Penn State MATH 140 Calculus I: Topics, Study Guide, Practice

Penn State MATH 140, Calculus With Analytic Geometry I, is the first calculus course for science and engineering students. It is a 4-credit course that fulfills the Quantification (GQ) general education requirement. This guide maps every MATH 140 topic to practice with instant feedback, so you can learn by working problems.

What Penn State MATH 140 covers

The Penn State bulletin describes MATH 140 as beginning with the limit, the idea everything else rests on. Differential calculus follows: derivatives and their use for rates of change, related rates, linearization, optimization and graphing. The course then introduces integral calculus with the Fundamental Theorem of Calculus, and uses antidifferentiation and substitution to find areas of plane regions and volumes of solids of revolution. The bulletin notes that trigonometric functions are included in every topic.

This lines up with a standard Calculus 1 course. One difference: logarithms, exponentials and inverse trig functions are listed as MATH 141 topics, so some schools' Calculus 1 material on e^x and \ln x lands in the second semester at Penn State.

MATH 140 topic map

The Penn State calculus sequence

Honors versions (MATH 140H, 141H, 230H) exist for each course in the main sequence. Continue with the MATH 141 guide and the MATH 230 guide, or see the MATH 110 guide for the business track.

Example problems at the MATH 140 level

1. A trig limit. Using \lim_{x \to 0} \frac{\sin x}{x} = 1,

2. Related rates. A circle's radius grows at 2 cm/s. How fast is the area growing when r = 5 cm? From A = \pi r^2,

3. A volume of revolution. Rotate y = \sqrt{x}, 0 \le x \le 4, about the x-axis. With disks,

How to do well in Penn State MATH 140

• Get trig solid in week one. Because trig is in every topic, the key trig values lesson pays off all semester.
• Practice related rates setups. Draw, label and write the equation relating the quantities before differentiating. The related rates guide walks through the pattern.
• Use the formula sheet for derivative rules and trig identities while learning, then drop it for timed practice exams.
• Avoid classic errors listed in common calculus mistakes, like forgetting the chain rule's inner derivative.
• Plan exam prep with how to prepare for a calculus exam.

Tip: for volumes of revolution, sketch the region and one representative slice first. The sketch tells you whether you need disks or washers.