Proof by Exhaustion (Edexcel A-Level Mathematics): Quizzes

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Proof by Exhaustion
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What is the key feature of proof by exhaustion?

Considering every possible case

In Step 2 of proof by exhaustion, what must you break the problem into?

A finite number of distinct cases

What are the single-digit odd numbers used in Example 1?

1,3,5,7,91, 3, 5, 7, 9

What is the result of 3+53 + 5 in Example 1?

88 (even)

What does Example 1 conclude about the sum of two odd numbers?

It is always even

When proving 4747 is prime, up to which value must you check for factors?

66 (last integer below 47\sqrt{47})

What is the result of 473\frac{47}{3} in Example 2?

15.615.6 (not a factor)

What is 475\frac{47}{5} equal to?

9.49.4

Why is 4747 proven to be prime?

All integers 2≤n≤472 \leq n \leq \sqrt{47} are not factors

Using the calculator method, what function checks if 4747 is prime?

f(x)=47xf(x) = \frac{47}{x}

In the calculator method for proving 4747 is prime, what is the start value for xx?

x=2x = 2

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