Exam-style practice (harder): Maths Advanced multiple choice

Why this set is harder than our topic quizzes

Our topic quizzes check rules and definitions. HSC Mathematics Advanced multiple-choice questions are small problems: each takes two or three steps, and every wrong option is what you get from one familiar slip, such as integrating across a root, forgetting to double a trigonometric domain, or stopping at the variance instead of the standard deviation.

These 14 questions are built the same way. They are original practice questions written by ExamExplained, not taken from any NESA paper. Each explanation starts with a Type tag and names the error behind every wrong option.

The question types

Question map

Five sanity checks that catch most distractors

1. Areas are positive. If a curve crosses the axis inside the interval, split the integral at the root.
2. Distance is not displacement. Check whether velocity changes sign before integrating.
3. Domains scale. For $\sin(2x)$ on $[0, 2\pi]$, solve for $2x$ on $[0, 4\pi]$.
4. Probability rules. Probabilities sum to 1, density functions have area 1, and a standard deviation is the square root of the variance.
5. Limiting sums need $|r| < 1$. If your ratio is 3 or 1.5, recheck the rearrangement.

What to do next

• Revise the calculus behind Questions 2 to 4 and 13 in the HSC Maths Advanced calculus guide.
• Revise Questions 9 to 11 and 14 in the statistical analysis guide.
• Then do a full NESA past paper under time and mark it with the official marking guidelines.