Yaadannoo boqonnaa fi gaaffii shaakalaa
Wanti fuula kana irra jiru hundi boqonnaa 3 kitaaba Herrega kutaa 11 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.
Kaardiiwwan fuula Herrega kutaa 11 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.
| Hojii | Adeemsa |
|---|---|
| Swapping | Rowwwan matrix lama wal jijjiiruu. |
| Scaling | Row matrix tokko constant zeeroo hin taaneen baayyisuu. |
| Pivoting | Dacha constant row tokkoo gara row kan biraatti dabaluu. |
Yoom akka itti fayyadamtu
Maatriksii tokko gara bifa tarree sirreeffamaatti jijjiiruuf hojiiwwan seera qabeeyyii kanneenitti fayyadamaa.
Grade 11 Mathematics, fuula 131-206 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Garagaltoo baayata iskweer maatriksotaa shallaguuf seerata kanatti fayyadamaa.
Of eeggadhu
Tartiibni maatriksotaa garagaltoo keessatti ni jijjiirama. Tartiiba osoo hin jijjiirin babalisuun dogoggora.
Grade 11 Mathematics, fuula 131-206 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Garagaltoo iskweer maatriksii barbaaduuf yookiin maatriksiin sun garagalfamuu danda'uu isaa mirkaneessuuf itti fayyadamaa.
Of eeggadhu
Tarreen maatriksii bitaa hundi eeroo ta'e yoo dhufe, maatriksiin sun siingulaarii dha, garagaltoo hin qabu.
Grade 11 Mathematics, fuula 131-206 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
| Gosa Maatriksii | Ulaagaa |
|---|---|
| Diagonal | Entries main diagonal ala jiran hundi zero dha. |
| Scalar | Diagonal matrix diagonal entries hundi walqixa ta'an. |
| Identity | Diagonal matrix diagonal entries hundi 1 ta'an. |
| Upper Triangular | Entries main diagonal gadi jiran hundi zero dha. |
| Lower Triangular | Entries main diagonal oli jiran hundi zero dha. |
Yoom akka itti fayyadamtu
Iskweer maatriksota qindoomina daayagonoolii fi eeroo isaanii irratti hundaa'uun adda baasuuf itti fayyadamaa.
Grade 11 Mathematics, fuula 131-206 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.
Gaaffii 1
What is the y-intercept of the graph of the rational function g(x) = (x + 1) / (x2 + 5x + 6)?
Deebii: A (0, 1/6)
Sababa
To find the y-intercept, evaluate the function at x = 0: g(0) = (0 + 1) / (02 + 5(0) + 6) = 1/6. Therefore, the y-intercept is (0, 1/6).
Gaaffii 2
Person A plants 50 flower bulbs in 2 hours, and Person B plants 45 flower bulbs in 3 hours. How many bulbs do they plant together in 1 hour?
Deebii: B 40 bulbs
Sababa
Person A plants 50 / 2 = 25 bulbs per hour. Person B plants 45 / 3 = 15 bulbs per hour. Working together, they plant 25 + 15 = 40 bulbs per hour.
Gaaffii 3
Legesse bought 150 USD with 7,500 Birr. At this same rate, how many USD can he buy with 30,000 Birr?
Deebii: C 600 USD
Sababa
Set up the proportion: 150 / 7500 = x / 30000. Solving for x gives x = (150 / 7500) * 30000 = 600 USD.
Gaaffii 4
The ratio of boys to girls in a high school is 4 : 5. If the total number of students in the school is 1,260, how many boys are in the school?
Deebii: B 560
Sababa
The total ratio parts are 4 + 5 = 9. The number of boys is (4 / 9) * 1260 = 560.
Gaaffii 5
A sample of 80 g of ice cream contains 15 g of fat. How many grams of fat are contained in 350 g of the same ice cream?
Deebii: C 65.625 g
Sababa
Set up the rational equation: x / 350 = 15 / 80. Solving for x gives x = (15 / 80) * 350 = 65.625 grams.
Gaaffii 6
What is the horizontal asymptote of the rational function h(x) = x2 / (x2 + 3x + 2)?
Deebii: B y = 1
Sababa
Since the degree of the numerator (2) is equal to the degree of the denominator (2), the horizontal asymptote is the ratio of their leading coefficients: y = 1 / 1 = 1.
Gaaffii 7
In the morning, a building that is 20 meters tall casts a shadow 15 meters long. How long is the shadow of a tree that is 10 meters tall at the same time?
Deebii: B 7.5 meters
Sababa
Using the proportion of shadow length to height: shadow / 10 = 15 / 20. Solving gives shadow = (15 / 20) * 10 = 7.5 meters.
Gaaffii 8
Two gardeners plant bulbs together at a combined rate of 40 bulbs per hour. Using the work formula W = r * t, how many hours will it take them to plant 160 bulbs?
Deebii: C 4 hours
Sababa
From W = r * t, we have t = W / r = 160 / 40 = 4 hours.
Gaaffii 9
What is the equation of the oblique asymptote to the graph of l(x) = (x3 + 1) / (x2 + 4x + 4)?
Deebii: A y = x - 4
Sababa
Using polynomial long division, dividing x3 + 1 by x2 + 4x + 4 gives a quotient of x - 4 plus a remainder of 12x + 17. Therefore, the oblique asymptote is y = x - 4.
Gaaffii 10
A mixing tank starts with 100 gallons of water and 5 pounds of sugar. Water is added at 10 gallons per minute, and sugar is added at 1 pound per minute. What is the concentration of sugar in pounds per gallon after 10 minutes?
Deebii: B 0.075 pounds per gallon
Sababa
The concentration function is C(t) = (5 + t) / (100 + 10t). At t = 10, C(10) = (5 + 10) / (100 + 10(10)) = 15 / 200 = 0.075 pounds per gallon.
Appiin boqonnaa kana irratti gaaffii 23 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.
Boqonnaan 3 Maxxansa Ministeera Barnootaa keessatti fuula 131 hanga fuula 206 ti.
Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 494
Temari boqonnaa kana gara shaakala yeroon daangeffametti jijjiira; utuu hojjettuu ni sirreessa; wanti si hin galinis barsiisaa AI tiin ni ibsama.
Bilisaan jalqabi
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