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 21 topics MATH 100 teaches, in the order it teaches them, under the test they come before: the midterm, Quiz 2, then the final. Two more topics, from CLP-1, which the course does not examine, sit in a group of their own. 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 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. Capstone questions, one or two per topic, combine several ideas from the topic and usually turn on a justification; they are the shape of the hardest question on a final.

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.

Every one of the 451 practice questions was written for this site: its own function, its own numbers, its own setting and its own answer, with a solution written to explain the reasoning. What the questions cover is decided by the course. Its textbook, UBC Math 100: Differential Calculus, with its Practice Book (Kelly Paton and Elyse Yeager), and CLP-1 Differential Calculus (Joel Feldman, Andrew Rechnitzer and Elyse Yeager), which it refers to, show which skills it teaches and which of them tend to be tested, and the bank is weighted accordingly. Each question page names the section of each book where the theory is explained, so you can go and read it.

Mock papers draw on what is taught before each test: short questions with an exact answer and, where the test has them, longer problems in parts, set out like a written test. No real test paper is reproduced. The questions on a paper are held out of the practice library, so sitting a paper is a real test.

The textbooks are cited for the theory only. Nothing on this site is reproduced or adapted from either book. Both textbooks are released under CC BY-NC-SA 4.0; the content of this site is not. © 2026 Longhand. All rights reserved. Nothing here is copied from a past paper, a homework system, a lecture handout, or any material distributed inside a course, and restricted or leaked assessments are not accepted regardless of how they are offered. A question you have already seen the answer to does not measure anything.

Read UBC Math 100: Differential Calculus

Mathematics written by one person will contain errors, however carefully it is checked. 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. Signed in, the report reaches the person who maintains the question bank; signed out, it opens in your email app, filled in. You can also write to hello@longhand.page.

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