# MTH 101 Elementary Mathematics I: Topics, Study Guide, Practice

> MTH 101 Elementary Mathematics I (Algebra and Trigonometry) study guide: every CCMAS topic, worked examples and the practice that prepares you for MTH 102.

Source: https://practicecalculus.com/courses/nuc-mth-101
Updated: 2026-11-03

## At a glance

- **Course code:** MTH 101 (Elementary Mathematics I, Algebra and Trigonometry)
- **Credit units:** 2 units, compulsory (30 lecture hours)
- **Level:** 100 level, core in the CCMAS B.Sc. Mathematics programme and many other science and computing programmes
- **Covers:** Sets and Venn diagrams, real numbers, mathematical induction, sequences and series, quadratic equations, the binomial theorem, complex numbers and De Moivre's theorem, 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 is the first mathematics course in the NUC CCMAS: a compulsory 2-unit course at 100 level.
- It is an algebra and trigonometry course, not calculus, but it supplies the skills every calculus course after it relies on.
- Its trigonometry, sequences and series, and complex numbers in polar form lead directly into MTH 102 and later courses.
- The Functions warm-up on PracticeCalculus drills the exponent, logarithm and trig skills MTH 101 builds.

**MTH 101 Elementary Mathematics I (Algebra and Trigonometry)** is the first mathematics course in the National Universities Commission's Core Curriculum and Minimum Academic Standards (CCMAS). It is a compulsory 2-unit course at 100 level, shared by mathematics students and by many science, computing and engineering-related programmes. It is not a calculus course, but it builds the algebra and trigonometry that calculus depends on. This guide maps the MTH 101 topics to practice on PracticeCalculus where we have it, and tells you plainly where we do not.

## What MTH 101 covers

The CCMAS outline opens with elementary set theory: subsets, union, intersection, 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. Complex numbers follow, with their algebra, the Argand diagram, De Moivre's theorem and the $n$th roots of unity. The course closes with circular measure, trigonometric functions of angles of any size, and the addition and factor formulae.

The learning outcomes ask students to explain the basic ideas of sets, solve quadratic equations, work with trigonometric functions, recognise the different kinds of numbers and use the binomial theorem.

In the language of other countries, MTH 101 is **precalculus**: the toolkit you need before Calculus 1.

## MTH 101 topic map

PracticeCalculus is a calculus site, so we have no lessons on sets, Venn diagrams or proof by induction. The rows below are the MTH 101 topics that feed straight into calculus.

| MTH 101 topic | Practice | Read |
| --- | --- | --- |
| Real numbers and functions of them | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Absolute value function](/functions/absolute-value-function), [linear function](/functions/linear-function) |
| Theory of quadratic equations | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Quadratic function](/functions/quadratic-function) |
| Indices and logarithms used throughout | [Exponent rules](/learn/calculus-1/functions-warmup/exponent-rules) | [Exponential functions](/functions/exponential-functions), [logarithmic functions](/functions/logarithmic-functions) |
| Binomial theorem | [Exponentials and logarithms](/learn/calculus-1/functions-warmup/exponentials-and-logs) | [Polynomial functions](/functions/polynomial-functions) |
| Real sequences and series | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Geometric series](/blog/geometric-series), [geometric series formula](/rules/geometric-series-formula) |
| Circular measure (radians) | [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values) | [Sine function](/functions/sine-function) |
| Trig functions of any angle | [Warm-up practice](/learn/calculus-1/functions-warmup/warmup-practice) | [Cosine function](/functions/cosine-function), [tangent function](/functions/tangent-function), [reciprocal trig functions](/functions/reciprocal-trig-functions) |
| Argand diagram and modulus-argument form | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Arctangent](/functions/arctangent) |

## Where MTH 101 sits in the CCMAS sequence

| Course | Level | Focus |
| --- | --- | --- |
| MTH 101 Elementary Mathematics I | 100 level | Algebra and trigonometry |
| [MTH 102](/courses/nuc-mth-102) Elementary Mathematics II | 100 level | Limits, derivatives and integrals |
| [MTH 103](/courses/nuc-mth-103) Elementary Mathematics III | 100 level | Vectors, coordinate geometry and dynamics |

Most of what goes wrong in MTH 102 is MTH 101 material: a misremembered trig value, a sign error in a quadratic, or a rule of indices used the wrong way round. Time spent on MTH 101 pays off for the whole degree.

## Example problems at the MTH 101 level

These are original practice problems, not past questions.

**1. A quadratic and its discriminant.** Solve $2x^2 - 3x - 2 = 0$.

The discriminant is $b^2 - 4ac = 9 + 16 = 25 > 0$, so there are two real roots. Factorising,

$$(2x + 1)(x - 2) = 0 \implies x = 2 \text{ or } x = -\tfrac{1}{2}$$

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

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

**3. De Moivre's theorem.** Evaluate $(1 + i)^8$. Since $1 + i = \sqrt{2}\left(\cos\frac{\pi}{4} + i\sin\frac{\pi}{4}\right)$,

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

**4. The binomial theorem.** The coefficient of $x^2$ in $(1 + 2x)^5$ is $\binom{5}{2}(2)^2 = 10 \cdot 4 = 40$.

## How to do well in MTH 101

- **Learn the special angles cold.** Values like $\sin 60^\circ = \frac{\sqrt{3}}{2}$ come up in MTH 101, MTH 102 and beyond. Drill them in [Key trig values](/learn/calculus-1/functions-warmup/key-trig-values).
- **Write out identities, then use them.** Practice the addition and factor formulae on fresh angles until you can pick the right one without looking.
- **Connect complex numbers to trig.** De Moivre's theorem is just trigonometry in modulus-argument form, so a solid grip on angles makes it much easier.
- **Preview calculus.** Once MTH 101 feels comfortable, start the [Limits](/learn/calculus-1/limits/what-is-a-limit) unit and skim the [calculus formula sheet](/formulas) so MTH 102 does not feel like a jump. The guide on [how to study calculus](/blog/how-to-study-calculus) shows how to build a daily habit.

## Frequently asked questions

### What is MTH 101?

MTH 101, Elementary Mathematics I (Algebra and Trigonometry), is the first 100 level mathematics course in the National Universities Commission core curriculum (CCMAS). It covers sets, the real number system, induction, sequences and series, quadratic equations, the binomial theorem, complex numbers and trigonometry.

### Is MTH 101 calculus?

No. MTH 101 is algebra and trigonometry. Calculus starts in MTH 102 Elementary Mathematics II, which uses the algebra and trig from MTH 101 in almost every problem.

### What comes after MTH 101?

MTH 102 Elementary Mathematics II (Calculus) follows it at 100 level. In the CCMAS B.Sc. Mathematics programme, MTH 103 Elementary Mathematics III (vectors, geometry and dynamics) is also taken at 100 level.

### Is MTH 101 hard?

Much of MTH 101 extends secondary school further mathematics, so students with a strong SSCE background usually find the start familiar. Complex numbers, De Moivre's theorem and induction are often new, and they reward steady practice rather than memorising.

### How should I study for MTH 101?

Work problems from each topic every week instead of saving them for the exam. Keep a short list of identities (addition formulae, factor formulae, the binomial expansion) and practice using them until you can recall them without notes.