HSC Mathematics Extension 1 Multiple-Choice Quiz

Try 4 original practice questions. Choose an answer for each question to see your score and the explanations.

1. In induction on n, what must be shown after establishing the base case? Assuming the statement at k, the statement at k + 1 follows The statement is true at two consecutive values The result is true for an arbitrarily chosen large n The right-hand side is greater than zero

2. How many distinct arrangements can be made using all four letters of the word NOON? 5 24 4 6

3. What is the dot product of (3, 1) and (−1, 3)? 3 0 6 2

4. What is the coefficient of x² in (1 + 2x)⁴? 6 16 24 8

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