# Purdue MA 16500 Calculus I: Topics, Study Guide and Practice

> A study guide for Purdue MA 16500 (Analytic Geometry and Calculus I): limits, derivatives, optimization, integrals and conic sections, with free practice.

Source: https://practicecalculus.com/courses/purdue-ma-16500
Updated: 2026-11-03

## At a glance

- **Course code:** MA 16500 (Indiana transfer course IMA 1602, Calculus - Long I)
- **Credit hours:** 4
- **Designed for:** Students with at least one semester of high school calculus with an A or B, and competence in college algebra and trigonometry
- **Covers:** Differential and integral calculus of one variable with applications, and conic sections
- **Alternative:** MA 16100 (5 credits) for students without high school calculus
- **Next course:** MA 16600 (Analytic Geometry And Calculus II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MA 16500 is Purdue's 4-credit first calculus course for students who already had some calculus in high school.
- It introduces differential and integral calculus of one variable, with applications and conic sections.
- Students without a semester of high school calculus with an A or B take the 5-credit MA 16100 instead.
- It continues in MA 16600, Analytic Geometry And Calculus II.

**Purdue MA 16500**, Analytic Geometry And Calculus I, is the first calculus course for Purdue students who already saw some calculus in high school. It carries 4 credit hours and leads into MA 16600 and then MA 26100. This guide maps every MA 16500 topic to practice with instant feedback, so you can sharpen each skill by solving problems.

## What Purdue MA 16500 covers

The math department describes MA 16500 as an introduction to differential and integral calculus of one variable with applications, plus conic sections. It is designed for students with at least one semester of high school calculus earning an A or B who do not place into MA 16200, MA 16600 or the advanced placement courses, and it expects competence in college algebra and trigonometry.

A Purdue Engineering course outline for MA 16500 lists the weekly topics: functions, exponentials and logarithms, limits and continuity, limits at infinity, the derivative, product, quotient and chain rules, trig and log derivatives, implicit differentiation, hyperbolic functions, exponential growth and related rates, linear approximation, max and min values, the Mean Value Theorem, curve shape, L'Hôpital's rule, optimization, and finally antiderivatives, the definite integral, the Fundamental Theorem and substitution.

That is a complete **Calculus 1** course, taught at a pace that assumes you have met the ideas before.

## MA 16500 topic map

| MA 16500 topic | Practice | Read |
| --- | --- | --- |
| Functions, exponentials and logarithms | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions), [logarithmic functions](/functions/logarithmic-functions) |
| Limits and limit laws | [Direct substitution](/learn/calculus-1/limits/direct-substitution) | [Limit laws](/rules/limit-laws), [how to evaluate limits](/blog/how-to-evaluate-limits) |
| Continuity and asymptotes | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Continuity](/blog/continuity), [limits at infinity](/blog/limits-at-infinity) |
| The derivative | [Tangent lines](/learn/calculus-1/the-derivative/tangent-lines) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Product, quotient and chain rules | [The quotient rule](/learn/calculus-1/derivative-rules/quotient-rule) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule](/blog/chain-rule) |
| Trig, log and hyperbolic derivatives | [Sine, cosine and tangent](/learn/calculus-1/derivative-rules/trig-derivatives) | [Derivatives of trig functions](/blog/derivatives-of-trig-functions), [hyperbolic functions](/functions/hyperbolic-functions) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/rules/implicit-differentiation) |
| Growth, decay and related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Linear approximation and the MVT | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation), [Mean Value Theorem](/theorems/mean-value-theorem) |
| Curve sketching | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| L'Hôpital's rule | [L'Hôpital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hôpital's rule](/blog/lhopitals-rule) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Definite integral and FTC | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Substitution and net change | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [U-substitution](/blog/u-substitution) |

## The Purdue calculus sequence

| Course | Title | Credit hours | Who it is for |
| --- | --- | --- | --- |
| MA 16100 | Plane Analytic Geometry And Calculus I | 5 | Students without a semester of high school calculus |
| MA 16500 | Analytic Geometry And Calculus I | 4 | Students with high school calculus (A or B) |
| MA 16600 | Analytic Geometry And Calculus II | 4 | Continuation of MA 16500 |
| MA 26100 | Multivariate Calculus | 4 | Multivariable calculus |
| MA 16010 | Applied Calculus I | 3 | Life, managerial and social sciences |

Continue with the [MA 16600 guide](/courses/purdue-ma-16600) and the [MA 26100 guide](/courses/purdue-ma-26100). If you are deciding between first courses, see the [MA 16100 guide](/courses/purdue-ma-16100), or the [MA 16010 guide](/courses/purdue-ma-16010) for applied calculus.

## Example problems at the MA 16500 level

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

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

**2. Exponential decay.** A sample decays as $A(t) = 80e^{-0.1t}$ grams. Its rate of change at $t = 0$ is $A'(0) = -0.1 \cdot 80 = -8$ grams per unit time.

**3. L'Hôpital's rule.** The limit $\lim_{x \to 0} \frac{e^x - 1}{x}$ has the form $\frac{0}{0}$, so

$$\lim_{x \to 0} \frac{e^x - 1}{x} = \lim_{x \to 0} \frac{e^x}{1} = 1$$

## How to do well in Purdue MA 16500

- **Do not coast on high school calculus.** The course assumes you have seen the basics and moves on quickly to applications. Fill gaps early with [mixed derivative practice](/learn/calculus-1/derivative-rules/derivative-rules-practice).
- **Make curve sketching systematic.** Use the first and second derivative together, as in the [concavity lesson](/learn/calculus-1/applications-of-derivatives/second-derivative).
- **Check your work for algebra errors.** The list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the ones that cost the most points.
- **Use the [formula sheet](/formulas)** while learning, then take timed [practice exams](/practice) before each exam.
- **Plan exam prep** with [how to prepare for a calculus exam](/blog/how-to-prepare-for-a-calculus-exam).

> **Tip:** L'Hôpital's rule only applies to $\frac{0}{0}$ or $\frac{\infty}{\infty}$ forms. Check the form first, every time.

## Frequently asked questions

### What is MA 16500 at Purdue?

MA 16500, Analytic Geometry And Calculus I, is a 4-credit introduction to differential and integral calculus of one variable with applications, plus conic sections. It is designed for students who took at least one semester of calculus in high school and earned an A or B.

### Should I take MA 16500 or MA 16100?

The math department designs MA 16500 for students with at least a semester of high school calculus with an A or B, and MA 16100 for students without that background. MA 16100 carries 5 credits, which gives more time per topic. The two exclude each other.

### What comes after MA 16500?

MA 16600, Analytic Geometry And Calculus II, which the department describes as the continuation of MA 16500. It covers vectors, techniques of integration, infinite series, polar coordinates and surfaces in three dimensions.

### Is MA 16500 hard?

Because it assumes some prior exposure to calculus, it moves faster than a first-time course. Students who are rusty on high school calculus should review limits and derivative rules before the semester starts.

### How should I prepare for MA 16500?

Refresh college algebra and trigonometry, which the course lists as expected competence, then review limits and derivative rules. The Calculus 1 path on PracticeCalculus covers both in order.