# UNN MTH 111 Elementary Mathematics I: Study Guide and Practice

> A study guide for UNN MTH 111 (Elementary Mathematics I): sets, sequences and series, binomial theorem, trigonometry and complex numbers, with practice.

Source: https://practicecalculus.com/courses/unn-mth-111
Updated: 2026-11-03

## At a glance

- **Course code:** MTH 111
- **Credit units:** 3 units
- **Level:** 100 level, first-year major course (first semester)
- **Covers:** Sets and Venn diagrams, real numbers, mathematical induction, sequences and series, quadratic equations, the binomial theorem, trigonometric functions and formulae, complex numbers and De Moivre's theorem
- **Taken with:** MTH 121 Elementary Mathematics II (limits, differentiation and integration)
- **Practice here:** [Functions warm-up](/learn/calculus-1/functions-warmup/function-notation) and [sequences](/learn/calculus-2/sequences-and-series/sequences) lessons

## Key takeaways

- MTH 111 is a 3-unit first-year course at the University of Nigeria, Nsukka that builds the algebra and trigonometry used in calculus.
- It covers sets, real numbers, induction, sequences and series, quadratic equations and the binomial theorem.
- Trigonometric functions of any angle and complex numbers, up to De Moivre's theorem and roots of unity, complete the course.
- It is taken alongside MTH 121, where limits, derivatives and integrals begin.

**UNN MTH 111**, Elementary Mathematics I, is the first mathematics course for students in the Department of Mathematics at the University of Nigeria, Nsukka. It is a 3-unit major course in the first semester of the first year, and it lays the algebra and trigonometry foundation that calculus depends on. This guide maps each MTH 111 topic to practice and reference pages, so you can strengthen the skills you will need in [MTH 121](/courses/unn-mth-121) and beyond.

## What UNN MTH 111 covers

According to the department's course description, MTH 111 begins with elementary set theory: subsets, unions, intersections, complements and Venn diagrams. It then studies the real numbers (integers, rational and irrational numbers), mathematical induction, real sequences and series, the theory of quadratic equations and the binomial theorem.

The second part is trigonometry: circular (radian) measure, the trigonometric functions of angles of any size, and the addition and factor formulae. The course ends with complex numbers: their algebra, the Argand diagram, De Moivre's theorem and the $n$th roots of unity.

In standard terms, MTH 111 is a **precalculus** course with an early look at sequences and series. None of it is calculus yet, but nearly every topic comes back in MTH 121 and later courses.

## MTH 111 topic map

Our lessons focus on calculus, so for MTH 111 the practice links point to the closest warm-up and series lessons, and the reading links point to reference pages that use these ideas.

| MTH 111 topic | Practice | Read |
| --- | --- | --- |
| Real numbers and functions | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Linear functions](/functions/linear-function) |
| Quadratic equations | [Warm-up practice](/learn/calculus-1/functions-warmup/warmup-practice) | [Quadratic function](/functions/quadratic-function) |
| Indices and logarithms (background) | [Exponent rules](/learn/calculus-1/functions-warmup/exponent-rules) | [Logarithmic functions](/functions/logarithmic-functions) |
| Real sequences | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Limits at infinity](/blog/limits-at-infinity) |
| Series and partial sums | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Geometric series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Geometric series formula](/rules/geometric-series-formula) |
| Circular measure and trig values | [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values) | [Sine function](/functions/sine-function), [cosine function](/functions/cosine-function) |
| Trig functions of any angle | [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values) | [Tangent function](/functions/tangent-function), [reciprocal trig functions](/functions/reciprocal-trig-functions) |
| Complex numbers and De Moivre's theorem | [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values) | [Natural exponential function](/functions/natural-exponential-function) |

## MTH 111 and the rest of the UNN first year

| Course | Units | Focus |
| --- | --- | --- |
| MTH 111 Elementary Mathematics I | 3 | Sets, numbers, series, trigonometry, complex numbers |
| MTH 121 Elementary Mathematics II | 3 | Limits, derivatives, integrals and their applications |
| MTH 122 Elementary Mathematics III | 3 | Vectors, coordinate geometry, particle mechanics |
| MTH 132 Elementary Mechanics I | 3 | Forces, equilibrium and particle dynamics |

MTH 111 and MTH 121 are both listed among the first-year major courses, so you may be learning trigonometric identities in one course while differentiating $\sin x$ in the other. Strong MTH 111 skills make MTH 121 much easier. At 200 level, [MTH 242 Mathematical Methods I](/courses/unn-mth-242) continues the calculus.

## Example problems at the MTH 111 level

**1. Sum of a geometric progression.** Find $3 + 6 + 12 + \cdots + 384$.

Here $a = 3$ and $r = 2$. Since $384 = 3 \cdot 2^7$, there are $8$ terms, so

$$S_8 = \frac{a(r^n - 1)}{r - 1} = \frac{3(2^8 - 1)}{2 - 1} = 3 \cdot 255 = 765$$

**2. The binomial theorem.** Find the coefficient of $x^3$ in $(1 + 2x)^5$.

The general term is $\binom{5}{k}(2x)^k$. With $k = 3$:

$$\binom{5}{3} \cdot 2^3 = 10 \cdot 8 = 80$$

**3. An addition formula.** Find the exact value of $\sin 75^\circ$.

$$\sin 75^\circ = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2}\cdot\frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$$

**4. De Moivre's theorem.** Compute $(1 + i)^8$.

In polar form $1 + i = \sqrt{2}\left(\cos\frac{\pi}{4} + i\sin\frac{\pi}{4}\right)$, so

$$(1 + i)^8 = (\sqrt{2})^8\left(\cos 2\pi + i \sin 2\pi\right) = 16$$

## How to do well in UNN MTH 111

- **Know the special angles by heart.** Values like $\sin 30^\circ = \frac{1}{2}$ and $\cos 45^\circ = \frac{\sqrt{2}}{2}$ appear in trigonometry, complex numbers and later in every calculus course. Drill them in [key trig values](/learn/calculus-1/functions-warmup/key-trig-values).
- **Write induction proofs in a fixed pattern.** State the base case, assume the result for $n = k$, then prove it for $n = k + 1$. Marks are often lost by skipping the assumption step.
- **Connect series to their formulas.** The [geometric series formula](/rules/geometric-series-formula) handles a large share of sequence and series questions.
- **Keep the formulas together.** The [calculus formula sheet](/formulas) includes the trig identities you will reuse in MTH 121.
- **Start calculus early.** Once MTH 111 feels comfortable, begin the [Calculus 1](/learn/calculus-1) path and read [how to study calculus](/blog/how-to-study-calculus) so MTH 121 does not arrive as a shock.

> **Tip:** practice with [practice exams](/practice) once you start MTH 121, and come back to the warm-up lessons whenever an algebra or trig step slows you down.

## Frequently asked questions

### What is MTH 111 at UNN?

MTH 111 Elementary Mathematics I is a 3-unit, 100-level course in the UNN Department of Mathematics. Its official description covers set theory, the real number system, mathematical induction, sequences and series, quadratic equations, the binomial theorem, trigonometry and complex numbers.

### Is MTH 111 a calculus course?

Not directly. MTH 111 is the precalculus foundation: the algebra, series and trigonometry that calculus relies on. The calculus itself starts in MTH 121 Elementary Mathematics II.

### What comes after MTH 111?

MTH 121 Elementary Mathematics II is listed beside MTH 111 among the first-year major courses and covers limits, differentiation and integration. MTH 122 Elementary Mathematics III follows with vectors, coordinate geometry and mechanics.

### Is MTH 111 hard?

Much of it extends secondary school further mathematics, so students with a strong O level background usually settle in quickly. Induction proofs and complex numbers in polar form are the parts most students need extra practice with.

### How should I prepare for MTH 111?

Revise indices, logarithms, quadratic equations and the trigonometric ratios of special angles. Then practice short problems every day rather than reading notes, because every topic in the course is learned by working examples.