Before the test get acquainted with time management during the test:
Eliminating wrong answers.
Substituting data - a reversed method of finding solution.
Estimating data.
Finding the solution and indicating the correct answer.
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Exercise 1
Wersja alternatywna ćwiczenia: Two coins are thrown at the same time. How many possibilities are there? Możliwe odpowiedzi: 1. 4, 2. 8, 3. 6, 4. 3
Wersja alternatywna ćwiczenia: Two coins are thrown at the same time. How many possibilities are there? Możliwe odpowiedzi: 1. 4, 2. 8, 3. 6, 4. 3
Two coins are thrown at the same time. How many possibilities are there?
4
8
6
3
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Exercise 2
Wersja alternatywna ćwiczenia: A coin and a dice are thrown. How many possibilities are there? Możliwe odpowiedzi: 1. 12, 2. 24, 3. 4, 4. 8
Wersja alternatywna ćwiczenia: A coin and a dice are thrown. How many possibilities are there? Możliwe odpowiedzi: 1. 12, 2. 24, 3. 4, 4. 8
A coin and a dice are thrown. How many possibilities are there?
12
24
4
8
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Exercise 3
Wersja alternatywna ćwiczenia: Four dices are thrown. How many possibilities are there? Możliwe odpowiedzi: 1. , 2. , 3. 24, 4. 10
Wersja alternatywna ćwiczenia: Four dices are thrown. How many possibilities are there? Możliwe odpowiedzi: 1. , 2. , 3. 24, 4. 10
Four dices are thrown. How many possibilities are there?
24
10
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Exercise 4
Wersja alternatywna ćwiczenia: Compute 0! Możliwe odpowiedzi: 1. 1, 2. 0, 3. 2, 4. no exist
Wersja alternatywna ćwiczenia: Compute 0! Możliwe odpowiedzi: 1. 1, 2. 0, 3. 2, 4. no exist
Compute 0!
1
0
2
no exist
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Exercise 5
Wersja alternatywna ćwiczenia: How many options are there when it comes to students arrangement 3 in two classes Możliwe odpowiedzi: 1. 9, 2. 12, 3. 6, 4. 8
Wersja alternatywna ćwiczenia: How many options are there when it comes to students arrangement 3 in two classes Możliwe odpowiedzi: 1. 9, 2. 12, 3. 6, 4. 8
How many options are there when it comes to students arrangement 3 in two classes
9
12
6
8
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Exercise 6
Wersja alternatywna ćwiczenia: How many three‑digit numbers can be formed from two numbers: 1, 5 Możliwe odpowiedzi: 1. 8, 2. 9, 3. 6, 4. 5
Wersja alternatywna ćwiczenia: How many three‑digit numbers can be formed from two numbers: 1, 5 Możliwe odpowiedzi: 1. 8, 2. 9, 3. 6, 4. 5
How many three‑digit numbers can be formed from two numbers: 1, 5
8
9
6
5
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Exercise 7
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers cannot be repeated Możliwe odpowiedzi: 1. 6, 2. 9, 3. 4, 4. 3
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers cannot be repeated Możliwe odpowiedzi: 1. 6, 2. 9, 3. 4, 4. 3
How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers cannot be repeated
6
9
4
3
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Exercise 8
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers can be repeated Możliwe odpowiedzi: 1. 9, 2. 6, 3. 4, 4. 12
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers can be repeated Możliwe odpowiedzi: 1. 9, 2. 6, 3. 4, 4. 12
How many two‑digit numbers can be formed from three numbers: 1, 5, 7. The numbers can be repeated
9
6
4
12
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Exercise 9
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 0, 7. The numbers cannot be repeated Możliwe odpowiedzi: 1. 4, 2. 6, 3. 9, 4. 3
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 1, 0, 7. The numbers cannot be repeated Możliwe odpowiedzi: 1. 4, 2. 6, 3. 9, 4. 3
How many two‑digit numbers can be formed from three numbers: 1, 0, 7. The numbers cannot be repeated
4
6
9
3
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Exercise 10
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 3, 4, 9. The numbers can be repeated Możliwe odpowiedzi: 1. 9, 2. 3, 3. 6, 4. 4
Wersja alternatywna ćwiczenia: How many two‑digit numbers can be formed from three numbers: 3, 4, 9. The numbers can be repeated Możliwe odpowiedzi: 1. 9, 2. 3, 3. 6, 4. 4
How many two‑digit numbers can be formed from three numbers: 3, 4, 9. The numbers can be repeated
9
3
6
4
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Exercise 11
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings or 2 queens from one deck of cards are there? Możliwe odpowiedzi: 1. 10, 2. 24, 3. 20, 4. 16
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings or 2 queens from one deck of cards are there? Możliwe odpowiedzi: 1. 10, 2. 24, 3. 20, 4. 16
How many possibilities of choosing 3 kings or 2 queens from one deck of cards are there?
10
24
20
16
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Exercise 12
Wersja alternatywna ćwiczenia: How many two‑persons groups can be formed out of four persons? Możliwe odpowiedzi: 1. 12, 2. 6, 3. 24, 4. 4
Wersja alternatywna ćwiczenia: How many two‑persons groups can be formed out of four persons? Możliwe odpowiedzi: 1. 12, 2. 6, 3. 24, 4. 4
How many two‑persons groups can be formed out of four persons?
12
6
24
4
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Exercise 13
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings or 3 queens or 3 aces from one deck of cards are there? Możliwe odpowiedzi: 1. 12, 2. 24, 3. 64, 4. 72
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings or 3 queens or 3 aces from one deck of cards are there? Możliwe odpowiedzi: 1. 12, 2. 24, 3. 64, 4. 72
How many possibilities of choosing 3 kings or 3 queens or 3 aces from one deck of cards are there?
12
24
64
72
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Exercise 14
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings and 2 queens or 2 kings and 3 queens from one deck of cards are there? Możliwe odpowiedzi: 1. 48, 2. , 3. 20, 4. 24
Wersja alternatywna ćwiczenia: How many possibilities of choosing 3 kings and 2 queens or 2 kings and 3 queens from one deck of cards are there? Możliwe odpowiedzi: 1. 48, 2. , 3. 20, 4. 24
How many possibilities of choosing 3 kings and 2 queens or 2 kings and 3 queens from one deck of cards are there?
48
20
24
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Exercise 15
Wersja alternatywna ćwiczenia: We have 3 white T‑shirts, 2 green T‑shirts and 4 pairs of white shorts and 3 pairs of green shorts. How many different ways are there to complete the uniforms in the same colour? Możliwe odpowiedzi: 1. 18, 2. 12, 3. 42, 4. 35
Wersja alternatywna ćwiczenia: We have 3 white T‑shirts, 2 green T‑shirts and 4 pairs of white shorts and 3 pairs of green shorts. How many different ways are there to complete the uniforms in the same colour? Możliwe odpowiedzi: 1. 18, 2. 12, 3. 42, 4. 35
We have 3 white T‑shirts, 2 green T‑shirts and 4 pairs of white shorts and 3 pairs of green shorts. How many different ways are there to complete the uniforms in the same colour?
Analyse your correct and incorrect answers to the Exercises.
Exercise 16
Choose 2 cards from the cards deck. How many possibilities are there?
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Wybierz jedno nowe słowo poznane podczas dzisiejszej lekcji i ułóż z nim zdanie.
Wybierz jedno nowe słowo poznane podczas dzisiejszej lekcji i ułóż z nim zdanie.
Language Exercises
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Exercise 17
Wersja alternatywna ćwiczenia: Match Polish terms with their English equivalents. średnia Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average różnica Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average moneta Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average położenie Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average ocena Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average
Wersja alternatywna ćwiczenia: Match Polish terms with their English equivalents. średnia Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average różnica Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average moneta Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average położenie Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average ocena Możliwe odpowiedzi: 1. difference, 2. grade, 3. arrangement, 4. coin, 5. average
Match Polish terms with their English equivalents.
arrangement, grade, coin, difference, average
średnia
różnica
moneta
położenie
ocena
Exercise 18
Describe the method of solving Exercises 1 and 2.
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Match Polish terms with their English equivalents.
