Worksheets — Set 18
Number theory · Divisibility and congruences
Print and write your answers. Use diagrams to show thinking.
Warm-up
1. How many subsets does a set with 22 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 21 fair tosses) = ___
_See printable PDF for diagram._
Written practice
1. How many subsets does a set with 21 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 20 fair tosses) = ___ 4. Write the recurrence aₙ = 20aₙ₋₁ with a₀ = 1 ___ 5. Graph with 22 vertices — minimum edges for connectivity? ___ 6. Convert 60₁₀ to base 21. = ___ 7. How many subsets does a set with 24 elements have? ___ 8. P(at least one head in 23 fair tosses) = ___
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More written practice
1. Write the recurrence aₙ = 23aₙ₋₁ with a₀ = 1 ___ 2. Graph with 25 vertices — minimum edges for connectivity? ___ 3. Convert 63₁₀ to base 24. = ___ 4. How many subsets does a set with 27 elements have? ___ 5. P(at least one head in 26 fair tosses) = ___ 6. Write the recurrence aₙ = 26aₙ₋₁ with a₀ = 1 ___
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Patterns and rules
1. How many subsets does a set with 38 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 37 fair tosses) = ___
_See printable PDF for diagram._
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Stretch
1. How many subsets does a set with 46 elements have? ___ 2. Prove or disprove: if n is even, n² is even.
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Parent tip: Use trees or tables for counting