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Nigerian universities (NUC CCMAS)

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.

Nigerian universities (NUC CCMAS) Updated 3 min read

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 in Calculus 1
On this page
  1. What MTH 101 covers
  2. MTH 101 topic map
  3. Where MTH 101 sits in the CCMAS sequence
  4. Example problems at the MTH 101 level
  5. How to do well in MTH 101

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 nth 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 Absolute value function, linear function
Theory of quadratic equations Slope and rate of change Quadratic function
Indices and logarithms used throughout Exponent rules Exponential functions, logarithmic functions
Binomial theorem Exponentials and logarithms Polynomial functions
Real sequences and series Sequences and their limits Geometric series, geometric series formula
Circular measure (radians) Key trig values Sine function
Trig functions of any angle Warm-up practice Cosine function, tangent function, reciprocal trig functions
Argand diagram and modulus-argument form Polar coordinates Arctangent

Where MTH 101 sits in the CCMAS sequence

Course Level Focus
MTH 101 Elementary Mathematics I 100 level Algebra and trigonometry
MTH 102 Elementary Mathematics II 100 level Limits, derivatives and integrals
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.
  • 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 unit and skim the calculus formula sheet so MTH 102 does not feel like a jump. The guide on how to study calculus shows how to build a daily habit.

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Functions and notation

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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.

Written by the PracticeCalculus team

We build interactive calculus lessons and write every page to be clear and correct. Spotted something off? Tell us and we will fix it.

Related university courses

NUC MTH 102 Calculus 1 Elementary Mathematics II (Calculus) MTH 102 Elementary Mathematics II (Calculus) study guide: limits, derivatives, curve sketching, integrals, areas and volumes, with free practice. NUC MTH 103 Calculus 3 (vectors) Elementary Mathematics III (Vectors, Geometry and Dynamics) MTH 103 Elementary Mathematics III study guide: vectors, dot and cross products, conics, tangents and particle motion from the NUC CCMAS, with practice. NUC MTH 201 Calculus 2 and 3 Mathematical Methods I MTH 201 Mathematical Methods I study guide: mean value theorem, Taylor series, partial derivatives, Lagrange multipliers and multiple integrals, with practice.