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

> A study guide for UBC MATH 100 (Differential Calculus with Applications): derivatives, graphing and optimization, how it compares to MATH 102, 104 and 180.

Source: https://practicecalculus.com/courses/ubc-math-100
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 100 (MATH_V 100, Vancouver campus)
- **Credits:** 3
- **Prerequisites:** 80% or higher in BC Pre-calculus 12; high school calculus strongly recommended
- **Covers:** Derivatives of elementary functions, with applications and modelling such as graphing and optimization
- **Similar courses:** MATH 102 (life sciences), MATH 104 (commerce and social sciences), MATH 180 (no previous calculus)
- **Next course:** MATH 101 (Integral Calculus with Applications)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- UBC MATH 100 is a 3-credit first course in differential calculus on the Vancouver campus.
- It covers derivatives of elementary functions and their applications to graphing and optimization.
- It expects 80% or higher in BC Pre-calculus 12, and the calendar strongly recommends high school calculus.
- MATH 180 covers the same topics for students with no previous calculus, and MATH 101 comes next.

**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](/courses/ubc-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 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [continuity](/blog/continuity) |
| The derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivatives of polynomials and powers | [The power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule), [power functions](/functions/power-functions) |
| Trig, exponential and log derivatives | [Sine, cosine and tangent](/learn/calculus-1/derivative-rules/trig-derivatives) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions), [exponential and log derivatives](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Product, quotient and chain rules | [Chain rule: any function](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/rules/chain-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/blog/implicit-differentiation) |
| Modelling with rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Linear approximation | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Graphing | [Concavity and the second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching with derivatives](/blog/curve-sketching-with-derivatives) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems), [Extreme Value Theorem](/theorems/extreme-value-theorem) |

## MATH 100 and UBC's other first calculus courses

| Course | Title | Credits | Notes |
| --- | --- | --- | --- |
| MATH 100 | Differential Calculus with Applications | 3 | Standard first course |
| MATH 102 | Differential Calculus with Applications to Life Sciences | 3 | Equivalent to MATH 100 and 104 |
| MATH 104 | Differential Calculus with Applications to Commerce and Social Sciences | 3 | Equivalent to MATH 100 and 102 |
| MATH 180 | Differential Calculus with Applications | 4 | Same topics as MATH 100, for students with no previous calculus |
| MATH 120 | Honours Differential Calculus | 4 | Needs 95%+ in Pre-calculus 12 or department permission |

Any of these leads to [MATH 101](/courses/ubc-math-101), and from there to [MATH 200](/courses/ubc-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 $f(x) = \dfrac{x^2}{x + 1}$:

$$f'(x) = \frac{2x(x + 1) - x^2}{(x + 1)^2} = \frac{x^2 + 2x}{(x + 1)^2}$$

**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](/rules/chain-rule) and [quotient rule](/rules/quotient-rule) take no thought. Daily short sets in [practice](/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](/formulas) has every derivative on one page.
- **Learn from common errors.** Our [common calculus mistakes](/blog/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.

## Frequently asked questions

### What is UBC MATH 100?

MATH 100, Differential Calculus with Applications, is UBC Vancouver's first-term calculus course. It covers derivatives of elementary functions and uses them for modelling, graphing and optimization.

### What comes after MATH 100 at UBC?

MATH 101, Integral Calculus with Applications, which covers definite integrals, integration techniques, applications and infinite series.

### What is the difference between MATH 100 and MATH 180?

The UBC calendar says MATH 180 covers the same topics as MATH 100 but is meant for students with no previous calculus. MATH 180 is worth 4 credits and is not for credit if you have AP Calculus AB or BC credit.

### MATH 100 vs MATH 102 vs MATH 104?

All three are first differential calculus courses. MATH 102 uses applications to the life sciences, MATH 104 uses applications to commerce and social sciences, and MATH 100 has general applications. Check your program and the credit exclusion list before choosing.

### Is UBC MATH 100 hard?

Because high school calculus is strongly recommended, the course moves quickly through the basics. Students who keep up with weekly practice on derivative rules and word problems usually find it manageable.