Question 1
Which statement is logically equivalent to the implication P ⇒ Q?
Correct Answer:
¬Q ⇒ ¬P
Question 2
To prove ∀n ∈ ℕ, P(n) by mathematical induction, which step is required after the base case?
Correct Answer:
Assume P(k) for some k ≥ n₀ and prove P(k+1)
Question 3
The negation of “∀x ∈ ℝ, x² ≥ 0” is which statement?
Correct Answer:
∃x ∈ ℝ such that x² < 0
Question 4
Proof by contradiction that √2 is irrational typically begins by assuming which statement?
Correct Answer:
√2 is rational
Question 5
If a|b and a|c for integers a, b, c with a ≠ 0, which conclusion must follow?
Correct Answer:
a|(b + c)
Question 1
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Prepare with the HSC Maths Ext 2 Practice Questions - HSC Mathematics Extension 2 (NSW Higher School Certificate) Exam practice quiz. This question bank includes 100 questions covering vector, equals, value, expression, and form. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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HSC Maths Ext 2 Practice Questions - HSC Mathematics Extension 2 (NSW Higher School Certificate) Exam

This practice set contains 100 questions from the matching question bank and focuses on vector, equals, value, expression, and form. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

This is an independent study resource intended for practice and review; it is not an official examination or an endorsement by any organization named in the title.

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