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University of Nigeria, Nsukka (UNN)

UNN MTH 121 Elementary Mathematics II: Study Guide and Practice

A study guide for UNN MTH 121 (Elementary Mathematics II): limits, differentiation, curve sketching and integration, with practice for every topic.

University of Nigeria, Nsukka (UNN) Updated 4 min read

At a glance

Course code
MTH 121
Credit units
3 units
Level
100 level, listed with MTH 111 among the first-year major courses
Covers
Functions and graphs, limits and continuity, the derivative as a limit of rate of change, techniques of differentiation, curve sketching, methods of integration, definite integrals, areas and volumes
Companion course
MTH 111 Elementary Mathematics I (sets, numbers, sequences, trigonometry, complex numbers)
Later calculus course
MTH 242 Mathematical Methods I (200 level)
Practice here
Calculus 1
On this page
  1. What UNN MTH 121 covers
  2. MTH 121 topic map
  3. Where MTH 121 sits in the UNN sequence
  4. Example problems at the MTH 121 level
  5. How to do well in UNN MTH 121

UNN MTH 121, Elementary Mathematics II, is the first calculus course for mathematics students at the University of Nigeria, Nsukka. It is a 3-unit major course in the first-year programme of the Department of Mathematics, taken alongside MTH 111, and many science and engineering students meet it in their first year too. This guide maps every MTH 121 topic to free practice, so you can learn each idea by solving problems with instant feedback.

What UNN MTH 121 covers

The department's official course description starts with functions of a real variable and their graphs, then moves to limits and continuity. The derivative is introduced as the limit of a rate of change, followed by the techniques of differentiation and curve sketching. The second half treats integration as the reverse of differentiation, methods of integration and definite integrals, and ends with using integration to find areas and volumes.

Despite the "Elementary Mathematics" title, that is a complete Calculus 1 course: limits, derivatives, applications of derivatives and the basic definite integral. The parts of a typical Calculus 2 course, such as series and advanced integration techniques, appear later at UNN.

MTH 121 topic map

Each row links to a lesson you can practice and a reference page or guide that explains the idea.

MTH 121 topic Practice Read
Functions of a real variable and graphs Functions and notation Polynomial functions, rational functions
Limits What is a limit? What is a limit?, limit laws
Continuity Continuity Continuity
The derivative as a limit of rate of change The limit definition Limit definition of the derivative
Techniques of differentiation The power rule Product rule, quotient rule, chain rule
Curve sketching Increasing and decreasing Curve sketching with derivatives
Integration as the inverse of differentiation Undoing derivatives Antiderivatives
Methods of integration U-substitution U-substitution, integration by parts
Definite integrals Evaluating definite integrals Fundamental Theorem of Calculus
Areas Area between curves Area between curves
Volumes Volumes with disks Volumes of revolution

Where MTH 121 sits in the UNN sequence

Course Units What it adds
MTH 111 Elementary Mathematics I 3 Sets, numbers, sequences and series, trigonometry, complex numbers
MTH 121 Elementary Mathematics II 3 Limits, differentiation, integration and their applications
MTH 122 Elementary Mathematics III 3 Vectors, coordinate geometry and particle mechanics
MTH 242 Mathematical Methods I 3 Taylor series, partial derivatives, Lagrange multipliers, line and multiple integrals

MTH 111 and MTH 121 appear together among the first-year major courses, so treat MTH 111's trigonometry and algebra as tools you will use in every MTH 121 derivative. When you reach 200 level, MTH 242 reviews differentiation and integration before taking them into several variables.

Example problems at the MTH 121 level

1. A limit that starts as 0/0. Evaluate \lim_{x \to 3} \dfrac{x^2 - 9}{x - 3}.

Factor the numerator and cancel:

\lim_{x \to 3} \frac{(x - 3)(x + 3)}{x - 3} = \lim_{x \to 3} (x + 3) = 6

2. Differentiation from first principles. Find the derivative of f(x) = x^2 from the definition.

f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h} = \lim_{h \to 0} \frac{2xh + h^2}{h} = \lim_{h \to 0} (2x + h) = 2x

3. Area between two curves. Find the area enclosed by y = x and y = x^2.

The curves meet at x = 0 and x = 1, and x \ge x^2 in between, so

A = \int_0^1 (x - x^2)\,dx = \left[\frac{x^2}{2} - \frac{x^3}{3}\right]_0^1 = \frac{1}{2} - \frac{1}{3} = \frac{1}{6}

4. A volume of revolution. Rotate y = \sqrt{x} for 0 \le x \le 4 about the x-axis. With disks,

V = \pi \int_0^4 (\sqrt{x})^2\,dx = \pi \int_0^4 x\,dx = \pi \left[\frac{x^2}{2}\right]_0^4 = 8\pi

How to do well in UNN MTH 121

  • Master first principles early. Lecturers like to ask for a derivative "from first principles". Practice the limit definition until the algebra of expanding and cancelling h is routine.
  • Drill the differentiation rules. Speed with the chain rule, product rule and quotient rule frees up time for curve sketching and applications in the exam.
  • Keep the formulas in one place. The calculus formula sheet lists the standard derivatives and integrals you need for MTH 121.
  • Learn from typical errors. Sign slips and dropped constants cost the most marks. Read common calculus mistakes before your first test.
  • Practice under time pressure with practice exams that give fresh numbers every time, and follow our guide on how to prepare for a calculus exam.

Tip: curve sketching combines almost everything in MTH 121: limits for asymptotes, derivatives for turning points and the second derivative for concavity. If you can sketch y = x^3 - 3x confidently, you are in good shape for the exam.

Practice it now

What is a limit?

Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.

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Frequently asked questions

What is MTH 121 at UNN?
MTH 121 Elementary Mathematics II is a 3-unit, 100-level course in the UNN Department of Mathematics. It covers functions of a real variable, limits and continuity, the derivative and techniques of differentiation, curve sketching, integration and its applications to areas and volumes.

Is MTH 121 the same as calculus?
Yes, in content. Although its title is Elementary Mathematics II, every topic in the official description is introductory differential and integral calculus, so it matches a Calculus 1 course.

What is the difference between MTH 111 and MTH 121?
MTH 111 covers the algebra and trigonometry foundation: sets, real numbers, induction, sequences and series, quadratic equations, the binomial theorem, trigonometric functions and complex numbers. MTH 121 is where limits, derivatives and integrals begin.

Is MTH 121 hard?
Most students find limits and the first-principles derivative unfamiliar at first, and integration techniques take practice. Weak algebra causes more trouble than the calculus itself, so steady daily practice makes a big difference.

How should I prepare for MTH 121?
Revise indices, logarithms, factorization and trigonometric values from secondary school, then practice limits and simple derivatives in short sessions. The free Calculus 1 path on PracticeCalculus follows the same order as the course.

Written by the PracticeCalculus team

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Related university courses

UNN MTH 111 Precalculus Elementary Mathematics I A study guide for UNN MTH 111 (Elementary Mathematics I): sets, sequences and series, binomial theorem, trigonometry and complex numbers, with practice. UNN MTH 242 Calculus 2 and 3 Mathematical Methods I A study guide for UNN MTH 242 (Mathematical Methods I): Taylor series, partial derivatives, Lagrange multipliers, line and multiple integrals, with practice.