UBC MATH 100 Differential Calculus: Topics, Study Guide, Practice

MATH 100 is UBC Vancouver's main first-term calculus course, titled Differential Calculus with Applications. Most science and engineering-bound students who have seen calculus in high school take it in their first fall. This guide maps every MATH 100 topic to free practice so you can learn derivatives by solving problems with instant feedback.

What UBC MATH 100 covers

The UBC Vancouver calendar describes MATH 100 briefly: derivatives of elementary functions, then applications and modelling, with graphing and optimization named as examples. It is a 3-credit course with three lecture hours per week, and it requires 80% or higher in BC Pre-calculus 12. The calendar strongly recommends high school calculus as well.

That matches the differential half of a standard Calculus 1 course, with integration left to MATH 101. The calendar entry is short, so the map below lays out the topics a differential calculus course usually builds on: limits, the derivative rules for elementary functions, and the applications the calendar names.

MATH 100 topic map

MATH 100 and UBC's other first calculus courses

Any of these leads to MATH 101, and from there to MATH 200, Calculus III. UBC's credit exclusion lists limit which combinations count, so check them before switching.

Example problems at the MATH 100 level

1. A quotient rule derivative. Differentiate f(x) = \dfrac{x^2}{x + 1}:

2. An optimization problem. A rectangle has perimeter 40 m. Its area is A = x(20 - x), so A'(x) = 20 - 2x = 0 gives x = 10. The largest area is a 10 \times 10 square with A = 100\ \text{m}^2.

3. Graphing with derivatives. For f(x) = x^3 - 3x, f'(x) = 3x^2 - 3 = 0 at x = \pm 1. Since f''(x) = 6x, there is a local maximum f(-1) = 2 and a local minimum f(1) = -2, with an inflection point at x = 0.

How to do well in UBC MATH 100

• Get the rules automatic early. Graphing and optimization questions are easy only when the chain rule and quotient rule take no thought. Daily short sets in practice help.
• Set up word problems carefully. Draw a picture, name the variables and write the quantity to optimize before differentiating.
• Keep a formula sheet. The calculus formula sheet has every derivative on one page.
• Learn from common errors. Our common calculus mistakes guide covers the algebra and sign slips that cost the most marks.

Tip: for every optimization answer, check the endpoints or use the second derivative to confirm you found a maximum and not a minimum.