Yaadannoo boqonnaa fi gaaffii shaakalaa
Wanti fuula kana irra jiru hundi boqonnaa 2 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.
Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.
Yoom akka itti fayyadamtu
Yeroo lakkoofsota lakkaawwii lama walitti qooddu bu'aa fi haftee adda baasuuf itti fayyadami.
Of eeggadhu
Hafteen r yeroo hunda 0 <= r < b ta'uu qaba. Lakkoofsa qoodu b caaluu yookiin lakkoofsa negatiivii ta'uu hin danda'u.
Grade 9 Mathematics, fuula 1-86 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Yeroo baay'ata lakkoofsota lamaa fi GCF yookiin LCM isaanii beektee isa hafe barbaaddu fayyadami.
Of eeggadhu
Seerri kun kan hojjetu lakkoofsota lama qofaafi. Lakkoofsota sadii fi isaa oliif hin hojjetu.
Grade 9 Mathematics, fuula 1-86 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Hundee lakkoofsotaa salphisuuf fi yeroo hundee lakkoofsa wal-fakkaatan walitti iddistu yookiin hir'istu fayyadami.
Of eeggadhu
Hundee lakkoofsaa walitti idduun kan danda'amu yoo lakkoofsi hundee keessaa wal fakkaate qofaadha.
Grade 9 Mathematics, fuula 1-86 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
Which of the following numbers is irrational?
Deebii: C √7
Sababa
7 is not a perfect square, so √7 has a decimal that never ends and never repeats. √16 equals 4, which is rational. A repeating decimal is always rational, so 0.3333... is 1/3. And 22/7 is a fraction, so it is rational, even though it is often used as an approximation for π.
Gaaffii 2
Simplify √50.
Deebii: B 5√2
Sababa
Split 50 into a perfect square times something else: 50 = 25 x 2. Then √50 = √25 x √2 = 5√2. Option A comes from forgetting to take the square root of 25.
Gaaffii 3
Write 0.363636... as a fraction in lowest terms.
Deebii: B 4/11
Sababa
Let x = 0.363636... Two digits repeat, so 100x = 36.363636... Subtracting gives 99x = 36, so x = 36/99. Divide top and bottom by 9 to get 4/11. Option A is right before simplifying, and the question asks for lowest terms.
Gaaffii 4
Rationalise the denominator of 6/√3.
Deebii: A 2√3
Sababa
Multiply top and bottom by √3: (6 x √3) / (√3 x √3) = 6√3 / 3 = 2√3. Option B forgets to divide by the 3 that appears in the denominator.
Gaaffii 5
What is the highest common factor of 36 and 60?
Deebii: B 12
Sababa
36 = 2² x 3² and 60 = 2² x 3 x 5. Take the shared primes at their lowest powers: 2² x 3 = 12. Option D is the lowest common multiple, which takes the highest power of every prime instead.
Gaaffii 6
Express 0.00056 in scientific notation.
Deebii: A 5.6 x 10⁻⁴
Sababa
Move the point four places to the right to reach 5.6, so the power is negative four. Options C and D have the right value but the wrong form, because scientific notation needs the first number to be at least 1 and below 10.
Gaaffii 7
Simplify 3√2 + 5√2 - √2.
Deebii: A 7√2
Sababa
Like surds add and subtract the way like terms do in algebra: 3 + 5 - 1 = 7, so the answer is 7√2. Option B forgets to subtract the last term, which counts as 1√2.
Gaaffii 8
Which set contains every rational and every irrational number?
Deebii: C The real numbers
Sababa
The real numbers are defined as the rationals together with the irrationals. The integers, naturals and whole numbers are all subsets of the rationals, so none of them can contain √2.
Gaaffii 9
Rationalise the denominator of 1/(4 + √3).
Deebii: A (4 - √3) / 13
Sababa
Multiply top and bottom by the conjugate 4 - √3. The denominator becomes 4² - (√3)² = 16 - 3 = 13, so the answer is (4 - √3) / 13. Option B uses the same sign instead of the conjugate, which leaves a surd in the denominator.
Gaaffii 10
Round 0.0045678 to three significant figures.
Deebii: B 0.00457
Sababa
Leading zeros are not significant, so the figures start at 4. The first three are 4, 5 and 6, and the next digit is 7, which rounds the 6 up to 7. That gives 0.00457. Option C keeps the 6 without rounding.
Boqonnaan 2 Maxxansa Ministeera Barnootaa keessatti fuula 17 hanga fuula 86 ti.
Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 337
Temari boqonnaa kana gara shaakala yeroon daangeffametti jijjiira; utuu hojjettuu ni sirreessa; wanti si hin galinis barsiisaa AI tiin ni ibsama.
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