How to use these pages

Answer the question first, on paper. Then click the answer to unfold it.

Reading a worked answer feels like learning and mostly is not — recognising an answer is a completely different skill from producing one, and only one of them is any use in an exam.

Every set below lands after the thinking — after the exploration, the boards, and the concept page that consolidated them. This is the calculus room, so the answers here show their reasoning in full: the limit taken honestly, the sign chart audited, the cross product checked against a dot product. Compare your reasoning against ours, not just your final number — a right answer by a wrong route is a debt that comes due in first-year calculus. Nothing here is timed, counted, or collected. Ever.

Stuck partway through a set? That is the set working. Start with Getting Unstuck, and remember that Checking Your Own Work beats checking ours.