# UI MTH 101 Elementary Mathematics I: Study Guide and Practice

> Study guide for MTH 101 Elementary Mathematics I at the University of Ibadan: algebra, sequences, complex numbers and trigonometry, plus calculus prep.

Source: https://practicecalculus.com/courses/university-of-ibadan-mth-101
Updated: 2026-11-03

## At a glance

- **Course code:** MTH 101 (Elementary Mathematics I)
- **Credit units:** 2 units
- **Status:** Compulsory at 100 level in the Department of Mathematics
- **Covers:** The national CCMAS outline for MTH 101: sets, real numbers, induction, sequences and series, quadratic equations, binomial theorem, complex numbers, circular measure and trigonometry
- **Next course:** MTH 102 Elementary Mathematics II (calculus)
- **Practice here:** [Functions warm-up](/learn/calculus-1/functions-warmup/function-notation) in Calculus 1

## Key takeaways

- MTH 101 Elementary Mathematics I 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 algebra and trigonometry rather than calculus.
- Its trig values, indices, sequences and complex numbers are used constantly in MTH 102 and MTH 103.
- The Functions warm-up on PracticeCalculus drills the MTH 101 skills that calculus relies on.

**MTH 101 Elementary Mathematics I** is the first mathematics course in the **University of Ibadan (UI)** Department of Mathematics course list: a compulsory 2-unit course at 100 level. UI lists its 100 level mathematics under the national CCMAS codes, so MTH 101 follows the National Universities Commission outline for Elementary Mathematics I (Algebra and Trigonometry). It is not calculus, but almost every step in UI's later calculus courses depends on it. This guide shows the topics that feed into calculus and where to practise them.

## What UI MTH 101 covers

The UI course list gives the code, title, units and status. The CCMAS outline for MTH 101 covers elementary set theory and Venn diagrams; the real numbers, from integers to irrational numbers; mathematical induction; real sequences and series; the theory of quadratic equations; and the binomial theorem. It then covers complex numbers, the Argand diagram, De Moivre's theorem and the $n$th roots of unity, and ends with circular measure, trigonometric functions of any angle, and the addition and factor formulae.

That is what other systems call **precalculus**. For the complete national outline, see the [NUC MTH 101 guide](/courses/nuc-mth-101).

## UI MTH 101 topic map

PracticeCalculus focuses on calculus, so there are no lessons here on sets or induction. These are the MTH 101 topics that calculus uses most.

| MTH 101 topic | Practice | Read |
| --- | --- | --- |
| Indices and surds | [Exponent rules](/learn/calculus-1/functions-warmup/exponent-rules) | [Power functions](/functions/power-functions), [square root function](/functions/square-root-function) |
| Logarithms | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Natural logarithm](/functions/natural-logarithm) |
| Quadratic equations | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Quadratic function](/functions/quadratic-function) |
| Sequences and series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Circular measure and special angles | [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values) | [Sine function](/functions/sine-function), [cosine function](/functions/cosine-function) |
| Trigonometric functions of any angle | [Warm-up practice](/learn/calculus-1/functions-warmup/warmup-practice) | [Tangent function](/functions/tangent-function) |
| Complex numbers in modulus-argument form | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Arctangent](/functions/arctangent) |
| Spotting algebra errors | [Find the mistake](/learn/calculus-1/functions-warmup/warmup-find-the-mistake) | [Common calculus mistakes](/blog/common-calculus-mistakes) |

## The UI 100 level mathematics courses

| Course | Units | Status | Focus (CCMAS outline) |
| --- | --- | --- | --- |
| MTH 101 Elementary Mathematics I | 2 | Compulsory | Algebra and trigonometry |
| [MTH 102](/courses/university-of-ibadan-mth-102) Elementary Mathematics II | 2 | Compulsory | Single-variable calculus |
| MTH 103 Elementary Mathematics III | 2 | Compulsory | Vectors, geometry and dynamics |
| UI-MAT 142 Introduction to Actuarial Mathematics | 4 | Elective | Listed by UI as a 100 level elective |

## Example problems at the MTH 101 level

These are original practice problems, not past questions.

**1. Sum of a geometric series.** Find $1 + \frac{1}{3} + \frac{1}{9} + \cdots$. Here $a = 1$ and $r = \frac{1}{3}$, so

$$S_\infty = \frac{a}{1 - r} = \frac{1}{1 - \frac{1}{3}} = \frac{3}{2}$$

**2. A factor formula.** Simplify $\sin 75^\circ + \sin 15^\circ$:

$$2\sin\frac{75^\circ + 15^\circ}{2}\cos\frac{75^\circ - 15^\circ}{2} = 2\sin 45^\circ \cos 30^\circ = 2\cdot\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} = \frac{\sqrt{6}}{2}$$

**3. Roots of unity.** The cube roots of unity are $1$ and $\cos\frac{2\pi}{3} \pm i\sin\frac{2\pi}{3} = -\frac{1}{2} \pm \frac{\sqrt{3}}{2}i$, and they add up to $0$.

## How to do well in UI MTH 101

- **Drill the special angles.** Knowing $\sin$, $\cos$ and $\tan$ at $30^\circ$, $45^\circ$ and $60^\circ$ without thinking saves time in MTH 101 and in every calculus course after it. Use [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values).
- **Show every step.** Induction proofs and complex number questions reward clear working, and clear working makes your own errors easier to spot.
- **Practise in short, regular sessions** with [practice](/practice), and look ahead to MTH 102 with the [formula sheet](/formulas) and the guide on [how to study calculus](/blog/how-to-study-calculus).

## Frequently asked questions

### What is MTH 101 at UI?

MTH 101 Elementary Mathematics I is a compulsory 2-unit course at 100 level in the University of Ibadan Department of Mathematics. It uses the national CCMAS code, and the CCMAS outline covers sets, the real number system, mathematical induction, sequences and series, quadratic equations, the binomial theorem, complex numbers and trigonometry.

### Is UI MTH 101 a calculus course?

No. MTH 101 is algebra and trigonometry. Calculus begins in MTH 102 Elementary Mathematics II, the next course in the UI list.

### What do I take with MTH 101 at UI?

The department lists MTH 102 and MTH 103 as the other compulsory 2-unit mathematics courses at 100 level, along with CSC 101, STA 112 and the general studies courses.

### How do I prepare for UI MTH 101?

Revise SSCE algebra and trigonometry, especially indices, logarithms, quadratic equations and the values of sine and cosine at special angles. Short daily practice is more effective than long sessions before tests.