ATARMAxxing · Mathematics Extension 1
HSC Mathematics Extension 1 Practice Questions
64 exam-style questions · full worked solutions
The 64 practice questions inside the HSC Mathematics Extension 1 Mastery Pack, grouped by area of study. Every question comes with a full worked solution.
- Functions and Polynomials
- Multiple choice × 12
- Solve × 1
- Find × 1
- Consider × 1
- Solve and sketch × 1
- Trigonometry and Combinatorics
- Multiple choice × 12
- Calculate × 2
- Prove × 2
- Calculus and Proof
- Multiple choice × 12
- Calculate × 2
- Evaluate × 1
- Prove × 1
- Vectors and Statistics
- Multiple choice × 12
- Calculate × 2
- Prove × 1
- Analyse × 1
Sample question
A student is proving by mathematical induction that 1(2) + 2(3) + 3(4) + ... + n(n+1) = n(n+1)(n+2)/3 for all integers n >= 1. Having assumed the statement is true for n = k, which expression must be added to the assumed sum k(k+1)(k+2)/3 to complete the inductive step for n = k+1?
- A. (k+1)(k+2)
- B. (k+1)(k+2)(k+3)/3
- C. k(k+1)
- D. (k+1)(k+2)/3
Show the worked answer
Answer: A
The (k+1)th term of the series is n(n+1) evaluated at n = k+1, which is (k+1)(k+2). This single term is added to the assumed sum. Indeed k(k+1)(k+2)/3 + (k+1)(k+2) = (k+1)(k+2)(k+3)/3, the required result.
Included in the HSC Mathematics Extension 1 Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
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