UI MTH 102 Elementary Mathematics II: Calculus Study Guide

Study guide for MTH 102 Elementary Mathematics II at the University of Ibadan: limits, derivatives, curve sketching and integrals, with free practice.

University of Ibadan (UI) Updated November 3, 2026 3 min read

Key takeaways

MTH 102 Elementary Mathematics II is a compulsory 2-unit, 100 level course in the University of Ibadan Department of Mathematics.

UI lists it under the national CCMAS code, whose outline is single-variable calculus: limits, derivatives and integrals.

It sits between MTH 101 (algebra and trigonometry) and MTH 201 Mathematical Methods I at 200 level.

Every topic maps to a free Calculus 1 lesson on PracticeCalculus.

MTH 102 Elementary Mathematics II is the first calculus course for mathematics students at the University of Ibadan (UI). The Department of Mathematics lists it as a compulsory 2-unit course at 100 level, next to MTH 101 and MTH 103. UI uses the national CCMAS course codes for this level, so MTH 102 follows the National Universities Commission outline for Elementary Mathematics II (Calculus). This guide maps every topic to free practice, so you can learn calculus by solving problems with instant feedback.

What UI MTH 102 covers

The department's course list gives the code, title, units and status. The content comes from the CCMAS outline for MTH 102, which starts with functions of a real variable, their graphs, limits and the idea of continuity. It defines the derivative as the limit of a rate of change, develops the techniques of differentiation, and applies them to extreme values and curve sketching. The second half treats integration as the reverse of differentiation, covers methods of integration and definite integrals, and applies them to areas and volumes.

Universities can add their own material to the CCMAS core, so check your lecturer's outline for anything extra. The shared core matches a standard Calculus 1 course. For the full national outline, see the NUC MTH 102 guide.

UI MTH 102 topic map

MTH 102 topic	Practice	Read
Functions and their graphs	Functions and notation	Rational functions
Limits and one-sided limits	One-sided and infinite limits	What is a limit?, limit laws
Continuity	Continuity	Intermediate value theorem
The derivative as a rate of change	Instantaneous rate of change	Limit definition of the derivative
Techniques of differentiation	Chain rule: any function	Product and quotient rules, chain rule
Derivatives of trig, exponential and log functions	Exponentials and logarithms	Derivatives of trig functions
Extrema	Absolute extrema on an interval	Optimization problems
Curve sketching	Increasing and decreasing	Curve sketching with derivatives
Integration as anti-differentiation	The reverse power rule	Antiderivatives
Methods of integration	U-substitution	u-substitution rule, integration by parts
Definite integrals	The definite integral as area	Definite integral properties
Areas and volumes	Volumes with washers	Area between curves, volumes of revolution

MTH 102 in the UI mathematics course list

Course	Level	Units	Status
MTH 101 Elementary Mathematics I	100	2	Compulsory
MTH 102 Elementary Mathematics II	100	2	Compulsory
MTH 103 Elementary Mathematics III	100	2	Compulsory
MTH 201 Mathematical Methods I	200	2	Compulsory
MTH 210 Vector Analysis	200	1	Compulsory

The 200 level list also includes UI-MAT 221 Analysis I and UI-MAT 222 Analysis II (4 units each), and the 100 level list offers UI-MAT 142 Introduction to Actuarial Mathematics as an elective.

Example problems at the MTH 102 level

These are original practice problems, not past questions.

1. A product rule derivative. Differentiate $inline$ :

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2. Integration by substitution. With $inline$ , $inline$ :

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3. An area. The area between $inline$ and $inline$ from $inline$ to $inline$ is

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How to do well in UI MTH 102

Practise the rules until they are automatic. Product, quotient and chain rule questions should take seconds, leaving your exam time for curve sketching and areas. Drill them on practice.
Keep the standard results in one place. The calculus formula sheet lists the derivatives and integrals you need.
Learn from errors. Read common calculus mistakes and redo every problem you got wrong a few days later.
Plan ahead for exams. The guide on how to prepare for a calculus exam shows how to build timed practice from your notes.

Frequently asked questions

What is MTH 102 at UI?

MTH 102 Elementary Mathematics II is a compulsory 2-unit course at 100 level in the Department of Mathematics, University of Ibadan. It uses the national CCMAS code, and the CCMAS outline for MTH 102 is the calculus of one variable: limits, continuity, differentiation, curve sketching, integration, and areas and volumes.

What other mathematics courses do UI 100 level maths students take?

The department lists MTH 101 Elementary Mathematics I and MTH 103 Elementary Mathematics III as compulsory 2-unit courses alongside MTH 102, with UI-MAT 142 Introduction to Actuarial Mathematics as an elective.

What comes after MTH 102 at UI?

At 200 level the department lists MTH 201 Mathematical Methods I, which extends calculus to Taylor series and functions of several variables, together with MTH 202 Elementary Differential Equations and MTH 210 Vector Analysis.

Is MTH 102 hard?

It is the first proper calculus course for most students, so expect some adjustment. The topics are standard, and steady weekly practice on limits and derivatives makes the second half on integration much easier.

How do I prepare for UI MTH 102?

Make sure your indices, logarithms and trig values from MTH 101 are solid, then practise limits and the differentiation rules with short daily sessions. The Calculus 1 path on PracticeCalculus follows the same order.