About Longhand

Practice material for a first-year calculus course is rarely missing. It is scattered. A worked example sits in a lecture slide, a similar problem sits in a textbook chapter, an old question sits in a shared folder somebody posted in a group chat, and none of it tells you which is worth your next thirty minutes.

Longhand is an attempt at the opposite: one place, one course, everything in the same format, and enough structure that you can tell what you have not done yet.

Questions are grouped into the eight topics of MATH 100, in the order the course takes them. Within a topic each question carries a difficulty, a question type, a mark value and a suggested time, so a set can be assembled to fit the twenty minutes you actually have.

Difficulty means something specific here. Introductory questions test one idea in isolation. Standard questions are the length and shape of a typical assignment or midterm question. Challenging questions combine two ideas, or require a justification step that is easy to skip.

Every question also records the prerequisite it leans on. That is what makes the recommendations possible: when a topic is untouched and the topic underneath it is solid, that is the natural next step, and the interface says so in those terms.

A final answer tells you whether you were right. It does not tell you why the first line of the solution was the first line. So every worked solution here opens with the strategy before any algebra, and annotates each step with the reason for that move rather than just the move itself.

Each solution also names the specific mistake the question was built to catch. Getting a question wrong is only useful if you can tell which of the plausible wrong routes you took, and most questions have one that is far more common than the others.

All 31 questions, hints and solutions in this prototype were written for it. Nothing is copied from a past paper, a textbook, an online homework system, a lecture handout, or any material distributed inside a course.

Restricted or leaked assessments are not accepted here, and will not be, regardless of how they are offered. Beyond the obvious problem with redistributing someone else’s work, a question you have already seen the answer to does not measure anything. The point of a mock exam is that it is not the real one.

Questions are written to the shape of the course rather than to any particular instructor’s paper: standard topics, standard techniques, standard traps.

Mathematics written by one person and checked by nobody will contain errors. If a marked answer looks wrong, a solution skips a step that matters, or a question is ambiguous, say so.

Every question page has a Report a problem control in the sidebar. It records the question reference and what you saw. In this prototype that report is saved in your own browser and goes no further; a released version would route it to whoever maintains the question bank.

Corrections are checked against the mathematics, not against how many people report them. One correct report is enough.