CURRICULUM BASED CURRICULUM BASED REASONING TEST REASONING TEST

forforUNIVERSITY ENTRANCE UNIVERSITY ENTRANCE

EXAMINATIONEXAMINATION

Susanto Imam RahayuIndonesian Academy of Sciences

UNIVERSITY ENTRANCE UNIVERSITY ENTRANCE EXAMINATION IN INDONESIAEXAMINATION IN INDONESIA

Historical PerspectiveHistorical Perspective

* In the 1950’s, there were no University Entrance Examination. Everyone having high school certificate were accepted.

* Due to high demand for some popular degree programs, in particular engineering and medicine, some faculties began to impose entrance examination

* With ever higher demand and limited space, the number of facuties and universities imposing entrance examination spread.

* By early 1970’s, the situation is getting chaotic:

- nearly all universities impose entrance examination

- the dates of examinations and subjects tested varied

- many exams were still conducted by faculties, where even in one university different faculties might test different subjects

- there were large student intercity movements, as many of them want to enrol to more than one university in different cities

- this created hardship for high school leavers from outside Jawa, dues to bad transportation, mainly by ship

- to overcome this situation, students from outside Jawa who want to enrol to universities in Jawa usually enrol their last high school clas in Jawa

• This unhealthy situation got the attention of five This unhealthy situation got the attention of five prominent universities at that time. In 1975 the fiveprominent universities at that time. In 1975 the five

- Universitasf Indonesia (UI), Jakarta- Universitasf Indonesia (UI), Jakarta - Institut Pertanian Bogor (IPB), Bogor- Institut Pertanian Bogor (IPB), Bogor - Institut Teeknologi Bandung (ITB), Bandung- Institut Teeknologi Bandung (ITB), Bandung - Universitas Gadjah Mada (UGM), Yogyakarta- Universitas Gadjah Mada (UGM), Yogyakarta - Universitas Airlangga, (UNAIR), Surabaya- Universitas Airlangga, (UNAIR), Surabaya established a working group, known by its acronym established a working group, known by its acronym

SKALU (Sekretariat Koordinasi Antara Lima Universitas), SKALU (Sekretariat Koordinasi Antara Lima Universitas), Cooperational Secretariate of Five Universities.Cooperational Secretariate of Five Universities.

* Through SKALU, they agreed to hold their entrance * Through SKALU, they agreed to hold their entrance examination among them at the same time, where examination among them at the same time, where prospective students may put their choice of degree prospective students may put their choice of degree programs in any one of them.programs in any one of them.

• SKALU also standardize the types of subject to be tested SKALU also standardize the types of subject to be tested in the entrance examination, irrespective of the faculties, in the entrance examination, irrespective of the faculties, into just nine subjects:into just nine subjects:

- Indonesia Language- Indonesia Language

- English- English

- Mathematics- Mathematics

- Physics- Physics

- Chemistry- Chemistry

- Biology- Biology

- History- History

- Economics- Economics

- Geography- Geography

• Considering that all entrance tests that were administered Considering that all entrance tests that were administered by the various universities were all “home made”, hence not by the various universities were all “home made”, hence not suitable to be used as entrance examination, SKALU began suitable to be used as entrance examination, SKALU began to conduct training programs on how to make test and do to conduct training programs on how to make test and do educational measurement.educational measurement.

• Starting from SKALU exam of five universities, by the years, Starting from SKALU exam of five universities, by the years, it now becomes a national entrance examination, involving it now becomes a national entrance examination, involving all state universities (now around 50), with the same all state universities (now around 50), with the same standardized subject as agreed by SKALU.standardized subject as agreed by SKALU.

• Establishment of national entrance examination not only Establishment of national entrance examination not only rectivies academic problem, also equity problems.rectivies academic problem, also equity problems.

AAchievement vs Predictive Tests

The problems of testing which were conducted by the The problems of testing which were conducted by the universities, prior to SKALU exams, are mostly of the universities, prior to SKALU exams, are mostly of the type of type of achievement testachievement test, testing proficiency in one fiels , testing proficiency in one fiels of subject.of subject.

By doing this, the exams were just some kind of By doing this, the exams were just some kind of prerequisite tests, prerequisite tests, testing ability of subjects thought to be testing ability of subjects thought to be prerequisiteprerequisite to unversity courses. to unversity courses.

Entrance examination belongs to the type of Entrance examination belongs to the type of predictive predictive teststests, with the purpose of predicting prospective , with the purpose of predicting prospective students expected succes in the university.students expected succes in the university.

mesurementmesurement

educational process

PurposePurpose Measuring how much of the taught subjects are Measuring how much of the taught subjects are mastered after undergoing an educational/ mastered after undergoing an educational/ learning process learning process

Knowing how large learning objectives of the Knowing how large learning objectives of the course or educational process are metcourse or educational process are met

Achievement Test

TesTest aftert after educational educational proprocecesss.s.

TEST

educational processTEST

measurementmeasurement

PurposePurpose Measurng prospective intake’s academic potential Measurng prospective intake’s academic potential

needed to undergo the educational process. needed to undergo the educational process.

Predicting the degree of success of applicants in Predicting the degree of success of applicants in undergoing the educational process. undergoing the educational process.

Predictive Test

Test Test before entering educational before entering educational processprocess

AchievementAchievement tests are easy to construct, is it tests are easy to construct, is it comes after an education process. It is all about comes after an education process. It is all about what were the subject of the process.what were the subject of the process.

Predictive tests, being prior to an education process, cannot be based on subject of the coming process. Following the ETS, it should logically be an aptitude test, as shown in their SAT tests.

University entrance exams in Indonesia, historically, are subject based. To change it to become a predictive test, some changes has to be conducted, by introducing concepts related to aptitude tests.

BLOOM’S TAXONOMY

OF EDUCATIONAL OBJECTIVES

Cognitive

Ruang lingkupRuang lingkup Know.Know.

C1C1

Comp.Comp.

C2C2

Appl.Appl.

C3C3

Ana.Ana.

C4C4

SynthSynth

C5C5

Eval.Eval.

C6C6

JumlahJumlah

1.1.

2.2.

JUMLAHJUMLAH

FORMAT OF BLUEPRINT/GRID

Ruang lingkupRuang lingkup Know.Know.

C1C1

Comp.Comp.

C2C2

Appl.Appl.

C3C3

Ana.Ana.

C4C4

SynthSynth

C5C5

Eval.Eval.

C6C6

JumlahJumlah

1.1. MekanikaMekanika -- 44 88 -- 66 -- 1818

2. Kalor2. Kalor -- 22 44 -- 44 -- 1010

3. Getaran, 3. Getaran, Gelombang dan Gelombang dan BunyiBunyi

-- 44 44 -- 44 -- 1212

4. Cahaya4. Cahaya -- 22 66 -- 44 -- 1212

5. Listrik & Magnet5. Listrik & Magnet -- 66 66 -- 66 -- 1818

6. IPBA6. IPBA -- 22 22 -- 22 -- 66

7. Fisika Moderen7. Fisika Moderen -- 66 66 -- 44 -- 1616

8. Antar ruang 8. Antar ruang lingkuplingkup

-- 22 44 -- 22 -- 88

JUMLAHJUMLAH -- 2828 4040 -- 3232 -- 100100

PHYSICS GRID FOR 2008

Test pattern before 2009Test pattern before 2009

Using Using UMPTN/Sipenmaru pattern, consisting , consisting of : of :

Basic AbilityBasic Ability ( (Basic Mathematics , Indonesian Language, Basic Mathematics , Indonesian Language, English), 75 items, 180 min..English), 75 items, 180 min..

Science AbilityScience Ability ( (Mathematics in Science, Physics, Mathematics in Science, Physics, Chemistry, Biology, Integrated Science), 75 items, 120 min..Chemistry, Biology, Integrated Science), 75 items, 120 min..

Social Science AbilitySocial Science Ability ( (Economy, History, Economy, History, Geography, Integrated Social Science), 75 items, 90 min.Geography, Integrated Social Science), 75 items, 90 min.

Constituted out of individual test items, while Constituted out of individual test items, while keeping the whole test being predictivekeeping the whole test being predictive

Apabila pohon pisang dipangkas dekat tanah, maka pada tempat pemangkasan tersebut akan keluar air. Hal ini membuktikan bahwa air yang keluar itu disebabkan oleh adanya

(A) proses eliminasi.

(B) proses gutasi.

(C) peristiwa imbibisi.

(D) proses menitik.

(E) pengaruh tekanan akar.

Dua buah bola lampu masing-masing tertulis 60 watt 120 volt dan 40 watt 120 volt. Jika kedua bola lampu tersebut dihubungkan seri pada tegangan 120 volt maka jumlah daya pada kedua lampu tersebut adalah

(A) 100 w

(B) 50 w

(C) 24 w

(D) 20 w

(E) 18 w

------------

The problem of this type of test here is that it The problem of this type of test here is that it has boceme the meat of coaching industry has boceme the meat of coaching industry (bimbel in Indonesia). Their effectiveness as (bimbel in Indonesia). Their effectiveness as tests became quetionable.tests became quetionable.

The challenge is to construct a new test which The challenge is to construct a new test which could measure more than these single item could measure more than these single item predictive test, and be imune toward attacks by predictive test, and be imune toward attacks by coaching industry.coaching industry.

To that purpose we construct what we call as To that purpose we construct what we call as Curriculum Based Reasoning Test.Curriculum Based Reasoning Test.

Test pattern since 2009Test pattern since 2009Using Using Curriculum Based Reasoning TestCurriculum Based Reasoning Test, , consisting of the following sectionsconsisting of the following sections : :

Mathematics and LanguageMathematics and Language ((Mathematics, Indonesian Mathematics, Indonesian Language, English), 70 items, 120 min.Language, English), 70 items, 120 min.

ScienceScience (Mathematics in Science, Physics, Chemistry, Biology), (Mathematics in Science, Physics, Chemistry, Biology), 55 items, 90 min.55 items, 90 min.

Social ScienceSocial Science (Economy, History, Geography), 70 items, 90 (Economy, History, Geography), 70 items, 90 min.min.

Except for Mathematics and Language, the test Except for Mathematics and Language, the test are not divided and evaluated according to its are not divided and evaluated according to its components.components.

Characteristics of Reasoning TestCharacteristics of Reasoning Test

Questions for test itemsQuestions for test items : :

emphasising those needing reasoning to answeremphasising those needing reasoning to answer

avoiding recall questionsavoiding recall questions

Percentage of questions on reasoning abilityPercentage of questions on reasoning ability ::

CConstitute 2/3 of items in tests for Mathematics, Science and onstitute 2/3 of items in tests for Mathematics, Science and Social Science, based on Social Science, based on reading paragraphsreading paragraphs followed by 3 to 4 followed by 3 to 4 questions.questions.

Types of reading paragraphs :Types of reading paragraphs : - - representation of data from observations or experimentsrepresentation of data from observations or experiments - conclusions or results of investigations or obervations- conclusions or results of investigations or obervations - exposition of contradictory opinions- exposition of contradictory opinions

Reasoning abilities tested in Reasoning abilities tested in questions consists of:questions consists of:

- reading graphs or tables- reading graphs or tables

- using graphs or tables- using graphs or tables

- understanding the meaning of graphs or tables in relation - understanding the meaning of graphs or tables in relation to naration in readingsto naration in readings

- taking the next steps, e.g. exptrapolation or interpolation, - taking the next steps, e.g. exptrapolation or interpolation, in relation to data in readingin relation to data in reading

- understanding or identifying implications from information- understanding or identifying implications from information

- finding and doing analysis on similarities and - finding and doing analysis on similarities and discrepancies of arguments discrepancies of arguments

- identifying special information from reading - identifying special information from reading

Di bawah ini adalah contoh data pengukuran tekanan osmotik untuk larutan hemoglobin pada berbagai konsentrasi yang diukur pada dua suhu yang ber beda.

Gambar 2. Tekanan osmotik terhadap konsentrasi hemoglobin pada 25oC dan 50oC.

Berdasarkan grafik pada Gambar 2, beda tinggi Berdasarkan grafik pada Gambar 2, beda tinggi silinder osmometer (silinder osmometer (hh) ketika osmometer diisi dengan ) ketika osmometer diisi dengan larutan hemoglobin 0,3 g/L pada 25 oC adalah (Pada larutan hemoglobin 0,3 g/L pada 25 oC adalah (Pada 25 oC 25 oC air = 1 g/cm3)air = 1 g/cm3)

(A) 5 cm(A) 5 cm(B) 10 cm(B) 10 cm(C) 15 cm(C) 15 cm(D) 20 cm(D) 20 cm(E) 25 cm(E) 25 cm

Silinder diisi gas argon pada Silinder diisi gas argon pada suhu 300 K, volum 5 liter dan suhu 300 K, volum 5 liter dan tekanan 1 atmosfer. Dengan tekanan 1 atmosfer. Dengan menjaga suhu tetap ada 300K, menjaga suhu tetap ada 300K, tekanan dinaikkan dengan tekanan dinaikkan dengan menekan piston. Pengamatan menekan piston. Pengamatan tekanan dan volum gas adalah tekanan dan volum gas adalah seperti Tabel 1 berikut.seperti Tabel 1 berikut.

tekanan volum

1.0 5.0

1.5 3.3

2.0 2.5

2.5 2.0

Silinder diisi dengan gas X Silinder diisi dengan gas X yang mengalami dissosiasi , yang mengalami dissosiasi , dengan volum awal 5 liter, dengan volum awal 5 liter, tekanan awal 1 atmosfer dan tekanan awal 1 atmosfer dan suhu 300K. Pada suhu yang suhu 300K. Pada suhu yang dijaga tetap, tekanan gas dijaga tetap, tekanan gas dibesarkandengan menekan dibesarkandengan menekan piston. Pengamatan tekanan piston. Pengamatan tekanan dan volum adalah seperti pada dan volum adalah seperti pada Tabel 2 berikut.Tabel 2 berikut.

tekanan volum

1.0 5.0

1.5 3.2

2.0 2.3

2.5 1.8

Dari pengamatan di Tabel 2, Percobaan 2 menunjukkan Dari pengamatan di Tabel 2, Percobaan 2 menunjukkan bahwa dibanding data di Tabel 1, pada tekanan dan bahwa dibanding data di Tabel 1, pada tekanan dan suhu yang sama, volum sistem reaksi lebih kecil dari suhu yang sama, volum sistem reaksi lebih kecil dari volum gas tunggal. Hal ini disebabkan kenaikan tekanan volum gas tunggal. Hal ini disebabkan kenaikan tekanan menimbulkanmenimbulkan

(A) (A) penambahan jumlah molekul, karena pembesaran penambahan jumlah molekul, karena pembesaran hharga arga ..

(B (B penggeseran kesetimbangan ke kanan.penggeseran kesetimbangan ke kanan.

(C) (C) penurunan jumlah molekul, karena pengurangan penurunan jumlah molekul, karena pengurangan harga harga ..

(D) (D) pengecilan volum, karena kekenyalan campuran pengecilan volum, karena kekenyalan campuran tinggi.tinggi.

(E)(E) pengecilan ukuran dari molekul-molekulpengecilan ukuran dari molekul-molekul

(61) In one experiment, team leaders were shown different videos

designed to put them in certain moods, then they were told to lead

groups in tasks. (62) However, it turns out that for emotions to

spread, two people do not have to be in the same room. (63) They

do not even have to know each other. Emotions can be transmitted

through mass media and (64) must extend far beyond their

originators.

(62) The word “However” should be replaced by the following: __________. (A) unchanged (B) replaced by “Therefore” (C) replaced by “In addition” (D) replaced by “For example” (E) replaced by “Likewise”

POPULASI MUSIMAN

Populasi suatu spesies yang hidup di suatu lingkung an selalu berubah sepanjang

tahun berjalan. Berdasar kan data masa lalu puncak populasinya tercapai pada bulan

Januari. Kemudian turun dan paling rendah pada bulan Juli. Populasinya naik

kembali sampai mencapai puncaknya pada bulan Januari tahun beri kutnya, Proses

ini berlangsung terus dan berulang setiap tahun.

Suatu pengamatan dari bulan Januari 2008 sampai Ja nuari 2009 memberikan data

berikut.

Waktu Jan April Juli Okt Jan

2008 2008 2008 2008 2009

Populasi 3000 1900 1000 2050 3000

Pengamat ini memperkirakan suatu fungsi periodik sebagai hampiran untuk populasi

pada setiap saat t, yang aturannya adalah

P(t) = 2000 + 1000 cos 2 t, 0 ≤ t ≤ 1.

Untuk fungsi ini, t = 0 adalah awal Januari 2008 dan t = 1 adalah awal Januari 2009

dengan setiap bulan t naik sebesar.

POPULASI MUSIMAN

Populasi suatu spesies yang hidup di suatu lingkungan selalu berubah sepanjang tahun berjalan. Berdasarkan data masa lalu puncak populasinya tercapai pada bulan Januari. Kemudian turu

n dan paling rendah pada bulan Juli. Pop ulasinya naik kembali sampai mencapai puncaknya pada bulan Januari tahun berikutnya, Proses ini berlangsung terus dan berulang setiap tahun.

Suatu pengamatan dari bulan Januari 2008 sampai Januari 2009 memberikan data berikut.

Pengamat ini memperkirakan suatu fungsi periodik sebagai hampiran untuk populasi pada setiap saat t, yang aturannya adalah

P(t) = 2000 + 1000 cos 2p t, 0 £ t £ 1.

Untuk fungsi ini, t = 0 adalah awal Januari 2008 dan t = 1 adalah awal Januari 2009 dengan setiap bulan t naik sebesar .

Dengan menggunakan fungsi hampiran pada Bacaan 2, populasi Dengan menggunakan fungsi hampiran pada Bacaan 2, populasi spesies pada bulan Mei 2008 adalahspesies pada bulan Mei 2008 adalah

(A) 1200(A) 1200

(B) 1250(B) 1250

(C) 1350(C) 1350

(D) 1500(D) 1500

(E) 1600(E) 1600

Pada tahun 2008, laju penurunan yang paling besar terjadi pada bulan

(A) Pebruari

(B) Maret

(C) April

(D) Mei

(E) Juni

Scoring of testScoring of test

Using two types of score:Using two types of score:

RAW SCORE xRAW SCORE x. . Obtained directly from answering the multiple choice, according to:

- right +4

- wrong -1

- omit 0

NATIONAL SCORE N. Obtained by assigning score 500 to average raw acore <x> and 100 for every standard deviation . With z = (x - <x>)/, the national score is defined as

N = 500 + 100z

Academic decision are based on ranking of national score.

Statistical Meaning of National ScoreStatistical Meaning of National Score

N > 700 : belonging to uppest 2,3% in the national rankingN > 700 : belonging to uppest 2,3% in the national ranking

700 > N > 600 : belonging to the next 13,6% under700 > N > 600 : belonging to the next 13,6% under

600 > N > 500 : belonging to 34,1% above the national average600 > N > 500 : belonging to 34,1% above the national average

PPercentile Distribution ercentile Distribution of Raw Scores for two of Raw Scores for two

test batteriestest batteries

IPA (Science Set)

IPS (Social Science Set)

NN OmitOmit AA BB C*C* DD EE MMtottot PP++ RRbisbis

MMOO MMAA MMBB MMCC MMDD MMEE

2161921619 1052510525 17371737 20702070 27582758 25852585 19441944 13.0013.00 0.120.12 0.700.70

11.9711.97 12.3912.39 12.7012.70 17.5817.58 13.1513.15 12.6612.66

Garis x+y=4 memotong parabol y=4x-x2 di titik A dan B. Panjang ruas garis AB adalah

(A) 2

(B) 2√3

(C) 3√2

(D) 4

(E) 4√2

ITEM ANALYSIS

on a Test Item

NN OmitOmit A*A* BB CC DD EE MMtottot PP++ RRbisbis

MMOO MMAA MMBB MMCC MMDD MMEE

2705027050 71087108 80728072 76627662 17881788 19521952 468468 13.0013.00 0.290.29 0.200.20

12.7012.70 13.9313.93 12.7012.70 11.7811.78 12.6612.66 12.0412.04

Di daerah yang memiliki perbedaan yang besar antara suhu udara terendah dan suhu udara tertinggi, pelapukan batuan secara mekanik menjadi lebih mudah terjadi.

SEBAB

Batuan umumnya tersusun atas mineralmineral dengan koeffisien muai yang berbeda.

Evaluation of Test Item EffectivenesEvaluation of Test Item EffectivenesBased on two measured quantities, by item analysis by item analysis

p+ = fraction of testees answering rightp+ = fraction of testees answering right

Rbis = point-bisserial correlation, measure of discriminating powerRbis = point-bisserial correlation, measure of discriminating power

Data for all test items are presented in a scatter plot:Data for all test items are presented in a scatter plot:

Rbis

p+difficult easy

0,0

0,25

more selective

Rough relation between p+ and Rbis

Rbis

p+

Items too difficult, nobody can do right, useless as testing item

Items too easy, everybody can do right, useless as test item

Evaluasi TNBK 2013

Evaluasi TNBK 2012

Evaluasi TNBK 2013

Evaluasi TNBK 2012

Evaluasi TNBK 2013

Evaluasi TNBK 2012

Evaluasi TNBK 2013

Evaluasi TNBK 2012

Evaluasi TNBK 2013

Evaluasi TNBK 2012

Distribution of Distribution of Raw ScoreRaw Score

IPSIPS

• IPA

Distribution of Distribution of NaNattionalional Score Score

Two final question on this test;Two final question on this test;

• How long does it take to produce this How long does it take to produce this kind of test ?kind of test ?

* How much does it cost ?* How much does it cost ?

THANK YOU

Profil Nilai MentahProfil Nilai Mentah

SETSET SOALSOAL NN MeanMean SS.D.D MinMin MaxMax

IPA-AIPA-ASemuaSemua

123031230349,249,2 42,3742,37 -69-69 260260

AnchorAnchor 11,2711,27 11,3711,37 -25-25 6565

IPA-BIPA-BSemuaSemua

140661406654,9354,93 40,7240,72 -55-55 329329

AnchorAnchor 15,5915,59 12,0412,04 -30-30 7474

IPS-AIPS-ASemuaSemua

116601166038,2338,23 29,5929,59 -50-50 212212

AnchorAnchor 9,719,71 10,8210,82 -33-33 6464

IPS-BIPS-BSemuaSemua

145271452743,8343,83 28,7728,77 -54-54 217217

AnchorAnchor 12,6912,69 10,9610,96 -28-28 6262

Nilai Rata-rata Per PanlokNilai Rata-rata Per PanlokKode PL IPA IPS

11 Banda Aceh 452,59 473,7712 Medan-UNIMED 464,87 482,5813 Medan-USU 487,44 498,7814 Padang 520,99 519,7216 Pekanbaru 509,1 511,2217 Jambi 461,55 476,718 Palembang 540,6 533,0820 Bandar Lampung 533,93 512,4421 Jakarta 531,52 520,823 Bogor 535,45 535,9224 Bandung 537,45 535,0428 Serang Banten 479,32 493,729 Lhokseumawe 454,35 466,7333 Tangerang 525,24 514,6841 Purwokerto 516,99 531,9242 Semarang 542,4 542,1844 Surakarta 531,13 531,9248 Palangka Raya 450,87 468,7250 Tarakan 437,45 465,0771 Surabaya 572,1 548,4695 UT-Denpasar/Makassar 563,53 493,94

PERBANDINGAN DENGAN KINERJA TAHUN 2012

TERIMA KASIHTERIMA KASIH

Bacaan 2Bacaan 2

POPULASI MUSIMANPOPULASI MUSIMAN

Populasi suatu spesies yang hidup di suatu lingkung an selalu berubah sepanjang tahun berjalan. Populasi suatu spesies yang hidup di suatu lingkung an selalu berubah sepanjang tahun berjalan. Berdasar kan data masa lalu puncak populasinya tercapai pada bulan Januari. Kemudian turun Berdasar kan data masa lalu puncak populasinya tercapai pada bulan Januari. Kemudian turun dan paling rendah pada bulan Juli. Populasinya naik kembali sampai mencapai puncaknya dan paling rendah pada bulan Juli. Populasinya naik kembali sampai mencapai puncaknya pada bulan Januari tahun beri kutnya, Proses ini berlangsung terus dan berulang setiap tahun.pada bulan Januari tahun beri kutnya, Proses ini berlangsung terus dan berulang setiap tahun.

Suatu pengamatan dari bulan Januari 2008 sampai Ja nuari 2009 memberikan data berikut.Suatu pengamatan dari bulan Januari 2008 sampai Ja nuari 2009 memberikan data berikut.

Waktu Jan April Juli Okt JanWaktu Jan April Juli Okt Jan 2008 2008 2008 2008 20092008 2008 2008 2008 2009Populasi 3000 1900 1000 2050 3000Populasi 3000 1900 1000 2050 3000

Pengamat ini memperkirakan suatu fungsi periodik sebagai hampiran untuk populasi pada Pengamat ini memperkirakan suatu fungsi periodik sebagai hampiran untuk populasi pada setiap saat setiap saat tt, yang aturannya adalah, yang aturannya adalah

PP((tt) ) 2000 2000 1000 cos 2 1000 cos 2 t t, 0 , 0 tt 1. 1.

Untuk fungsi ini, Untuk fungsi ini, tt 0 adalah awal Januari 2008 dan 0 adalah awal Januari 2008 dan t t 1 adalah awal Januari 2009 dengan 1 adalah awal Januari 2009 dengan setiap bulan setiap bulan tt naik sebesar. naik sebesar.

Bacaan 2 untuk menjawab soal nomor 16 sampai 19Bacaan 2 untuk menjawab soal nomor 16 sampai 19 ..

16..Dengan menggunakan fungsi hampiran pada Bacaan 2, populasi spesies pada bulan Mei 16..Dengan menggunakan fungsi hampiran pada Bacaan 2, populasi spesies pada bulan Mei 2008 adalah2008 adalah

(A) 1200(A) 1200(B) 1250(B) 1250(C) 1350(C) 1350(D) 1500(D) 1500(E) 1600(E) 1600

17. Untuk bulan April 2008, jika 17. Untuk bulan April 2008, jika pp adalah data dari tabel pada Bacaan 2 dan adalah data dari tabel pada Bacaan 2 dan qq adalah nilai fungsi adalah nilai fungsi hampiran hampiran PP((tt), maka ), maka pp - - qq = =

(A) -150(A) -150(B) -100(B) -100(C) 0(C) 0(D) 100(D) 100(E) 150(E) 150