# Rutgers Math 135 (01:640:135) Calculus I: Study Guide and Practice

> A study guide for Rutgers Math 135, Calculus I for the Life and Social Sciences: limits, derivatives, applications and basic integration, with practice.

Source: https://practicecalculus.com/courses/rutgers-01-640-135
Updated: 2026-11-03

## At a glance

- **Course code:** 01:640:135 (Math 135)
- **Credits:** 4
- **Offered:** Fall, spring and summer
- **Prerequisites:** Math 112 or Math 115, or placement
- **Covers:** Limits and continuity, the derivative and tangent lines, applications of the derivative, basic integration
- **Who takes it:** Many biological and social science majors, and Rutgers Business School students
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- Math 135 is the Rutgers New Brunswick Calculus I course intended for many biological and social science majors.
- It is a 4-credit course offered in fall, spring and summer, with the same prerequisite as Math 151.
- It covers limits and continuity, the derivative and tangent lines, applications of the derivative and basic integration.
- The School of Engineering does not accept Math 135, and Math 136 does not lead to Math 251.

**Rutgers Math 135** (01:640:135, Calculus I for the Life and Social Sciences) is the Calculus I course at Rutgers New Brunswick intended for many biological and social science majors, and Rutgers Business School currently requires it. It is a full introduction to calculus with a focus on rates of change and their applications. This guide maps each Math 135 topic to a lesson you can practice with instant feedback.

## What Rutgers Math 135 covers

The Rutgers math department describes Math 135 as an introduction to calculus covering limits and continuity, the derivative and tangent lines, applications of the derivative, and basic integration.

In standard terms, that is **Calculus 1**, with integration covered at an introductory level. On PracticeCalculus it lines up with the Calculus 1 path from limits through the integrals unit. Growth models and rates of change in biology and economics make the rate-of-change lessons especially useful.

## Math 135 topic map

| Math 135 topic | Practice | Read |
| --- | --- | --- |
| Functions, exponentials and logs | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Exponential functions](/functions/exponential-functions), [natural logarithm](/functions/natural-logarithm) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| Rates of change | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| The derivative and tangent lines | [Tangent lines](/learn/calculus-1/the-derivative/tangent-lines) | [Power rule](/blog/power-rule) |
| Derivative rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule](/blog/chain-rule) |
| Exponential growth | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Derivatives of exponential and log functions](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Applications: graphs and optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems), [curve sketching](/blog/curve-sketching-with-derivatives) |
| Basic integration | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals and net change | [Net change and displacement](/learn/calculus-1/applications-of-integrals/net-change) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |

## Math 135 vs Math 151

| Question | Math 135 | [Math 151](/courses/rutgers-01-640-151) |
| --- | --- | --- |
| Intended for | Many biological and social science majors, Rutgers Business School | Mathematical and physical sciences, School of Engineering |
| Credits | 4 | 4 |
| Next course | Math 136, or [Math 152](/courses/rutgers-01-640-152) (not recommended) | Math 152 |
| Leads to Math 251? | Not through Math 136 | Yes, through Math 152 |

The department's advice is simple: if your major might need Math 152 or Math 251, take Math 151. If you are unsure, ask an adviser in your major. Also note that students who fail Calculus I (135 or 151) twice cannot take it again at New Brunswick without an approved appeal.

## Example problems at the Math 135 level

**1. Marginal cost.** If $C(q) = 0.5q^2 + 10q + 100$ dollars, then $C'(q) = q + 10$. At $q = 20$ units, the marginal cost is $C'(20) = 30$ dollars per unit.

**2. Exponential growth rate.** A population grows as $P(t) = 500e^{0.04t}$. Then

$$P'(t) = 500 \cdot 0.04\,e^{0.04t} = 20e^{0.04t}$$

so at $t = 0$ it is growing by $20$ individuals per year.

**3. Net change from a rate.** If water flows in at $r(t) = 2t + 1$ liters per minute, the amount added in the first 3 minutes is

$$\int_0^3 (2t + 1)\,dt = \left[t^2 + t\right]_0^3 = 12 \text{ liters}$$

## How to do well in Math 135

- **Master exponentials and logs.** Growth and decay models are everywhere in life and social science applications. The [exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) warm-up is a good start.
- **Always state units.** A derivative is a rate, so its units are "output per input". Writing units catches many setup mistakes.
- **Drill the rules** with the [formula sheet](/formulas) open at first, then closed.
- **Review [common calculus mistakes](/blog/common-calculus-mistakes)** and take timed [practice exams](/practice) before each midterm.

> **Tip:** "marginal" in economics just means "derivative". Marginal cost, revenue and profit are $C'$, $R'$ and $P'$.

## Frequently asked questions

### What is Rutgers Math 135?

Math 135 (01:640:135) is Calculus I for the Life and Social Sciences at Rutgers New Brunswick. It introduces limits and continuity, the derivative and tangent lines, applications of the derivative and basic integration.

### What is the difference between Math 135 and Math 151?

Math 135 is intended for many biological and social science majors, and Rutgers Business School requires it with a C. Math 151 is for the mathematical and physical sciences and is required by the School of Engineering, which does not accept Math 135. If you will need Math 152 or Math 251, the department strongly recommends Math 151.

### What comes after Math 135?

The second course in the 135 sequence is Math 136. Students can also take Math 152 after Math 135, but the department says this is not a recommended sequence. Math 136 does not satisfy the prerequisite for Math 251.

### Is Math 135 easier than Math 151?

Both are full Calculus I courses worth 4 credits with the same prerequisite. They differ mainly in audience and emphasis, so choose the one your major requires rather than the one that sounds easier.

### How should I prepare for Math 135?

Refresh algebra, functions, exponents and logarithms, which appear constantly in growth and rate problems. Then start on limits and the idea of a rate of change.