Sources, coverage and document notes

PDFs with a text layer were converted with pdftotext; scanned PDFs were OCR'd with tesseract and the formulas were checked against the page images. Where a problem statement mixed text and a figure, only the text-complete parts became questions.

Each item below was found by checking our computed answer against the printed one (or when an exercise turned out to be impossible as printed). The quiz uses the computed result.

• Computation problems 5, Q10: The printed key says 'local maximum $y(-\pi/3)=-\pi/3-\sqrt3/2$, local minimum $y(\pi/3)=\pi/3+\sqrt3/2$'. Since $y(-\pi/3)<y(\pi/3)$ this is impossible for a max/min pair at those points: the sign of $y'$ shows a local MINIMUM at $-\pi/3$ and a local MAXIMUM at $\pi/3$. We follow the computation.
• Tutorial 8, Q6(c): The printed key shows $\frac{512\pi}{3}$ for revolving the triangle $2y=x+4$, $y=x$, $x=0$ about $x=4$ (shell method). Direct integration $2\pi\int_0^4(4-x)\frac{4-x}{2}dx=\frac{64\pi}{3}$, and Pappus' theorem (area $4$, centroid distance $\frac83$) gives the same $\frac{64\pi}{3}$; the key entry appears to be mistaken.
• Computation problems 11, Q11: The printed key says the series DIVERGES. With $a_{n+1}=\frac{1+\tan^{-1}n}{n}a_n$ the ratio tends to $0$, so the Ratio Test gives convergence (partial sums computed numerically stabilise). The key entry appears to be mistaken (a version with $a_{n+1}=\frac{n}{1+\tan^{-1}n}a_n$ would diverge).
• Tutorial 12, Q9: The key gives $8$ (counting the zero constant term of $\ln(1+x)$ as a term). With the Lagrange bound $|R_n(0.1)|\le\frac{0.1^{n+1}}{n+1}$ the polynomial $P_7$ already works ($1.25\times10^{-9}<10^{-8}$), i.e. $7$ non-zero terms $x-\frac{x^2}2+\cdots+\frac{x^7}7$.

• All answers are produced by code (sympy exact arithmetic, never typed by hand) and, for source problems, compared with the printed answer key; the build stops if they disagree.
• Distractors are realistic mistakes (sign errors, missing chain-rule factor, transposed matrices, wrong-order composition…), and every distractor is checked to be different from the correct answer.
• Option positions are shuffled with a fixed seed and balanced (A/B/C/D each 25%); the correct option is not systematically the longest.