Worksheets — Set 4

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 8 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 7 fair tosses) = ___

_See printable PDF for diagram._

Written practice

1. How many subsets does a set with 7 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 6 fair tosses) = ___ 4. Write the recurrence aₙ = 6aₙ₋₁ with a₀ = 1 ___ 5. Graph with 8 vertices — minimum edges for connectivity? ___ 6. Convert 46₁₀ to base 7. = ___ 7. How many subsets does a set with 10 elements have? ___ 8. P(at least one head in 9 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 9aₙ₋₁ with a₀ = 1 ___ 2. Graph with 11 vertices — minimum edges for connectivity? ___ 3. Convert 49₁₀ to base 10. = ___ 4. How many subsets does a set with 13 elements have? ___ 5. P(at least one head in 12 fair tosses) = ___ 6. Write the recurrence aₙ = 12aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 24 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 23 fair tosses) = ___

_See printable PDF for diagram._

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Parent tip: Use trees or tables for counting