UNN MTH 111 Elementary Mathematics I: Study Guide and Practice

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 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 nth 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 and the rest of the UNN first year

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 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

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:

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

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

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.
• 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 handles a large share of sequence and series questions.
• Keep the formulas together. The calculus formula sheet includes the trig identities you will reuse in MTH 121.
• Start calculus early. Once MTH 111 feels comfortable, begin the Calculus 1 path and read how to study calculus so MTH 121 does not arrive as a shock.

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