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Concept Review · Quick review guide

Differential Calculus Quick Review

Twenty-three topics, each cut down to what you need to walk into the exam with: the ideas in a few lines, the formulas on cards, one graph that shows the concept, the errors markers see every term, and a handful of exam-style problems to test yourself on. It follows the order of UBC MATH 100 and SFU MATH 151, and it is free.

topics
23
formula cards
168
quick checks
138
minutes of reading
≈110
Start with topic 01How to use it
Plan

The night-before plan

Three passes, in this order
  1. Pass 1≈ 60 min

    Ideas and formulas

    Read only the key ideas and the formula cards of every topic, in order. Skip anything you can already say out loud.

  2. Pass 2≈ 30 min

    Watch out

    Go through every Watch out section and note the mistakes you have actually made this term. Those topics are your list.

  3. Pass 3As long as it takes

    Quick checks

    Work the quick checks on your list. Commit to an answer before you reveal one; the steps show what a marker needs to see.

Unit 1

Limits & Continuity

What a limit is, how to compute one, and what continuity buys you.

Unit 2

The Derivative & Its Rules

From the limit definition to every rule you need to differentiate anything.

Unit 3

Applications of the Derivative

Rates, limits by l'Hôpital, extrema, the shape of a graph, optimization.

Unit 4

Approximation

Tangent lines, Taylor polynomials and Newton's method — calculus as estimation.

Unit 5

Differential Equations

Equations about rates: solving the simple ones and reading the rest.

Courses

Which course is this for?

The same syllabus, whichever code is on your transcript. Each link goes to what we offer for that course.

FAQ

Questions students ask

Is this a replacement for the textbook?

No. It is the review you do after the course and before the exam: every topic reduced to the ideas, formulas and pitfalls you must have at your fingertips, with a few problems to prove you do. Learn the material first, then use this to make it stick.

Which courses does it cover?

Any first-year differential calculus course. The topic order follows UBC MATH 100, 110, 120 and 180 and SFU MATH 150, 151, 154 and 157, and the same material appears in BC Calculus 12 and AP Calculus AB.

How should I use it the night before an exam?

Three passes. First, read only the key ideas and formula cards for every topic — about an hour. Second, go through every Watch out section and tick the mistakes you have made yourself. Third, do the quick checks for the topics you ticked most, revealing each answer only after committing to your own.

Where are the full worked solutions?

Under every quick-check problem. Click Show answer to see the final answer and the steps a marker needs to see. The steps are deliberately compact; if one of them is not obvious, that is the topic to open your notes on.

Is it free, and can I use it without an account?

Yes to both. Every page is free and public. If you find an error, the Report error link on each section sends it straight to us.

Need more than a review?

Go through it with a tutor who teaches this course every term.

Online across Canada and the US, or in person in Vancouver. Tell us the course code and your exam date and we will build the session around what is left.

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Formula sheet