 2 2 4 5 74 16 42 +

2 8 21 49

So f (2) = 49 = remainder

b. Polynomial division by (ax + b)

Example:

LESSON PLAN Page 9

-

-

-49

Determine the results and the remainder of f(x) = by way of a double

decker and Horner!

b. Students formed 10 groups (4 person / group) by counting 1-10, but a clever spread c. Learners work and discuss the questions given by the teacher for each group, and then

collected.

Cover

a. Learners and teachers to reflect. b. Students are given homework related to the division of polynomial by linear forms.

Fourth Meeting

Indicator:

5. Determine the quotient and remainder of the division polynomial by linear or quadratic shape and determine the degree of the quotient and the remainder of the division by using the division and synthetic polynomial long form (Horner).

Topic:

1. Relationships divisor, the quotient and remainder (division polynomial by quadratic forms).

Model and Method of Learning:

a. Learning Model :   Cooperative Learning Model NHT (Numbered Heads Together)

b. Methods of Learning :   Lectures, discussions, questioning

Scenario of Learning

Preliminary

Motivation: There are two ways through life, through by the miracles or live with mediocrity

Apersepsi: - Discussing homework

- recall 2 ways of polynomial division

Core Activities

a. Learners are given a stimulus materials by teachers about the division polynomial by quadratic forms.

Note: Horner method can only be used if the divisor can be factored.

The general form:

f(x) = . H (x) + S(x) = P1 . P2 . H(x) + S(X)

LESSON PLAN Page 10

Example: Determine the results and the remainder of the division by ! Answer: Step 1

factorized become (x-2) (x+1) = P1 . P2

f(x) = divided by P1 = (x-2), by result H0 (x) and remainder S1 .

x = 2 1 0 -3 1 -22 4 2 6 +

x = -1 1 2 1 3 4Step 2 -1 -1 0

1 1 0 3

Step 3

Quotient of f(x) by is H (x) = , and remainder is S(x) = P1 . S2 + S1 = (x-2) . 3 + 4 = 3x -2

b. Learners form groups (each group are numbered 1-4). c. Learners work and discuss some of the questions given by the teacher group.

d. Students were randomly selected to present the results of focus group discussions.

Cover

a. Learners and teachers to reflect. b. Students are given homework related to the division of polynomial by quadratic forms.

I. Source / Facilities / Equipment

Sources:

a. Buku Matematika Interaktif Program IPA SMA Kelas XI Semester Genap jilid 2B karangan Drs. Herynugroho dkk (Penerbit : Yudhistira)

b. Buku Seribu pena Matematika SMA Kelasj XI jilid 2, karangan Drs. Husein Tamponas (penerbit: Erlangga).

c. Buku mMatematika SMA Kelas XI Semester 2, karangan Sartono Wirodikromo (penerbit: Erlangga).

J. Assessment

Techniques: groupwork, individual tasks, remedials

Form of Instruments: essay

Example Instrument:

LESSON PLAN Page 11

1. Student Worksheet

No. Question Problem Solving Score1 Tentukan koefisien dan derajat suku banyak Suku banyak dalam x berderajat 2 dan

koefisiennya 35

2 Hitunglah

a.

b.

a. f(2) = 22 + 2.2 = 4 + 4 = 8

b. f(-1) = - (-1) – 2 = 1 – 2 = -1

5

3 Tentukan nilai dari

untuk x

= -2 dengan menggunakan cara substitusi

dan Horner!

Cara 1

By substitution : we substitude the value of x

into the equation

f(-2) = 2(-2)5 + 3(-2)4 – 5(-2)2 + (-2) – 7

= -45

Cara 2

By Horner :

-2 2 3 0 -5 1 -7

-4 2 -4 18 -38

2 -1 2 -9 19 -45

10

4 Tentukan suku banyak dari:

a. f (x) + g (x) b. f (x) – g (x)

c. f (x) . g (x)

Jika f (x) = 3x – 2 dan g (x) = x + 1

a. (3x – 2) + (x + 1) = 4x – 1

b. (3x – 2) – (x + 1) = 2x – 1

c. (3x – 2) . (x + 1) = 3x2 + 3x – 2x – 2 = 3x2 + x – 2

5

5 Tentukan m supaya habis dibagi 2x – 1 !

4 -12 m 0 2

2 -5

4 -10 m-5 0

2+ = 0 m = -3

10

6 Bila dibagi x – 1 memberikan sisa yang sama, maka tentukan p !

Jika f(x) : (x – a ) maka sisanya = f(a)

5

LESSON PLAN Page 12

7 Jika x – y + 1 merupakan sebuah faktor dari , maka

tentukan nilai a, b dan c !

20

8 Bila f(x) dibagi x + 2 mempunyai sisa 14 dan jika dibagi x – 4 sisanya –4. Tentukan sisanya jika f(x) dibagi !

Misal sisanya = ax + b 20

9 Tentukan hasil bagi dan sisa dari pembagian

!

10

10 Tentukan sisa pembagian

!

10

Medan, _____ 2010

Knowing,

Headmaster Teacher Mathematics

LESSON PLAN Page 13

Name of Headmaster Name of Teacher Mathematics

NIP _____ NIP ______

LESSON PLAN Page 14