Not Showing Enough Working in Proofs
Extension 1 has more proof-style questions than Advanced, and markers expect structured, logical arguments. Students who skip steps or write vague justifications lose marks even when their final answer is correct. A proof is not complete just because you arrived at the right conclusion.
Each step needs to follow logically from the previous one, and each claim needs to be justified. Write as if the reader cannot fill in any gaps. In an induction proof, explicitly state the base case, the assumption, and the inductive step. In any proof, label what you are showing and why each line follows.
Every induction proof needs all three steps. Missing one means losing marks even if the algebra is correct.
Misapplying Combinatorics Formulas
Counting problems require careful thought about whether order matters, whether repetition is allowed, and whether items are identical. Students who reach for nCr or nPr without thinking through the structure of the problem get wrong answers on questions that look deceptively simple.
The fix is to slow down. Before writing a formula, describe in plain words how you would count the outcomes. If you can explain the logic, the formula follows naturally. If you cannot explain the logic, the formula will not save you.
Two questions decide the formula. If you cannot answer them, you do not understand the problem yet.
Weak Algebra Under Pressure
Extension 1 questions require more algebraic manipulation than Advanced. Students who are slow or error-prone with algebra spend too long on routine steps and run out of time for the harder parts of questions. Sign errors, factoring mistakes, and incorrect expansions are the most common culprits.
Algebra fluency is a prerequisite for Extension 1, not something you develop alongside it. If you are making frequent algebra errors, go back to basics. Practise expanding, factoring, and simplifying until these operations are automatic. The time investment pays off across every topic in the course.
Ignoring Domain Restrictions
Inverse trigonometric functions have restricted domains and ranges. Students who forget these restrictions produce answers that are technically outside the valid range. In calculus problems involving inverse trig, missing a domain restriction can invalidate an entire solution.
Write the domain and range restrictions at the top of your working whenever you use an inverse trig function. This takes three seconds and prevents errors that cost entire marks.
Treating Extension 1 Like Advanced
Advanced questions are usually direct applications of a method. Extension 1 questions often require combining multiple ideas or applying a method in an unfamiliar context. Students who study by memorising worked examples struggle because the exam questions are deliberately different from anything they have practised.
Study by doing unfamiliar problems, not by repeating familiar ones. Work through questions from different textbooks, past HSC papers, and trial papers. The goal is to develop problem-solving flexibility, not a library of memorised solutions.
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