የምዕራፍ ማስታወሻዎችና የመልመጃ ጥያቄዎች
በዚህ ገጽ ያለው ሁሉ ለ11ኛ ክፍል የሒሳብ መፅሐፍ ምዕራፍ 8 ነው፦ ምዕራፉ የሚሸፍነው፣ አጭር ማስታወሻዎቹ፣ የመልመጃ ጥያቄዎች ከመልሶቻቸው ጋር፣ እና ቪዲዮ ባለበት የትምህርቱ ቪዲዮ።
በዚህ ምዕራፍ ላይ የተጻፉ 10 የምርጫ ጥያቄዎች፣ እያንዳንዳቸው መልሱና ምክንያቱ አላቸው። መልሱን ከመክፈትዎ በፊት ይሞክሩ። ጥያቄዎቹ በእንግሊዝኛ ናቸው።
ጥያቄ 1
A fair die is rolled once. How many outcomes are in the event of getting an odd number?
መልስ፦ B 3
ምክንያቱ
The event of getting an odd number is {1, 3, 5}. This event has 3 outcomes. The sample space {1, 2, 3, 4, 5, 6} has 6 outcomes, but the question asks only about the odd numbers.
ጥያቄ 2
A fair coin is tossed three times. How many outcomes are in the sample space?
መልስ፦ C 8
ምክንያቱ
The textbook lists the sample space as HHH, HHT, HTH, THH, TTH, THT, HTT and TTT. That is 8 outcomes. Each toss has 2 results, so 2 x 2 x 2 = 8.
ጥያቄ 3
A coin is tossed and a die is rolled at the same time. How many possible outcomes are there for this sequence of events?
መልስ፦ C 12
ምክንያቱ
A coin has 2 outcomes (H and T) and a die has 6 outcomes (1 to 6). By the multiplication principle, 2 x 6 = 12 possible outcomes.
ጥያቄ 4
When a die is rolled, the event of getting an odd number is which type of event?
መልስ፦ B Compound event
ምክንያቱ
A simple event has only one sample element. A compound event has more than one. The event of getting an odd number is {1, 3, 5}, which has three elements, so it is a compound event.
ጥያቄ 5
Tigist is choosing an outfit. She has 5 different pairs of pants, 4 different skirts and 12 different T-shirts. She wears either pants or a skirt, and always wears a T-shirt. How many outfits are possible?
መልስ፦ D 108
ምክንያቱ
Pants with a T-shirt give 5 x 12 = 60 outfits. Skirts with a T-shirt give 4 x 12 = 48 outfits. Because she cannot wear pants and a skirt together, we add: 60 + 48 = 108.
ጥያቄ 6
In how many ways can five people be seated at a round table?
መልስ፦ B 24
ምክንያቱ
For circular arrangements, the number of permutations of n elements in a circle is (n - 1)!. Here n = 5, so (5 - 1)! = 4! = 4 x 3 x 2 x 1 = 24.
ጥያቄ 7
Compute P(7, 4).
መልስ፦ C 840
ምክንያቱ
P(n, r) = n! / (n - r)!. So P(7, 4) = 7! / 3! = 7 x 6 x 5 x 4 = 840.
ጥያቄ 8
Using Pascal's triangle, what is the coefficient of a2b2 in the expansion of (a + b)4?
መልስ፦ B 6
ምክንያቱ
The row for n = 4 in Pascal's triangle is 1, 4, 6, 4, 1. The expansion is a4 + 4a3b + 6a2b2 + 4ab3 + b4. The coefficient of a2b2 is 6.
ጥያቄ 9
How many different permutations can be made from the letters of the word ADDIS if the arrangement must start with the letter S?
መልስ፦ A 12
ምክንያቱ
If S is fixed as the first letter, four letters remain: A, D, D and I. There are 2 D's, so the number of arrangements is 4! / 2! = 24 / 2 = 12. The textbook lists these 12 arrangements.
ጥያቄ 10
In an HIV/AIDS club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different committees are possible?
መልስ፦ D 350
ምክንያቱ
The 3 women can be chosen from 7 in C(7, 3) = 35 ways. The 2 men can be chosen from 5 in C(5, 2) = 10 ways. Because the women and men are chosen separately, we multiply: 35 x 10 = 350.
መተግበሪያው በዚህ ምዕራፍ ላይ 12 ጥያቄዎች አሉት፤ እየሠሩ ያርምዎታል። እዚህ ያሉት የመጀመሪያዎቹ 10 ናቸው።
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