Multiplication II

We draw the circles below the numbers and subtract the numbers we are multiplying from 10. We write 4 and 3 in the circles. Our problem looks like this:

Now we subtract crossways: 3 from 6 or 4 from 7 is 3. We write 3 after the equals sign.

Four times 3 is 12, so we write 12 after the 3 for an answer of 312.

Is this the correct answer? No, obviously it isn’t.

answer

Let’s do the calculation again, this time using the reference number.


Th at’s more like it.

Test yourself

Try these problems using a reference number of 10:

a) 6 × 7 =

b) 7 × 5 =

c) 8 × 5 =

d) 8 × 4 =

e) 3 × 8 =

f) 6 × 5 =

The answers are:

a) 42                 b) 35             c) 40

d) 32                 e) 24             f) 30

What was our reference number for 96 × 97 in Chapter 1? One hundred, because we asked how many more do we need to make 100.

The problem worked out in full would look like this :

answer

Th e technique I explained for doing the calculations in your head actually makes you use this method. Let’s multiply 98 by 98 and you will see what I mean.

If you take 98 and 98 from 100 you get answers of 2 and 2. Then take 2 from 98, which gives an answer of 96. If you were saying the answer aloud, you would not say, “Ninety-six,” you would say, “Nine thousand, six hundred and . . .” Nine thousand, six hundred is the answer you get when you multiply 96 by the reference number, 100.

Now multiply the numbers in the circles: 2 times 2 is 4. You can now say the full answer: “Nine thousand, six hundred and four.” Without using the reference number we might have just written the 4 after 96.

Here is how the calculation looks written in full:

answer

Test yourself

Do these problems in your head:

a) 96 × 96 =

b) 97 × 97 =

c) 99 × 99 =

d) 95 × 95 =

e) 98 × 97 =

Your answers should be:

a) 9,216                        b) 9,409                         c) 9,801

d) 9,025                        e) 9,506

Multiplication I

Berapakah hasilnya?


berapakah nilai yang mendekati 10

Tulis dibawahnya dalam lingkaran. 10-7 = 3, dan 10-8 = 2. kemudian kurangkan secara silang untuk mendapatkan digit pertama yaitu 7-2 = 5 dan 8-3 = 5, maka digit pertama adalah 5 dan kemudian cari digit kedua dengan cara mengkalikan 3 x 2 = 6 maka hasil perkalian tersebut adalah 56


mari kita coba dengan nilai 8 x 9.


10-8 = 2 dan 10 - 9 = 1, kemudian cari digit pertama 8-1 = 7 dan 9-1 = 7 maka digit pertama adalah 7, untuk digit kedua kalikanlah 1 dan 2 sama dengan 2 maka hasil yang didapat adalah 72.
cobalah dengan nilai dibawah ini :

hasilnya adalah 81, 64, 49, 63, 72, 54, 45 dan 56. mudah bukan?

sekarang kita akan menggunakan angka yang lebih besar yaitu 96 x 97


sama dengan yang atas hanya saja pengurangnya adalah 100. 100-96 = 4 dan 100-97 = 3, sekarang dengan cara yang sama 96 - 3 = 93 dan 97 - 4 = 93 jadi digit awal adalah 93_ _ berapakah 2 digit terakhir caranya kalikan 4 x 3 = 12 maka didapatkan 9312

sekarang cobalah nilai dibawah ini


Hasilnya adalah 9,216, 9,215, 9,025, 9,310, 9,212, 9,118, 9,016, 9,021, 7,350.
pada soal terakhir juga harus di ingat bahwa pengurangnya adalah 100

semoga dapat membantu!!

Current State of Mobile Learning

JOHN TRAXLER ( UNIVERSITY OF WOLVERHAMPTON ; UNITED KINGDOM)

Since the start of the current millennium, experience and expertise in the development and delivery of mobile learning have blossomed and a community of practice has evolved that is distinct from the established communities of “tethered” e-learning. This community is currently visible mainly through dedicated international conference series, of which MLEARN is the most prestigious, rather than through any dedicated journals. So far, these forms of development and delivery have focused on short-term small-scale pilots and trials in the developed countries of Europe, North America, and the Pacifi c Rim, and there is a taxonomy emerging from these pilots and trials that suggests tacit and pragmatic conceptualisations of mobile learning. What has, however, developed less confi dently within this community is any theoretical conceptualisation of mobile learning and with it any evaluation methodologies specifically aligned to the unique attributes of mobile learning. Some advocates of mobile learning attempt to defi ne and conceptualize it in terms of devices and technologies; other advocates do so in terms of the mobility of learners and the mobility of learning, and in terms of the learners’ experience of learning with mobile devices.

Inilah Planet-planet Layak Huni

TEMPO.CO, Jakarta - Lebih dari 600 planet ekstrasolar telah ditemukan. Beberapa di antaranya memiliki kondisi yang sangat cocok untuk tempat persemaian kehidupan. Berikut beberapa planet yang mungkin menopang makhluk hidup.

1. Gliese 581d
Waktu penemuan: 24 April 2007
Massa: 5,6 massa Bumi
Periode orbit: 67 hari
 

Gliese 581d

Dari sudut pandang kosmis, planet yang terletak 20 tahun cahaya dari Bumi ini amat dekat. GLiese 581d memiliki posisi istimewa karena terletak di tepian zona layak huni bintang induknya, sebuah bintang katai merah.

Planet ini cukup hangat dan basah, sehingga menjadi lahan yang tepat untuk bersemainya kehidupan. Atmosfer karbon tebal mengelilingi planet ini dan memberikan perlindungan bagi permukaannya.

2. Gliese 581g
Waktu penemuan: 29 September 2010
Massa: 3,1 massa Bumi
Periode orbit: 36 hari

Bumi dan Gliese 581g

 Saat ditemukan tahun lalu Gliese 581g tampak sebagai kandidat terbaik untuk planet mirip Bumi. Planet ini berada dalam sistem yang sama dengan Gliese 581d yang telah diketahui sebelumnya. Planet bermassa tiga kali Bumi ini berada di dalam zona layak huni dan mungkin memiliki atmosfer.

Penelitian lebih lanjut menunjukkan jejak yang terekam pada penelitian sebelumnya bukan berasal dari planet baru. Karena itu diperkirakan planet ini mungkin tidak pernah ada.

3. GJ 1214b
Waktu penemuan: 16 Desember 2009
Massa: 6,5 massa Bumi
Periode orbit: 1,5 hari
 

GJ 1214b

Planet ini disebut-sebut sebagai "dunia air", dan terletak 42 tahun cahaya dari bumi. Sebuah bintang katai merah bermassa seperlima massa matahari bercokol di jantung sistem, memberikan energi bagi planet ini.

Keunikan planet ini adalah seluruh permukaannya digenangi oleh air. Permukaan air dikelilingi oleh atmosfer beruap yang tebal dan awan hidrogen. Perhitungan terhadap unsur kimia menunjukkan planet ini mungkin ditinggali kehidupan. Massa planet sebesar 6,5 kali Bumi dengan diameter 2,7 kali lebih besar membuat planet ini disebut sebagai superbumi.

4. HD 209458b (Osiris)
Waktu penemuan: 5 November 1999
Massa: 218 massa Bumi
Periode orbit: 3,5 hari
 

HD 209458b

Planet ini terjarak 150 tahun cahaya dari Bumi. Atmosfer yang mengelilinginya diperkirakan mengandung uap air dan beberapa elemen organik yang juga dimiliki Bumi purba. Elemen ini menjadi adonan penting dalam pembentukan kehidupan.

Sayangnya, planet ini sangat dekat dengan bintang induknya, sehingga terlalu panas untuk ditinggali. Pun dengan kondisi planet yang berupa gas, sehingga tidak memiliki daratan.

5. Kepler-10b
Waktu penemuan: 10 Januari 2011
Massa: 4,5 massa Bumi
Periode orbit: 20 jam

Kepler-10b 

Andai terletak sedikit lebih jauh dari bintang induk, Kepler-10b bisa saja menyimpan kehidupan. Planet yang ditemukan pada 2011 ini pernah disebut sebagai bukti bahwa planet batuan seperti Bumi bisa tercipta di sekitar bintang lain. Karena itu Kepler-10b juga menjadi mata rantai penelitian ilmu keplanetan.

Elemen pendukung kehidupan seperti air dan atmosfer tak berlimpah di planet ini. Kondisi ini membuat planet ini sulit menjadi tempat munculnya kehidupan.

6. HD 85512b
Waktu penemuan: 17 Agustus 2011
Massa: 3,6 massa Bumi
Periode orbit: 54 hari

HD 85512b

 Planet yang baru ditemukan ini terletak 36 tahun cahaya dari bumi. Massanya yang cukup moderat, yaitu 3,6 kali massa Bumi, membuat planet batuan ini bisa menyimpan atmosfer. Penelitian lebih jauh mengungkap H2O, CO2, dan N2 bisa muncul di atmosfer planet.

Jarak planet ke bintang induk juga berada di tepian zona layak huni. Banyaknya kondisi menguntungkan ini membuat planet HD 85512b sebagai tempat paling mungkin menyimpan kehidupan.

6. Kepler-22b
Waktu penemuan: Desember 2011
Massa: 2,4 massa Bumi


Hampir semua karakteristik Bumi ada pada Kepler-22b. Tak mengherankan bila pakar astronomi menjuluki planet baru ini sebagai kembaran Bumi.

Planet ini, yang ditemukan observatorium antariksa NASA, Kepler, mengitari satu bintang, yang juga amat mirip dengan matahari kita. Bintang ini tergolong sebagai bintang kelas G yang sangat mirip dengan matahari. Begitu pula dengan jarak antara bintang dan planetnya
 DISCOVERY | ANTON WILLIAM

ebook fisika

Fisika SMA kelas X

• Gerak Lurus Beraturan (GLB)
• Gerak Lurus Berubah Beraturan (GLBB)
• Gerak Melingkar Beraturan (GMB)
• Gaya Gesekan
• Hukum I Newton
• Hukum II Newton
• Hukum III Newton
• Hukum Newton pada Bidang Datar dan Bidang Miring
• Kalor dan Perubahan Wujud
• Asas Black
• Pemuaian
• Perpindahan Kalor

Fisika SMA kelas XI

• Gerak Parabola
• Gerak Melingkar
• Hukum Newton tentang Gravitasi
• Hukum Kepler
• Hukum Hooke dan Elastisitas
• Getaran
• Usaha dan Energi
• Momentum, Impuls dan Tumbukan
• Dinamika rotasi
• Keseimbangan benda tegar
• Fluida Statis
• Fluida Dinamis
• Teori Kinetik Gas
• Termodinamika

Presidential Percentages

Each U.S. President’s name in the Choice Box has a number beside it. Your task is to calculate the answers and place the president’s name in the puzzle that corresponds with the problem number and the number beside the president’s name.

Across

1. 35% of 798

3. 14% of 654

6. 75% of 720

9. 25% of 125

10. 75% of 860

13. 80% of 204

15. 24% of 175

16. 12.5% of 96

17. 145% of 327

Down

1. 225% of 454

2. 87.5% of 900

4. 5% of 24

5. 10% of 720

7. 647% of 94

8. 60% of 81

11. 20% of 67

12. 84% of 84

14. 89% of 45

Building Assembled in 6 Days

16-storey hotel build in six days

Watch as workers in China build The New Ark Hotel, breaking construction records by starting with an empty plot in Changsha and leaving the site with a 50m tall building in just 136 hours.

 

Developer Broad Sustainable Building, who worked until 10pm each night, say the five days and 16 hour construction time is thanks to the use of pre-fabricated parts.
The frame of the 50m building - which is built to withstand a magnitude nine earthquake - took just 46 hours to put together, with the building enclosure taking another 90.

Video

30-storey Chinese hotel built in 15 days

Chinese firm The Broad Group – the company that wowed the construction world last year when it build a 16-storey residential block in just five days – has done it again.
This time, the company has constructed a 30-storey, 17,000m² hotel tower on the shores of the Dongting Lake in China’s Hunan Province in just 15 days.
The building has been designed to withstand magnitude 9 earthquakes and is claimed to be five times more energy efficient than standard towers, both in construction and materials used, and in the energy required to maintain and run the building.

Video

Pasport - Jawapos 8 Agustus 2011

Setiap saat mulai perkuliahan, saya selalu bertanya kepada mahasiswa berapa orang yang sudah memiliki pasport. Tidak mengherankan, ternyata hanya sekitar 5% yang mengangkat tangan. Ketika ditanya berapa yang sudah pernah naik pesawat, jawabannya melonjak tajam. Hampir 90% mahasiswa saya sudah pernah melihat awan dari atas. Ini berarti mayoritas anak-anak kita hanyalah pelancong lokal. Maka, berbeda dengan kebanyakan dosen yang memberi tugas kertas berupa PR dan paper, di kelas-kelas yang saya asuh saya memulainya dengan memberi tugas mengurus pasport. Setiap mahasiswa harus memiliki "surat ijin memasuki dunia global.". Tanpa pasport manusia akan kesepian, cupet, terkurung dalam kesempitan, menjadi pemimpin yang steril. Dua minggu kemudian, mahasiswa sudah bisa berbangga karena punya pasport. Setelah itu mereka bertanya lagi, untuk apa pasport ini? Saya katakan, pergilah keluar negeri yang tak berbahasa Melayu. Tidak boleh ke Malaysia, Singapura, Timor Leste atau Brunei Darussalam. Pergilah sejauh yang mampu dan bisa dijangkau. "Uang untuk beli tiketnya bagaimana, pak?" Saya katakan saya tidak tahu. Dalam hidup ini, setahu saya hanya orang bodohlah yang selalu memulai pertanyaan hidup, apalagi memulai misi kehidupan dan tujuannya dari uang. Dan begitu seorang pemula bertanya uangnya dari mana, maka ia akan terbelenggu oleh constraint. Dan hampir pasti jawabannya hanyalah tidak ada uang, tidak bisa, dan tidak mungkin. Pertanyaan seperti itu tak hanya ada di kepala mahasiswa, melainkan juga para dosen steril yang kurang jalan-jalan. Bagi mereka yang tak pernah melihat dunia, luar negeri terasa jauh, mahal, mewah, menembus batas kewajaran dan buang-buang uang. Maka tak heran banyak dosen yang takut sekolah ke luar negeri sehingga memilih kuliah di almamaternya sendiri. Padahal dunia yang terbuka bisa membukakan sejuta kesempatan untuk maju. Anda bisa mendapatkan sesuatu yang yang terbayangkan, pengetahuan, teknologi, kedewasaan, dan wisdom. Namun beruntunglah, pertanyaan seperti itu tak pernah ada di kepala para pelancong, dan diantaranya adalah mahasiswa yang dikenal sebagai kelompok backpackers. Mereka adalah pemburu tiket dan penginapan super murah, menggendong ransel butut dan bersandal jepit, yang kalau kehabisan uang bekerja di warung sebagai pencuci piring. Perilaku melancong mereka sebenarnya tak ada bedanya dengan remaja-remaja Minang, Banjar, atau Bugis, yang merantau ke Pulau Jawa berbekal seadanya.Ini berarti tak banyak orang yang paham bahwa bepergian keluar negeri sudah tak semenyeramkan, sejauh, bahkan semewah di masa lalu. Seorang mahasiswa asal daerah yang saya dorong pergi jauh, sekarang malah rajin bepergian. Ia bergabung ke dalam kelompok PKI (Pedagang Kaki Lima Internasional) yang tugasnya memetakan pameran-pameran besar yang dikoordinasi pemerintah. Disana mereka membuka lapak, mengambil resiko, menjajakan aneka barang kerajinan, dan pulangnya mereka jalan-jalan, ikut kursus, dan membawa dolar. Saat diwisuda, ia menghampiri saya dengan menunjukkan pasportnya yang tertera stempel imigrasi dari 35 negara. Selain kaya teori, matanya tajam mengendus peluang dan rasa percaya tinggi. Saat teman-temannya yang lulus cum-laude masih mencari kerja, ia sudah menjadi eksekutif di sebuah perusahaan besar di luar negeri. The Next Convergence Dalam bukunya yang berjudul The Next Convergence, penerima hadiah Nobel ekonomi Michael Spence mengatakan, dunia tengah memasuki Abad Ke tiga dari Revolusi Industri. dan sejak tahun 1950, rata-rata pendapatan penduduk dunia telah meningkat dua puluh kali lipat. Maka kendati penduduk miskin masih banyak, adalah hal yang biasa kalau kita menemukan perempuan miskin-lulusan SD dari sebuah dusun di Madura bolak-balik Surabaya-Hongkong. Tetapi kita juga biasa menemukan mahasiswa yang hanya sibuk demo dan tak pernah keluar negeri sekalipun. Jangankan ke luar negeri, tahu harga tiket pesawat saja tidak, apalagi memiliki pasport.Maka bagi saya, penting bagi para pendidik untuk membawa anak-anak didiknya melihat dunia. Berbekal lima ratus ribu rupiah, anak-anak SD dari Pontianak dapat diajak menumpang bis melewati perbatasan Entekong memasuki Kuching. Dalam jarak tempuh sembilan jam mereka sudah mendapatkan pelajaran PPKN yang sangat penting, yaitu pupusnya kebangsaan karena kita kurang urus daerah perbatasan. Rumah-rumah kumuh, jalan berlubang, pedagang kecil yang tak diurus Pemda, dan infrastruktur yang buruk ada di bagian sini. Sedangkan hal sebaliknya ada di sisi seberang. Anak-anak yang melihat dunia akan terbuka matanya dan memakai nuraninya saat memimpin bangsa di masa depan. Di universitas Indonesia, setiap mahasiswa saya diwajibkan memiliki pasport dan melihat minimal satu negara. Dulu saya sendiri yang menjadi gembala sekaligus guide nya. Kami menembus Chiangmay dan menyaksikan penduduk miskin di Thailand dan Vietnam bertarung melawan arus globalisasi. Namun belakangan saya berubah pikiran, kalau diantar oleh dosennya, kapan memiliki keberanian dan inisiatif? Maka perjalanan penuh pertanyaan pun mereka jalani. Saat anak-anak Indonesia ketakutan tak bisa berbahasa Inggris, anak-anak Korea dan Jepang yang huruf tulisannya jauh lebih rumit dan pronounciation-nya sulit dimengerti menjelajahi dunia tanpa rasa takut. Uniknya, anak-anak didik saya yang sudah punya pasport itu 99% akhirnya dapat pergi keluar negeri. Sekali lagi, jangan tanya darimana uangnya. Mereka memutar otak untuk mendapatkan tiket, menabung, mencari losmen-losmen murah, menghubungi sponsor dan mengedarkan kotak sumbangan. Tentu saja, kalau kurang sedikit ya ditomboki dosennya sendiri. Namun harap dimaklumi, anak-anak didik saya yang wajahnya ndeso sekalipun kini dipasportnya tertera satu dua cap imigrasi luar negeri. Apakah mereka anak-anak orang kaya yang orangtuanya mampu membelikan mereka tiket? Tentu tidak. Di UI, sebagian mahasiswa kami adalah anak PNS, bahkan tidak jarang mereka anak petani dan nelayan. Tetapi mereka tak mau kalah dengan TKW yang meski tak sepandai mereka, kini sudah pandai berbahasa asing. Anak-anak yang ditugaskan ke luar negeri secara mandiri ternyata memiliki daya inovasi dan inisiatif yang tumbuh. Rasa percaya diri mereka bangkit. Sekembalinya dari luar negeri mereka membawa segudang pengalaman, cerita, gambar dan foto yang ternyata sangat membentuk visi mereka. Saya pikir ada baiknya para guru mulai membiasakan anak didiknya memiliki pasport. Pasport adalah tiket untuk melihat dunia, dan berawal dari pasport pulalah seorang santri dari Jawa Timur menjadi pengusaha di luar negeri. Di Italy saya bertemu Dewi Francesca, perempuan asal Bali yang memiliki kafe yang indah di Rocca di Papa. Dan karena pasport pulalah, Yohannes Surya mendapat bea siswa di Amerika Serikat. Ayo, jangan kalah dengan Gayus Tambunan atau Nazaruddin yang baru punya pasport dari uang negara. Rhenald Kasali Guru Besar Universitas Indonesia postingan ini diambil dari sini

Worksheet

For IX Grade all about Algebra

Numbers

• A.1Classify numbers
• A.2Compare and order rational numbers
• A.3Absolute value and opposites
• A.4Number lines
• A.5Convert between decimals and fractions
• A.6Square roots
• A.7Cube roots

Operations

• B.1Add, subtract, multiply, and divide integers
• B.2Order of operations with integers
• B.3Evaluate variable expressions involving integers
• B.4Add and subtract rational numbers
• B.5Multiply and divide rational numbers
• B.6Order of operations with rational numbers
• B.7Evaluate variable expressions involving rational numbers

Ratios and proportions

• C.1Identify equivalent ratios
• C.2Equivalent ratios: fill in the missing number
• C.3Unit rates
• C.4Unit prices
• C.5Solve proportions
• C.6Solve proportions: word problems
• C.7Scale drawings and scale factors

Percents

• D.1Convert between percents, fractions, and decimals
• D.2Solve percent equations
• D.3Percent word problems
• D.4Percent of change
• D.5Percent of change: word problems
• D.6Percent of a number: tax, discount, and more
• D.7Find the percent: tax, discount, and more
• D.8Multi-step problems with percents

Measurement

• E.1Convert rates and measurements: customary units
• E.2Convert rates and measurements: metric units
• E.3Unit prices with unit conversions
• E.4Precision
• E.5Greatest possible error
• E.6Minimum and maximum area and volume
• E.7Percent error
• E.8Percent error: area and volume

Geometry

• F.1Perimeter
• F.2Area
• F.3Volume
• F.4Surface area
• F.5Similar figures: side lengths and angle measures
• F.6Similar triangles and indirect measurement
• F.7Dilations and scale factors
• F.8Area and perimeter of similar figures
• F.9Similar solids
• F.10Volume and surface area of similar solids
• F.11Perimeter, area, and volume: changes in scale
• F.12Pythagorean theorem
• F.13Pythagorean theorem: word problems
• F.14Converse of the Pythagorean theorem: is it a right triangle?
• F.15Special right triangles

Coordinate graphs

• G.1Coordinate graph review
• G.2Midpoints
• G.3Distance between two points

Properties

• H.1Properties of addition and multiplication
• H.2Distributive property
• H.3Simplify variable expressions using properties
• H.4Properties of equality

Variable expressions and equations

• I.1Write variable expressions
• I.2Simplify variable expressions involving like terms and the distributive property
• I.3Write variable equations
• I.4Does x satisfy the equation?
• I.5Find solutions from a replacement set
• I.6Solve equations using order of operations

Solve equations

• J.1Model and solve equations using algebra tiles
• J.2Write and solve equations that represent diagrams
• J.3Solve one-step linear equations
• J.4Solve two-step linear equations
• J.5Solve advanced linear equations
• J.6Solve equations with variables on both sides
• J.7Identities and equations with no solutions
• J.8Solve linear equations: word problems
• J.9Solve linear equations: mixed review

Single-variable inequalities

• K.1Graph inequalities
• K.2Write inequalities from graphs
• K.3Identify solutions to inequalities
• K.4Solve one-step linear inequalities: addition and subtraction
• K.5Solve one-step linear inequalities: multiplication and division
• K.6Solve one-step linear inequalities
• K.7Graph solutions to one-step linear inequalities
• K.8Solve two-step linear inequalities
• K.9Graph solutions to two-step linear inequalities
• K.10Solve advanced linear inequalities
• K.11Graph solutions to advanced linear inequalities
• K.12Graph compound inequalities
• K.13Write compound inequalities from graphs
• K.14Solve compound inequalities
• K.15Graph solutions to compound inequalities

Absolute value equations and inequalities

• L.1Solve absolute value equations
• L.2Graph solutions to absolute value equations
• L.3Solve absolute value inequalities
• L.4Graph solutions to absolute value inequalities

Matrices

• M.1Matrix vocabulary
• M.2Matrix operation rules
• M.3Add and subtract matrices
• M.4Multiply a matrix by a scalar
• M.5Multiply two matrices

Charts and graphs

• N.1Interpret bar graphs, line graphs, and histograms
• N.2Create bar graphs, line graphs, and histograms
• N.3Circle graphs
• N.4Interpret stem-and-leaf plots
• N.5Interpret box-and-whisker plots
• N.6Interpret a scatter plot
• N.7Scatter plots: line of best fit

Problem solving

• O.1Word problems: mixed review
• O.2Word problems with money
• O.3Consecutive integer problems
• O.4Rate of travel: word problems
• O.5Weighted averages: word problems

Number sequences

• P.1Identify arithmetic and geometric sequences
• P.2Arithmetic sequences
• P.3Geometric sequences
• P.4Evaluate variable expressions for number sequences
• P.5Write variable expressions for arithmetic sequences
• P.6Write variable expressions for geometric sequences
• P.7Number sequences: mixed review

Relations and functions

• Q.1Relations: convert between tables, graphs, mappings, and lists of points
• Q.2Domain and range of relations
• Q.3Identify independent and dependent variables
• Q.4Identify functions
• Q.5Identify functions: vertical line test
• Q.6Complete a function table
• Q.7Evaluate function rules I
• Q.8Evaluate function rules II
• Q.9Graph a function
• Q.10Write a function rule: word problems
• Q.11Find points on a function graph
• Q.12Write a rule for a function table

Direct and inverse variation

• R.1Identify proportional relationships
• R.2Find the constant of variation
• R.3Graph a proportional relationship
• R.4Write direct variation equations
• R.5Write and solve direct variation equations
• R.6Identify direct variation and inverse variation
• R.7Write inverse variation equations
• R.8Write and solve inverse variation equations

Linear functions

• S.1Identify linear functions
• S.2Find the slope of a graph
• S.3Find slope from two points
• S.4Slope-intercept form: find slope and y-intercept
• S.5Slope-intercept form: graph an equation
• S.6Slope-intercept form: write an equation from a graph
• S.7Slope-intercept form: write an equation
• S.8Linear function word problems
• S.9Write equations in standard form
• S.10Standard form: find x- and y-intercepts
• S.11Standard form: graph an equation
• S.12Equations of horizontal and vertical lines
• S.13Graph a horizontal or vertical line
• S.14Point-slope form: graph an equation
• S.15Point-slope form: write an equation from a graph
• S.16Point-slope form: write an equation
• S.17Slopes of parallel and perpendicular lines
• S.18Write an equation for a parallel or perpendicular line

Linear inequalities

• T.1Does (x, y) satisfy the inequality?
• T.2Linear inequalities: solve for y
• T.3Graph a linear inequality in two variables
• T.4Linear inequalities: word problems
• T.5Is (x, y) a solution to the system of inequalities?

Systems of linear equations

• U.1Is (x, y) a solution to the system of equations?
• U.2Solve a system of equations by graphing
• U.3Solve a system of equations by graphing: word problems
• U.4Find the number of solutions to a system of equations by graphing
• U.5Find the number of solutions to a system of equations
• U.6Classify a system of equations by graphing
• U.7Classify a system of equations
• U.8Solve a system of equations using substitution
• U.9Solve a system of equations using substitution: word problems
• U.10Solve a system of equations using elimination
• U.11Solve a system of equations using elimination: word problems
• U.12Solve a system of equations using augmented matrices
• U.13Solve a system of equations using augmented matrices: word problems
• U.14Solve a system of equations using any method
• U.15Solve a system of equations using any method: word problems

Exponents

• V.1Exponents with integer bases
• V.2Exponents with decimal and fractional bases
• V.3Negative exponents
• V.4Multiplication with exponents
• V.5Division with exponents
• V.6Multiplication and division with exponents
• V.7Power rule
• V.8Simplify expressions involving exponents

Scientific notation

• W.1Convert between standard and scientific notation
• W.2Compare numbers written in scientific notation
• W.3Multiply numbers written in scientific notation
• W.4Divide numbers written in scientific notation

Exponential functions

• X.1Evaluate an exponential function
• X.2Match exponential functions and graphs
• X.3Exponential growth and decay: word problems

Monomials

• Y.1Identify monomials
• Y.2Multiply monomials
• Y.3Divide monomials
• Y.4Multiply and divide monomials
• Y.5Powers of monomials

Polynomials

• Z.1Polynomial vocabulary
• Z.2Model polynomials with algebra tiles
• Z.3Add and subtract polynomials using algebra tiles
• Z.4Add and subtract polynomials
• Z.5Add polynomials to find perimeter
• Z.6Multiply a polynomial by a monomial
• Z.7Multiply two polynomials using algebra tiles
• Z.8Multiply two binomials
• Z.9Multiply two binomials: special cases
• Z.10Multiply polynomials

Factoring

• AA.1GCF of monomials
• AA.2Factor out a monomial
• AA.3Factor quadratics with leading coefficient 1
• AA.4Factor quadratics with other leading coefficients
• AA.5Factor quadratics: special cases
• AA.6Factor by grouping
• AA.7Factor polynomials

Quadratic equations

• BB.1Characteristics of quadratic functions
• BB.2Solve a quadratic equation using square roots
• BB.3Solve an equation using the zero product property
• BB.4Solve a quadratic equation by factoring
• BB.5Complete the square
• BB.6Solve a quadratic equation by completing the square
• BB.7Solve a quadratic equation using the quadratic formula
• BB.8Using the discriminant

Functions: linear, quadratic, exponential

• CC.1Identify linear, quadratic, and exponential functions from graphs
• CC.2Identify linear, quadratic, and exponential functions from tables
• CC.3Write linear, quadratic, and exponential functions

Absolute value functions

• DD.1Complete a function table: absolute value functions
• DD.2Domain and range of absolute value functions

Radical expressions

• EE.1Simplify radical expressions
• EE.2Simplify radical expressions by rationalizing the denominator
• EE.3Multiply radical expressions
• EE.4Add and subtract radical expressions
• EE.5Simplify radical expressions using the distributive property
• EE.6Simplify radical expressions: mixed review

Radical functions and equations

• FF.1Evaluate a radical function
• FF.2Domain and range of radical functions
• FF.3Solve radical equations I
• FF.4Solve radical equations II

Rational functions and expressions

• GG.1Rational functions: asymptotes and excluded values
• GG.2Simplify complex fractions
• GG.3Simplify rational expressions
• GG.4Multiply and divide rational expressions
• GG.5Divide polynomials
• GG.6Add and subtract rational expressions
• GG.7Solve rational equations

Logic

• HH.1Identify hypotheses and conclusions
• HH.2Counterexamples

Probability

• II.1Theoretical probability
• II.2Experimental probability
• II.3Compound events: find the number of outcomes
• II.4Identify independent and dependent events
• II.5Probability of independent and dependent events
• II.6Permutations
• II.7Combinations
• II.8Permutation and combination notation

Statistics

• JJ.1Mean, median, mode, and range
• JJ.2Quartiles
• JJ.3Identifying biased samples
• JJ.4Mean absolute deviation
• JJ.5Variance and standard deviation

Mobile and Personal Communication : Past, Present and Future

PAST
From the introduction of public mobile radio in the United States in 1946 until the first analog cellular system went into operation in Chicago in 1983,mobile radio systems were based on the trunking principle. In other words,the available frequency spectrum (in the 150 or 450 MHz band) was divided into a suitable number of frequency channels. A centralized, high power antenna was used to transmit signals to mobile receivers. Large mobile receivers were installed in automobiles (in the trunks), and the telephone sets also were rather large. A call originating from or terminating on a mobile terminal had to compete for one of the limited number of channels. The quality of service in terms of call blocking probabilities was very high—in the order of 20-25%. However, the users were willing to trade off the convenience of mobility against the poor quality of service in terms of call blocking and received signal quality. These systems were also severely limited in terms of capacity and coverage.

To alleviate the high blocking problem in the early systems, efforts were made to allow call originations from the mobile telephones to wait for a free channel. In the so-called automated mobile telephone system (AMTS), the mobile telephone user would key in the called number and press the send button. The receiver system would then start scanning for an idle channel by cycling through all the channels in the system. In some systems, the number of scan cycles was restricted, so that if an idle channel was not found within the allowed number of scans, the call would be blocked. However, incoming calls to mobile terminals (mostly originating from fixed terminals in public switched telephone networks) had no mechanism for awaiting a free channel and were blocked on all-channels-busy condition. Though the improvement in the quality of service in these systems was only marginal, they did provide some interesting performance modeling problems

PRESENT
Since the initial commercial introduction of advanced mobile phone system (AMPS) service in 1983, mobile communications has seen an explosive growth worldwide. Besides the frequency reuse capabilities provided by the cellular operation, advances in technologies for wireless access, digital signal processing, integrated circuits, and increased battery life have contributed to exponential growth in mobile and personal communication services. Systems are evolving to address a range of applications and markets, which include digital cellular, cordless telephony, satellite mobile, and paging and specialized mobile radio systems. Data capabilities of these systems are also coming into focus with the increasing user requirements for mobile data communications, driven by the need for e-mail and Internet access. Whereas the analog cellular mobile systems fall in the category of first-generation mobile systems, the digital cellular, low power wireless, and personal communication systems are now perceived as second-generation mobile/PCS systems.

The first digital cellular system specification was released in 1990 by the European Telecommunications (ETSI) for the global system for mobile communication (GSM) system. The GSM, DCS 1800 (1800 MHz version of GSM), and DECT (digital enhanced cordless telecommunications) systems developed by ETSI form the basis for mobile and personal communication services not only in Europe but in many other parts of the world including North America. The number of GSM subscribers worldwide exceeds 100 million and is growing rapidly.

FUTURE
To complement the cellular and personal communication networks, whose radio coverage will be confined to populated areas of the world (less than 15% of the earth's surface), a number of global mobile satellite systems are in advanced stages of planning and implementation. These systems are generally referred as global mobile personal communications by satellites (GMPCS).GMPCS systems like Iridium, Globalstar, and ICO use constellations of low earth orbit (LEO) or medium earth orbit (MEO) satellites and operate as overlay networks for existing cellular and PCS networks. Using dual-mode terminals, they will extend the coverage of cellular and PCS networks to any and all locations on the earth's surface. On the other hand, a LEO satellite system like Teledesic aims to provide high capacity satellite links to enable delivery of high bitrate and multimedia services to every location on the earth.
International Mobile Telecommunications -2000 (IMT-2000) is the standard being developed by the ITU to set the stage for the third generation of mobile communication systems. The IMT-2000 standard not only will consolidate under a single standard different wireless environments (cellular mobile, cordless telephony, satellite mobile services), but will also ensure global mobility in terms of global seamless roaming and delivery of services. ETSI is also developing a third-generation mobile communication system called Universal Mobile Telecommunication System (UMTS), which will belong to the family of IMT-2000 systems.