UI MTH 101 Elementary Mathematics I: Study Guide and Practice

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 nth 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.

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.

The UI 100 level mathematics courses

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

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

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.
• 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, and look ahead to MTH 102 with the formula sheet and the guide on how to study calculus.