MTH 102 Elementary Mathematics II (Calculus): Study Guide

MTH 102 Elementary Mathematics II (Calculus) is the first calculus course in the National Universities Commission's Core Curriculum and Minimum Academic Standards (CCMAS). It is a compulsory 2-unit course at 100 level, taken by mathematics students and by students in many other science, computing and engineering-related programmes that follow the CCMAS. Because so many universities use the same code, students often search for it simply as "MTH 102 calculus". This guide maps every MTH 102 topic to free practice, so you can learn each idea by solving problems with instant feedback.

What MTH 102 covers

The CCMAS outline for MTH 102 starts with functions of a real variable and their graphs, then moves to limits and the idea of continuity. The derivative is introduced as the limit of a rate of change, followed by techniques of differentiation and their use in finding extreme values and sketching curves. The second half treats integration as the reverse of differentiation, methods of integration, definite integrals, and applications to areas and volumes.

The stated learning outcomes are that students can tell the different rules of differentiation and integration apart, explain functions, limits and continuity, and apply definite integrals to areas and volumes.

That is a close match for a standard Calculus 1 course. Universities add their own material to the CCMAS core (the CCMAS sets about 70 percent of each programme), so your department may go further, but the topics below are the shared foundation.

MTH 102 topic map

Each row links to a lesson you can practice and to a page that explains the idea.

Where MTH 102 sits in the CCMAS sequence

MTH 101 supplies the algebra and trigonometry you use in every MTH 102 calculation. MTH 201 then reviews MTH 102 and extends calculus to functions of two and three variables.

Example problems at the MTH 102 level

These are original practice problems of the kind the course covers.

1. A limit by factorising. Evaluate \lim_{x \to 3} \frac{x^2 - 9}{x - 3}.

2. Turning points. Find and classify the stationary points of y = x^3 - 3x.

At x = 1, y'' = 6 > 0, so (1, -2) is a minimum. At x = -1, y'' = -6 < 0, so (-1, 2) is a maximum.

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

How to do well in MTH 102

• Master the differentiation rules early. The product, quotient and chain rule appear in almost every later topic, including curve sketching and integration by substitution.
• Practice a little every day. Short daily sessions on practice beat one long session before the exam, because calculus skills fade without repetition.
• Keep a formula sheet beside you. The calculus formula sheet puts the standard derivatives and integrals on one page.
• Watch for algebra slips. Our list of common calculus mistakes covers sign errors, dropped constants and the other errors that cost marks.
• Plan your revision. The guide on how to prepare for a calculus exam shows how to turn your notes into timed practice.

Tip: if limits feel abstract, start with direct substitution and only reach for factorising when you get \frac{0}{0}.