# Western Calculus 1000A/B Calculus I: Topics, Guide and Practice

> A study guide for Western University Calculus 1000A/B (Calculus I): derivatives, inverse trig, L'Hospital's rule, the FTC, areas and volumes.

Source: https://practicecalculus.com/courses/western-university-calculus-1000
Updated: 2026-11-08

## At a glance

- **Course code:** Calculus 1000A/B
- **Course weight:** 0.50 (4 lecture hours)
- **Prerequisites:** Ontario Secondary School MCV4U or Mathematics 0110A/B
- **Antirequisites:** Calculus 1500A/B, Numerical and Mathematical Methods 1412A/B, the former Applied Mathematics 1412A/B and 1413
- **Covers:** Review of limits and derivatives of exponential, log and rational functions, trig functions and inverses and their derivatives, L'Hospital's rule, the definite integral, the Fundamental Theorem, simple substitution, areas and volumes of revolution
- **Next course:** Calculus 1501A/B or Calculus 1301A/B
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- Calculus 1000A/B is Calculus I at Western University, a half course (0.50) with 4 lecture hours.
- It starts with a review of limits and derivatives, since it assumes MCV4U.
- It adds trig and inverse trig functions, L'Hospital's rule, the definite integral and the Fundamental Theorem.
- It ends with areas and volumes of revolution, and leads to Calculus 1501A/B or 1301A/B.

**Calculus 1000A/B** is Calculus I at Western University in London, Ontario. It is a half course (0.50 weight) with four lecture hours a week, and the A/B means it can run in either term. Because students arrive with MCV4U, it starts with a review of limits and derivatives and quickly moves on to trig functions, L'Hospital's rule and integration. This guide maps every Calculus 1000 topic to free practice.

## What Western Calculus 1000A/B covers

The Western academic calendar lists the topics as: review of limits and derivatives of exponential, logarithmic and rational functions; trigonometric functions and their inverses; the derivatives of the trig functions and their inverses; L'Hospital's rules; the definite integral; the Fundamental Theorem of Calculus; simple substitution; and applications including areas of regions and volumes of solids of revolution. The prerequisite is Ontario Secondary School MCV4U or Mathematics 0110A/B.

This is a full **Calculus 1** course. Since MCV4U covers basic limits and derivatives, Western treats them as review and spends more time on inverse trig functions and integration.

## Calculus 1000A/B topic map

| Calculus 1000 topic | Practice | Read |
| --- | --- | --- |
| Limits (review) | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Derivatives of exp, log and rational functions | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives), [quotient rule](/learn/calculus-1/derivative-rules/quotient-rule) | [Derivatives of exp and log](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Trig functions and their derivatives | [Trig derivatives](/learn/calculus-1/derivative-rules/trig-derivatives), [chain rule with trig](/learn/calculus-1/derivative-rules/chain-rule-trig) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions) |
| Inverse trig functions | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Arcsine](/functions/arcsine), [derivative of arcsin x](/derivatives/arcsin-x) |
| L'Hospital's rule | [L'Hopital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hopital's rule guide](/blog/lhopitals-rule), [the rule](/rules/lhopitals-rule) |
| The definite integral | [Riemann sums](/learn/calculus-1/integrals/riemann-sums), [signed area](/learn/calculus-1/integrals/signed-area) | [Riemann sums guide](/blog/riemann-sums) |
| The Fundamental Theorem | [FTC part 1](/learn/calculus-1/integrals/fundamental-theorem-part-1), [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Simple substitution | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution guide](/blog/u-substitution) |
| Areas of regions | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves guide](/blog/area-between-curves) |
| Volumes of revolution | [Disks](/learn/calculus-1/applications-of-integrals/volumes-disks), [washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |

## Calculus 1000 vs Calculus 1500

| Course | Title | Who it is for |
| --- | --- | --- |
| Calculus 1000A/B | Calculus I | Most students who need first-year calculus |
| Calculus 1500A/B | Calculus I for the Mathematical Sciences | Students heading to math, statistics, physics, actuarial science and similar degrees |

They are antirequisites. After Calculus 1000, take [Calculus 1501A/B](/courses/western-university-calculus-1501) (at least 60%) or Calculus 1301A/B (at least 55%), and later [Calculus 2302A/B](/courses/western-university-calculus-2302) for several variables.

## Example problems at the Calculus 1000 level

**1. An inverse trig derivative.** $\frac{d}{dx}\arctan(x^2) = \frac{2x}{1 + x^4}$.

**2. L'Hospital's rule.**

$$\lim_{x\to\infty}\frac{\ln x}{x} = \lim_{x\to\infty}\frac{1/x}{1} = 0$$

**3. Substitution with an inverse trig result.**

$$\int \frac{dx}{1 + 4x^2} = \frac{1}{2}\arctan(2x) + C$$

**4. A volume.** Rotating $y = \sqrt{x}$ on $[0, 4]$ about the $x$-axis gives $V = \pi\int_0^4 x\,dx = 8\pi$.

## How to do well in Calculus 1000A/B

- **Do not coast through the review.** The first weeks feel familiar after MCV4U, but the pace picks up quickly. Use that time to make derivative rules automatic.
- **Memorise the inverse trig derivatives.** They show up again as integrals, so learning them both ways pays off twice.
- **Check the form before L'Hospital.** The rule only applies to $\frac{0}{0}$ or $\frac{\infty}{\infty}$. Other forms must be rewritten first.
- **Sketch volume problems.** Identify the axis, the radius and the limits on a picture before writing the integral.
- **Aim above the threshold.** If you plan to take Calculus 1501, you need at least 60% in Calculus 1000.

> **Tip:** in a substitution, change the limits of integration to the new variable so you never have to substitute back.

## Frequently asked questions

### What is Calculus 1000A/B at Western?

Calculus 1000A/B is Calculus I. The Western academic calendar lists a review of limits and derivatives of exponential, logarithmic and rational functions; trigonometric functions and their inverses and their derivatives; L'Hospital's rules; the definite integral; the Fundamental Theorem of Calculus; simple substitution; and applications including areas of regions and volumes of solids of revolution.

### Calculus 1000 vs Calculus 1500?

They are antirequisites, so you take one. Calculus 1500A/B is Calculus I for the Mathematical Sciences, for students intending to study actuarial science, applied mathematics, astrophysics, mathematics, medical physics, physics or statistics. It adds basic set theory, mathematical rigour and the precise definition of a limit.

### What comes after Calculus 1000A/B?

Calculus 1501A/B (needs at least 60% in Calculus 1000) or Calculus 1301A/B (needs at least 55%). Calculus 1501 is the one for mathematical and physical science degrees.

### What do I need for Calculus 1000A/B?

Ontario Secondary School MCV4U (Calculus and Vectors) or Mathematics 0110A/B.