Alberta Diploma Exams · Mathematics 30-1

Permutations, Probability and Sequences

25 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 25 questions

  1. A fair coin is tossed 4 times. What is the probability of exactly 2 heads?
  2. A fair coin is tossed 5 times. What is the probability of exactly 1 head?
  3. The first term of an arithmetic series is 8, the common difference is 4 and there are 8 terms. What is the sum?
  4. A fair die is rolled 2 times. What is the probability of getting at least one six?
  5. A colony of 1000 bacteria doubles every 4 hours. How many bacteria are there after 8 hours?
  6. What is the minimum value of f(x) = x^2 - 4x + 3?
  7. A colony of 200 bacteria doubles every 2 hours. How many bacteria are there after 4 hours?
  8. In a class, 27 students play football, 21 play volleyball and 12 play both. 10 play neither. How many students are in the class?
  9. Pipe A fills a tank in 12 hours and pipe B fills it in 4 hours. Working together, how many hours do they need?
  10. In how many ways can 2 students be chosen from a group of 6 to represent the class?
  11. In how many ways can 2 students be chosen from a group of 5 to represent the class?
  12. A fair coin is tossed 4 times. What is the probability of exactly 1 head?
  13. The first term of an arithmetic series is 6, the common difference is 6 and there are 12 terms. What is the sum?
  14. A fair coin is tossed 3 times. What is the probability of exactly 2 heads?
  15. $5000 is invested at compound interest of 10% per year. What is the amount after 2 years?
  16. The first term of an arithmetic series is 2, the common difference is 6 and there are 10 terms. What is the sum?
  17. What is the sum of the infinite series 4 + 4/3 + 4/9 + ... in which each term is 1/3 of the previous one?
  18. Five numbers have a mean of 9. When one of them, 21, is removed, what is the mean of the remaining four?
  19. A colony of 200 bacteria doubles every 5 hours. How many bacteria are there after 10 hours?
  20. A price of $800 rises by 10% and then falls by 10%. What is the final price?
  21. What is the sum of the infinite series 3 + 2 + 4/3 + ... in which each term is 2/3 of the previous one?
  22. Pipe A fills a tank in 12 hours and pipe B fills it in 6 hours. Working together, how many hours do they need?
  23. $1000 is invested at compound interest of 5% per year. What is the amount after 2 years?
  24. Five numbers have a mean of 20. When one of them, 32, is removed, what is the mean of the remaining four?
  25. In a class, 26 students play football, 22 play volleyball and 8 play both. 10 play neither. How many students are in the class?

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