PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
Form 04 – D1-7.3.b - 00 |
LESSON PLAN
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the term n-th the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explain the symbol
· Name the properties of
V. Teaching Material
Sigma
The symbol (“Sigma”) means sum and it is defined as follows:
Here, n is natural number and .
The Properties of Sigma
· If k is a constant, then:
Proof:
· If q is a constant, then:
(b – a + 1) times |
(b – a + 1) times |
· If f1, f2, f3, … , is functions, then:
· If then:
VI. Target of Study
Ø The students can list name of the symbol of sum.
Ø The students can define the symbol
Ø The students can list name of the properties of the symbol
Ø The students can proof the properties of the symbol
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (10’)
Ø Teacher gives opener greeting.
Ø Reminding material back about the sequence and series concept already been accepted student at the time sits in SMP.
Ø Teacher gives motivation to the students.
B. Whilst Activity (70’)
Ø Teacher divide students become some groups and each group consist two students.
Ø Teacher distributes module to each group.
Ø Student is given time more or less 10 minutes for read and studying module of study.
Ø Teacher asks for one of student to explain the meaning of the symbol .
Ø Teacher explains the properties of the symbol .
Ø Teacher asks each groups for proof the properties of the symbol
Ø Teacher pointed some groups for present product of their proof.
Ø Teacher research product or their work.
Ø Teacher gives the problem exercise and worked together with the students.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : individual quiz
The Problems:
Write the value of:
1.
2.
3.
Solution:
1.
2.
3.
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
LESSON PLAN
Form 04 – D1-7.3.b - 00 |
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the n-th term the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explain the mean of arithmetic sequence.
· Find the formula of arithmetic sequence.
· Determine n-th term of arithmetic sequence.
V. Teaching Material
Arithmetic Sequence
Consider the following sequence.
1, 4, 7, 10, 13, …
We find that the difference between any term and the preceding is constant.
Or in the diagram:
3 |
3 |
3 |
3 |
This sequence is called arithmetic sequence of common difference = 3
The other examples are:
Arithmetic Sequence Common difference
5, 7, 9, 11, 13, … 2
a, a + b, a + 2b, a + 3b, … b
Now suppose that the following sequence is an arithmetic sequence:
is called the first term , is called the second term, …, is called n-th.
If b is the common difference, then:
and
. . .
The regularities can be seen as follows:
And we obtain that:
It is often used the notation a for , so that the formula becomes
Consider the arithmetic sequence:
Then between each two terms of the sequence are inserted n terms, so that a new arithmetic sequence is formed.
n |
n |
Notice that in the new sequence, is the first term and is the (n + 2) th term, so that:
Where b’ is the common difference of the new arithmetic sequence. Since then or
VI. Target of Study
· Students can explain the mean of arithmetic sequence.
· Students can find the formula of arithmetic sequence.
· Students can determine term to n of arithmetic sequence.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (15’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Teacher back to remember about before material.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (65’)
Ø Teacher gives example the sequence.
Ø Teacher explains the common difference of the sequence.
Ø Teacher gives some example again the other about the sequence and asks students for list names of its common difference.
Ø Teacher explains about the arithmetic sequence.
Ø Teacher ask student for list names of the arithmetic sequence formula from what that explains by teacher.
Ø Teacher explains about the common difference of arithmetic sequence that new.
Ø Teacher gives some examples for research together.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : individual quiz
The Problems:
1. The n-th term of an arithmetic sequence is given by the formula:
Find the common difference of the sequence.
2. Find the formula for the n-th term of the sequence: log 2, log 4, log 8, log 16, . . .
Solution:
1.
So, the its common difference is 12.
2. log 4 - log 2 = log = log 2
log 8 - log 4 = log = log 2
log 16 - log 8 = log = log 2
So, this is an arithmetic sequence of first term log 2 and of common difference log 2.
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
LESSON PLAN
Form 04 – D1-7.3.b - 00 |
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 -2011
-
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the n-th term the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explanation the mean of arithmetic series.
· Find the formula of arithmetic series.
· Calculate the n-th term and sum n term of arithmetic series.
V. Teaching Material
Arithmetic Series
If is the n-th term of an arithmetic sequence, then what is called arithmetic series is:
Here is also the sum of first n terms of the series, and we may write it as . Consider the following arithmetic sequence (of first term a, common difference b, and of last term l:
Begin with l, we obtain:
Adding, we have:
But , so that
VI. Target of Study
· Students can explanation the mean of arithmetic series.
· Students can find the formula of arithmetic series.
· Students can calculate the n-th term and sum n term of arithmetic series.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (15’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Teacher back to remember about before material.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (65’)
Ø Teacher asks to student what the meaning of arithmetic series.
Ø Teacher repeats or clarifies back the meaning of arithmetic series.
Ø Teacher asks student for find the formula self of arithmetic series.
Ø Teacher leads student on find its formula.
Ø Teacher asks one of student to explain it.
Ø Teacher asks some example for work together.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : individual quiz
The Problems:
1. Find the sum of first 30 terms of the series:
4 + 7 + 10 + 13 + . . .
2. In an arithmetic series given that . Find the common difference.
3. In an arithmetic series given that . Find .
4. Account:
a. The sum of 1000 the firs real number.
b.
Solution:
1.
2.
So, the common difference of arithmetic series is 14.
3.
4. a.
b.
50 terms (of 51 until 100) =
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
LESSON PLAN
Form 04 – D1-7.3.b - 00 |
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the n-th term the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explain the mean of geometric sequence.
· Find the formula of geometric sequence.
· Determine n-th term of geometric sequence.
V. Teaching Material
Geometric Sequence
Consider the following sequence:
If this sequence is a geometric sequence, then:
. . . . . . . . . .(1)
Examples are:
Geometric Sequence r
3, 6, 12, 24, 48, . . . 2
125, 25, 5, 1, . . .
4, -12, 36, -108, . . . -3
r
So the following is a geometric sequence of first term a and of ratio r:
or
So that we obtain:
. . . . . . . . . . . (2)
Example:
Find the formula for the n-th term of the geometric sequence:
4, 8, 16, 32, 64, . . .
Solution:
Since and then
So,
Now suppose that geometric sequence has , where A and B are constants.
We obtain:
And according for formula (1), then
or r = B
VI. Target of Study
· Student can explain the mean of geometric sequence.
· Student can find the formula of geometric sequence.
· Student can determine n-th term of geometric sequence.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (15’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Teacher back to remember about before material.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (65’)
Ø Teacher explains to student about the meaning of geometric sequence.
Ø Teacher explains to student how seek ratio (r) of a sequence.
Ø Teacher gives some examples of geometric sequence and then asks student for seek ratio it.
Ø Teacher divide students become some groups and each group consist three students.
Ø Each group gets task for seek the formula of n-th term geometric sequence of some examples that giving of teacher.
Ø Teacher monitors and controlling the way that group discussion.
Ø Their work result gathered.
Ø Teacher pointed some group for present their work result.
Ø Teacher concludes and explain again the result of presentation some its groups.
Ø Teacher asks student to proof that r = B, if know a geometric sequence have , where A and B is constant.
Ø Teacher asks one a student for write the proof result it in the white board and then teacher discuss it.
Ø Teacher asks students to list names of the difference between arithmetic sequence and geometric sequence.
Ø Teacher concludes the answer from students.
Ø Teacher gives some examples about geometric sequence and does together with student.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : task group and individual quiz
The Problems:
1. A geometric sequence has . Find its ratio.
2. From a geometric series given that : and , then
3. If the first term of a geometric series is where while the 5-th term is , then the 21-th term is. . .
4. Three numbers form a geometric sequence of ratio 3. If the second term is added by 8, then an arithmetic sequence is formed. Write down the three numbers..
Solution:
1.
2.
3.
4. Suppose that the three numbers are:
Arithmetic sequence:
The property of arithmetic sequence :
So those numbers are or 4, 12, 36.
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
LESSON PLAN
Form 04 – D1-7.3.b - 00 |
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the term n-th the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explain the mean of geometric series.
· Find the formula of geometric series.
· Counting n-th term and the sum of n-th geometric series.
V. Teaching Material
Geometric Series
The following is a geometric series of first term a and of ratio r:
The sum of n terms is , then
Multiplying by r we obtain:
Subtracting
VI. Target of Study
· Student can explain the mean of geometric series.
· Student can find the formula of geometric series.
· Student can count n-th term and the sum of n-th geometric series.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (15’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Teacher back to remember about before material.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (65’)
Ø Teacher explains to student about the mean of geometric series.
Ø Teacher gives some examples of geometric sequence and then asks student for seek ratio it.
Ø Teacher divide students become some groups and each group consist three students.
Ø Each group gets task for seek the formula of first n terms .
Ø Teacher monitors and controlling the way that group discussion.
Ø Their work result gathered.
Ø Teacher asks some group for present their work result. And other groups that not presentation asks for receive the presentation result from the other group.
Ø Teacher concludes and explain again the result of presentation some its groups.
Ø Teacher asks students to list names of the difference between arithmetic series and geometric series.
Ø Teacher concludes the answer from students.
Ø Teacher gives some examples about geometric sequence and does together with student.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : task group and individual quiz
The Problems:
1. Find the formula for the sum of first n terms of the geometric series:
2 + 4 + 8 + 16 + 32 + . . .
2. A geometric series has . Find its ratio.
3. A geometric series has . Find its ratio.
Solution:
1.
2.
So if , then
3.
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
Form 04 – D1-7.3.b - 00 |
LESSON PLAN
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
Determine the term n-th the sequence and sum n the arithmetic and geometry series term.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Explain the mean of infinite geometric series.
· Find the formula of infinite geometric series.
· Counting n-th term and the sum of n-th infinite geometric series.
V. Teaching Material
Infinite Geometric Series
Consider the following geometric series:
Since and then
If the series continuous infinitely, then approaches 0, so that:
We write , so that in the example above .
If exist, then the series is said convergent.
We have already learned that in a geometric series:
The geometric series is convergent if: . . . . . . . . . . . . . (1)
If the condition (1) is satisfied the , so that:
. . . . . . . . . . . . . (2)
VI. Target of Study
· Student can explain the mean of infinite geometric series.
· Student can find the formula of infinite geometric series.
· Student can count n-th term and the sum of n-th infinite geometric series.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (15’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Teacher back to remember about before material.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (65’)
Ø Teacher asks a question to student about the mean of infinite geometric series.
Ø Teacher concludes the answer from students.
Ø Teacher gives some examples about infinite geometric series.
Ø Teacher explains to student what the examples above are convergent or not.
Ø Teacher explain the condition if geometric series is convergent.
Ø Of what already been explained, teacher asks student for list name of the formula of geometric series is convergent.
Ø Teacher gives some examples about geometric series is convergent and do together with student.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
Suherman. 2009. 1000 Soal Matematika Dasar SMA. Jakarta: TransMedia.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : task group and individual quiz
The Problems:
1. Find the sum of the infinite geometric series: 9 + 3 + 1 + . . .
2. The value of x then geometric series have the sum is . . .
3. The sum of an infinite geometric series is 6 and the sum of terms that odd number is 4. Its 6 is . . .
4. For the geometric series , its sum has a limit, the value of x should satisfy ...
Solution:
1. Since (satisfies (1)), then according to formula (2)
2. The condition have sum or convergent
The logarithm condition:
The result of the section two limitation it x:
3.
4.
The condition (1):
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
PEMERINTAH KOTA SALATIGA
DINAS PENDIDIKAN PEMUDA DAN OLAH RAGA
SEKOLAH MENENGAH ATAS NEGERI 1
(SMA N 1)
(SMA N 1)
Jl. Kemiri No. 1 Telp. (0298) 326867 Fax. (0298) 326867
SALATIGA
SALATIGA
50711
LESSON PLAN
Form 04 – D1-7.3.b - 00 |
School Name : SMA Negeri 1 Salatiga
Subject Study : Mathematics
Grade / Semester : XII / 2
Program : Language
Meeting to :
Academic Years : 2010 - 2011
I. Competence Standard
Use the sequence and series concept in problem solving.
II. Basic Competence
The problem solving that be related to with series and interpret the solution it.
III. Time Allocation
2 x 45 minutes
IV. Indicator
· Determine the solution of mathematics model that be related to with arithmetic series.
· Determine the solution of mathematics model that be related to with geometric series.
· Give interpretation about the result of the solution that gets.
V. Teaching Material
The problem solving of arithmetic and geometric series.
VI. Target of Study
· Student can determine the solution of mathematics model that be related to with arithmetic series.
· Student can determine the solution of mathematics model that be related to with geometric series.
· Student can give interpretation about the result of the solution that gets.
VII. Strategy and Methods
Lecturing, answer question, discussion, and giving an assignment.
VIII. Classroom Activities
A. Pre Activity (10’)
Ø Teacher gives opener greeting.
Ø Teacher gives motivation to the students.
Ø Discuss home work if student difficult in work it.
B. Whilst Activity (70’)
Ø Teacher remembers again to student about arithmetic series and geometric series.
Ø Teacher gives some the story problem examples that be related to life everyday about arithmetic series and geometric series.
Ø The examples it does together with students.
Ø Teacher gives exercises.
Ø Teacher asks student to doing self and gathered.
C. Post activity (10’)
Ø Student together with teacher makes conclusion of product of study.
Ø Teacher gives PR (Home Work).
Ø Teacher gives shell greeting.
IX. Source and Media
Loedji, Wilia Adrian Soekotjo. 2007. Matematika Bilingual. Bandung: Yrama Widya.
Suherman. 2009. 1000 Soal Matematika Dasar SMA. Jakarta: TransMedia.
X. Assessment
Estimation consisting of : affective' estimation and cognitive
Bill type : task group and individual quiz
The Problems:
1. Lengths of the ribbon divide to 10 a part with length that forms arithmetic series. If the ribbon that most short 20 cm and that longest 155 cm then determine length of the ribbon originally.
2. Long the side of a right triangle forms arithmetic sequence. Determine area of triangle if the surrounding area it 72.
3. A ball is released of height 10 m and reflects back of height times the preceding height. This reflection continuous until the ball stops. Determine the sum of all path travelled by he ball?
Solution:
1. Known : Lengths of the ribbon divide to 10 a part
Long of ribbon that most short is 20 cm
Long of ribbon that longest is 155 cm
Asked : Determine length of the ribbon originally.
Answer :
So, length of the ribbon originally is 875.
2. Known : Long the side of a right triangle forms arithmetic sequence
The surrounding area = 72
Asked : Determine area of triangle it.
4h |
3h |
5h |
A right triangle forms arithmetic sequence is:
The surrounding area =
Bottom =
High =
Area =
So, if the surrounding area it 72 then area of triangle it is 216.
3. Known : A ball is released of height 10 m
Reflects back of height times
Asked : Determine the sum of all path travelled by he ball
Answer :
So, the sum of all path travelled by he ball is 70 m.
Approved by, The Principal of SMA N 1 Salatiga Drs. Saptono Nugrohadi, M.Pd, M.Si NIP. 19680921 199003 1 006 | Salatiga, 2010 Mathematics’ Teacher Dra. Wahyu Tri Astuti, M.Pd NIP 19670908 199802 2 004 | |
CHECKING BY WAKA CURICULUM | VALIDATING BY QMR | |
Dra. Zulianti Utami NIP. 19601223 198603 2 009 | Jaka Agus Pramana, S.Pd, M.Pd NIP. 195908151984031006 | |
