NUC CCMAS

Calculus begins where algebra ends. This course builds the exact foundation you need to understand function behaviour. You will study function types, graph transformations, and arithmetic operations before moving to limit evaluation and continuity analysis. The lessons progress from basic definitions to advanced techniques, including factorisation, rationalisation, the squeeze theorem, and the intermediate value theorem. Each topic pairs instruction with targeted practice problems to confirm your grasp.

These concepts drive engineering calculations, economic modelling, physics simulations, and algorithm design. You will manipulate functions to predict system responses, evaluate limits to handle sudden data changes, and apply continuity principles when modelling physical or financial processes. Mastering this material replaces formula memorisation with reliable problem-solving for technical work.

You will identify the domain and range of complex expressions, sketch transformed graphs, and calculate composite and inverse functions. You will evaluate limits through direct substitution, algebraic manipulation, trigonometric identities, and the squeeze theorem. You will test for continuity at specific points, classify discontinuity types, and apply the intermediate value theorem across intervals.

This course serves university students preparing for first-year mathematics, secondary school graduates entering science programmes, and developers or analysts needing quantitative skills. Professionals returning to mathematics will rebuild speed and accuracy through structured exercises. Anyone processing technical data will apply these methods daily, regardless of degree title.

functions-limits-and-continuity-calculus-undergraduate

Calculus

Functions, Limits and Continuity - Calculus (Undergraduate Foundation)

Differentiation measures how quantities change at exact moments. This course builds your complete calculus foundation from first principles to advanced methods. We start with rates of change and formal notation, then cover definitions, continuity, differentiability, and direct proofs. The sequence moves through core rules, composite functions, implicit techniques, parametric systems, and higher-order operations. Each concept links to targeted exercises that test your accuracy before you proceed.

These methods solve real problems in physics, engineering, finance, and software development. You will track speed, predict growth, calculate structural stress, and measure market sensitivity. Software developers apply these calculations to optimise machine learning models. Business analysts use them to adjust variables for target profits. The techniques here convert abstract equations into working tools for daily technical tasks.

You will calculate derivatives for polynomial, trigonometric, exponential, logarithmic, and hyperbolic functions without reference material. You will apply the product rule, quotient rule, and chain rule to complex expressions. You will perform implicit, parametric, and logarithmic differentiation. You will compute second-order and higher-order derivatives for standard forms. You will verify differential equations through systematic steps. Every lesson forces active practice and precise calculation.

The material suits first-year university students, polytechnic learners, and independent learners who require a solid calculus base. Secondary school graduates will gain the exact preparation needed for advanced science and mathematics exams. Technical professionals can use the content to refresh forgotten methods or build reliable calculation habits. The explanations skip heavy theory and focus on working steps. Anyone who handles data, graphs, or mathematical models will apply the methods immediately. You will solve standard calculus problems independently.

fundamentals-and-techniques-of-differentiation-calculus

Fundamentals and Techniques of Differentiation - Calculus (Undergraduate Foundation)

Finding turning points is the core of this calculus course. You will locate stationary points where change stops and reverses. We cover identifying maxima and minima using direct mathematical tests. You will find points of inflection where a curve changes its bend. You will learn to sketch complex graphs by hand using these specific markers.

Engineers and managers use these tools for optimisation and reducing waste. You can find the best size for a tank to use the least metal or the best speed to save petrol. In business, these methods help find the price that earns the most profit while keeping costs at the lowest level. Mastering these applications helps you solve real problems where you must find the best possible outcome for a physical system.

By the end, you will find and name all stationary points on any graph. You will use derivative tests to prove if a point is a maximum, a minimum, or an inflection point. You will identify where a curve is concave or convex. You will sketch extreme curves showing all intercepts, turning points, and asymptotes clearly without needing a calculator.

This course serves undergraduate foundation students and those entering engineering or management. It is for anyone needing to understand how different factors change together in science or business. Even those outside these fields gain the logic needed for technical problem-solving. These skills are essential for anyone who needs to study physical systems and find the most efficient ways to work.

applications-of-differentiation-calculus-undergraduate

Applications of Differentiation - Calculus (Undergraduate Foundation)

Integration is the essential tool for summing tiny changes into whole totals. This course covers the reversal of differentiation to find areas, volumes, and precise solutions. You will learn how to handle indefinite integrals and master core methods like substitution and integration by parts. The curriculum also includes reduction formulae to simplify repeated, complex calculations. Mastering these techniques is the first step toward solving the advanced problems found in engineering and the physical sciences.

Engineers and scientists use these methods to design structures, predict natural events, and build hardware. Knowledge of integration allows you to calculate the work done by varying forces or the exact flow of fluids in a system. If you plan to work in technical fields or handle data-driven projects, these calculations are unavoidable. This course provides the practical math needed to turn abstract formulas into real-world applications and professional results.

After completing these modules, you will correctly identify and apply the right integration technique for any given problem. You will solve indefinite integrals using standard rules and perform variable changes through the substitution method. You will also manage products of functions using integration by parts and apply reduction formulae to streamline long processes. These skills prepare you to tackle the differential equations required in higher university years and professional licensing exams.

This course is for undergraduate students in engineering, mathematics, and the sciences seeking a firm foundation in calculus. It also serves secondary school leavers who want to prepare for the rigours of university-level technical courses. Even for those outside of science tracks, the logic and step-by-step methods taught here improve general analytical thinking and problem-solving. This training ensures you meet the international standards expected in any modern technical career.

fundamentals-and-techniques-of-integration-calculus

Fundamentals and Techniques of Integration - Calculus (Undergraduate Foundation)

Calculate exact areas and volumes using definite integrals and numerical approximations. You will solve definite integrals using standard integration techniques and handle complex shapes with the Trapezium and Simpson's rules. This content focuses on finding the total area under a curve and the volume of objects formed when a shape rotates around an axis.

These methods are essential for measuring irregular land plots, designing water tanks, and calculating the weight of machine parts. Civil, mechanical, and agricultural engineers use these tools daily to ensure structures are safe and materials are used efficiently. Knowing how to approximate answers is vital when you face real-life data that does not fit a simple textbook formula.

You will evaluate definite integrals, find the area between two curves, and calculate the volume of solids of revolution. You will also master numerical methods like the Trapezium rule and Simpson's rule to get accurate results from experimental data. This training enables you to solve practical measurement problems in any technical field.

This course is for undergraduate science and engineering students who need a strong mathematical base. Secondary school leavers intending to study technical courses will find this a necessary head start. Even those not in engineering will improve their ability to handle data and understand how physical objects are measured in the real world.

definite-integrals-and-numerical-methods-calculus

Definite Integrals and Numerical Methods - Calculus (Undergraduate Foundation)

Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world.

This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential.

After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

Our mission is to simplify complex concepts by teaching from first principles. We go beyond simple problem-solving to build a deep, foundational understanding of the "why" behind the "how."

Our content is meticulously designed for undergraduates navigating the rigorous curricula of top engineering and physical science programmes in Nigeria and globally.

As a core academic partner on UniDrills, we are committed to upholding the highest standards of clarity, precision, and professional excellence in education.

Max Engineering Tutorials

Olowojaye Rufus

An academic and graduate engineer dedicated to explaining complex concepts in mathematics, computer science and engineering. I founded UniDrills to bring this vision to life, creating a world-class e-learning marketplace with a global outlook. I apply a first-principles approach to software architecture to build a professional and intuitive learning experience.

Elementary Mathematics II

MTH 102: Elementary Mathematics II - Calculus

Static charges power every electronic device you use. This course explains how stationary charges create forces and fields without physical contact. You will move from basic atomic structure to advanced field calculations using Coulomb's law and Gauss's law. It covers charge conservation, induction, superposition, and symmetry. You will learn to model invisible forces that act across space. This foundation is critical for understanding all electrical phenomena.

These principles explain lightning, photocopiers, and spray painting. In engineering, this knowledge helps design capacitors and manage electromagnetic interference. You will learn to protect circuits from static discharge and predict high-voltage behaviour. Understanding field distribution around conductors and insulators is vital for real-world applications. This skill set allows you to solve practical problems in power systems and electronics. It connects abstract physics to tangible technology used daily.

By the end, you will calculate force between multiple charges using vector addition. You will determine electric field strength at any point in space for various shapes. You will apply Gauss's law to solve complex problems for spheres, cylinders, and plates. You will explain induction, conduction, and dipole behaviour. These skills enable accurate modelling of electrical interactions in academic and industrial settings. You will master the mathematical tools needed for electromagnetism.

This course is for first-year university students and engineering aspirants. It suits science teachers and technical professionals needing a refresher on core physics laws. Even non-engineers will benefit from the analytical thinking developed here. You will gain a clear understanding of the laws governing modern electronic devices. It builds a strong base for further study in physics or electrical engineering. Anyone interested in how electricity works will find value in this structured approach.

static-charges-and-fields-physics-undergraduate-foundation

Physics

Static Charges and Fields - Physics (Undergraduate Foundation)

Electricity is more than just flowing current; it is about stored energy and the pressure that moves it. This course explains electric potential energy and potential difference, showing how charges interact in space. You will learn about electric dipoles and how capacitors hold electrical energy in fields. We cover calculating capacitance for components in series and parallel, alongside the role of dielectrics in increasing storage capacity.

Understanding these concepts is vital for anyone working with electronics or power systems. Capacitors are in almost every device, from camera flashes to computer motherboards, where they smooth out power or store quick bursts of energy. Mastering these principles allows you to design better circuits and understand how modern energy storage works in real-world hardware. This knowledge forms the base for advanced studies in electrical engineering and applied physics.

By the end of this module, you will calculate electric potential and work done on charges with precision. You will solve complex problems involving capacitor networks in different configurations. You will explain how dielectric materials change the behaviour of electric fields and increase energy density. These skills ensure you can analyse and build functional electronic paths that handle energy efficiently.

This course is for undergraduate science and engineering students needing a solid foundation in electromagnetism. It also benefits secondary school leavers preparing for university-level physics or technical exams. Even hobbyists building simple electronic gadgets will find these lessons useful for choosing the right components for their projects. The focus remains on clear, practical physics that translates directly to classroom success and technical work.

electric-potential-and-capacitors-physics-undergraduate

Electric Potential and Capacitors - Physics (Undergraduate Foundation)

This course covers the movement of electrical charges through circuits that do not change direction. You will learn the exact definitions of current, voltage, and resistance and how they relate through Ohm’s law. The syllabus explains resistivity in different materials, the electromotive force (EMF) provided by power sources, and the internal resistance of batteries. You will master the use of Kirchhoff’s rules to solve complex networks of resistors and power supplies.

Mastering these principles is necessary for anyone building or fixing electrical devices and power systems. You will understand why certain wires heat up more than others and how to choose the right components for a circuit. These skills are used daily by electrical engineers, solar technicians, and hobbyists repairing household electronics or designing battery-powered gadgets. Practical knowledge of DC circuits ensures you can calculate power needs and prevent electrical failures in real-world projects.

By the end of this course, you will be able to calculate current, voltage, and resistance in any part of a DC circuit using Ohm’s law. You will know how to determine the resistivity of a wire based on its material and physical dimensions. You will gain the ability to distinguish between terminal voltage and EMF while accounting for internal resistance. Most importantly, you will be able to apply Kirchhoff’s current and voltage laws to find unknown values in circuits with multiple loops and junctions.

This course is for undergraduate students in engineering or science who need a solid foundation in electricity. It is also suitable for secondary school leavers preparing for university entrance exams or technical vocational training. Even for those not pursuing a degree, the course provides essential logic for electricians and tech enthusiasts who want to understand the science behind the tools they use. Anyone looking to move from basic guessing to precise electrical calculation will find this material vital.

direct-current-circuits-physics-undergraduate-foundation

Direct Current Circuits - Physics (Undergraduate Foundation)

Magnetism moves the world, from the small compass in your hand to the massive motors in factories. This course teaches you how magnetic fields work and how they push or pull moving electric charges. You will learn the Lorentz force formula, the way magnetic dipoles behave, and the specific rules for calculating magnetic strength using the Biot-Savart law and Ampere’s law. We focus on the core physics that connects electricity to magnetic forces.

Knowing these laws is the first step to building or fixing electric motors, generators, and transformers. Engineers and technicians use this math to design medical imaging machines like MRI scanners and to manage power grids. If you want to work in renewable energy, robotics, or telecommunications, you must understand how currents create magnetic fields. This knowledge helps you solve real problems in electrical and mechanical systems.

By the end of this study, you will be able to calculate the force on a wire carrying current and predict the path of a charge moving through a field. You will master the use of Ampere’s law to find the magnetic field around different wire shapes. You will also understand how to find the torque on a magnetic loop. These skills allow you to analyse how magnets and electricity interact in any device.

This course is for first-year university students and polytechnic students studying engineering or science. It also helps secondary school leavers who want a head start before resuming at a higher institution. Even if you are just a hobbyist building simple electronics at home, these lessons provide the clear facts you need to make your projects work. It turns confusing theories into tools you can use immediately.

magnetic-fields-and-forces-physics-undergraduate

Magnetic Fields and Forces - Physics (Undergraduate Foundation)

Most electricity comes from moving magnets. This course explains how changing magnetic fields create electric currents. You will learn magnetic flux, Faraday’s law, and Lenz’s law to understand how motion creates power. We also cover self and mutual inductance alongside the core principles of how transformers change voltage levels.

These principles run the modern power grid, motors, and generators. This knowledge is essential for careers in power engineering, electronics, and renewable energy. You will use these concepts to design circuits, maintain industrial machines, or build stable power supply units for various technical projects.

You will learn to calculate magnetic flux and predict induced current directions accurately. You will solve equations for electromotive force and inductance in different conductors. You will also learn how step-up and step-down transformers work to move electricity over long distances while reducing energy loss.

This course suits undergraduate engineering and physics students needing a strong start. It helps secondary school leavers prepare for university-level science. Hobbyists building electrical tools or motors will also benefit from learning exactly how coils and magnets interact.

electromagnetic-induction-and-inductance-physics

Electromagnetic Induction and Inductance - Physics (Undergraduate Foundation)

This course covers the four Maxwell's equations in integral form, displacement current, and electromagnetic oscillations. You will learn how Gauss's Law for electricity, Gauss's Law for magnetism, Faraday's Law, and the Ampere-Maxwell Law provide a single framework for all electromagnetic phenomena. The module explains how changing electric fields create magnetic fields and how these interactions produce self-propagating electromagnetic waves that travel at the speed of light.

Understanding these equations is the foundation of modern telecommunications, radio engineering, and electronics. This knowledge allows you to understand how signals travel through space, how antennas work, and how light itself behaves as a wave. Whether you are building a simple radio circuit or designing complex wireless networks, these principles govern every device that uses electricity and magnetism to transmit information.

By the end of this course, you will be able to apply the four fundamental equations to calculate electric and magnetic flux, identify the role of displacement current in capacitors, and describe the mathematical properties of electromagnetic waves. You will gain the skill to determine the speed, frequency, and wavelength of these waves in different media. You will also master the relationship between oscillating charges and the radiation they produce.

This course is for undergraduate engineering and physics students who need a solid grasp of field theory. It is especially useful for those aiming for careers in electrical engineering, telecommunications, or renewable energy. Even if you are just starting your degree or transitioning from secondary school, this module provides the clarity needed to handle advanced technical concepts in electromagnetism and wave optics.

maxwell-s-equations-and-electromagnetic-waves-physics

Maxwell’s Equations and Electromagnetic Waves - Physics (Undergraduate Foundation)

The electricity in your wall socket does not flow in one direction like a battery; it reverses direction many times every second. This course teaches the essential physics of Alternating Current (AC) by examining how voltage and current vary as sine waves. You will learn to calculate peak and Root Mean Square (RMS) values to determine the actual power used by appliances. We analyse how inductors and capacitors oppose current through reactance and how these elements combine with resistors to form total impedance in RLC circuits.

AC Power is the global standard for homes and industries because it moves efficiently over long distances. For anyone in civil, mechanical, or electrical engineering, mastering AC theory is mandatory. This knowledge applies directly to designing power grids, maintaining factory motors, and managing household wiring. You will understand how to handle electrical loads and ensure equipment operates safely within professional infrastructure projects.

You will learn to derive and use formulas for AC voltage and current. The course teaches you to find the relationship between peak and RMS values for accurate power measurements. You will gain the skills to calculate inductive and capacitive reactance and solve for the total impedance of RLC circuit combinations. By the end, you will understand phase differences and how they affect the efficiency of electrical systems.

This module targets undergraduate engineering and physics students requiring a firm grasp of circuit dynamics. It also assists technical college students and secondary school leavers preparing for university-level science. Beyond formal students, anyone interested in how modern power systems function will find this useful. It provides the technical literacy needed to bridge the gap between classroom physics and industrial application.

alternating-current-theory-physics-undergraduate

Alternating Current Theory - Physics (Undergraduate Foundation)

Electricity and magnetism run every home, factory, and phone all over the world. This track builds the technical foundation to master laws governing electrical energy and signals. You will progress from stationary charges to alternating current and electromagnetic waves. It simplifies the NUC CCMAS syllabus into actionable knowledge for solving practical technical problems.

The programme is for first-year university and polytechnic students in engineering or physical sciences. It also serves school leavers preparing for university physics or technical entrance exams. Science teachers and technicians who need a solid refresher on core electrical principles will find the material direct and relevant to their work.

You will learn to calculate electrical forces, design functional DC and AC circuits, and predict how magnetic fields drive motors and generators. You will master the use of Gauss's Law, Kirchhoff's rules, and Maxwell's equations to solve engineering challenges. Completing this track ensures success in PHY 102 exams and prepares you for a career in power systems, telecommunications, or renewable energy.

General Physics II

Electricity and Magnetism

PHY 102: General Physics II - Electricity and Magnetism

Mathematics requires absolute precision. This course provides a rigorous grounding in real number operations, from integers and rational numbers to complex systems and algebraic laws. You will learn to handle polynomials, solve equations ranging from linear to biquadratic, and navigate simultaneous systems. The syllabus covers inequalities, sign tables, partial fractions, indices, logarithms, and the systematic simplification of surds.

These tools are essential for success in engineering, accounting, and the sciences. Clear mathematical thinking allows you to model financial risks, calculate structural loads, and write efficient computer code. Proficiency in these operations ensures accuracy in any career that relies on quantitative data and logical deduction.

You will gain the ability to classify number systems, apply algebraic theorems, and solve complex equations in one or more unknowns. You will acquire the skills to manipulate inequalities, resolve algebraic fractions, and simplify expressions using the laws of indices and logarithms. The course provides the technical competence required to handle surds and find roots of compound expressions effectively.

This training is built for undergraduate foundation students and secondary school leavers entering university. It provides a necessary bridge for anyone needing to strengthen their mathematical base before advanced study. Even those in non-technical roles will find value in the disciplined analytical approach required to master these foundational concepts.

operations-with-real-numbers-mathematics-undergraduate

Mathematics

Operations with Real Numbers - Mathematics (Undergraduate Foundation)

Mathematical induction proves a statement is true for every whole number using a starting point and a logical link. It works like a chain reaction where one step confirms the next. This course explains the core principle and applies it to many types of problems. You will study standard series, fractional series, divisibility, and inequalities. The content also covers recursive sequences, matrix powers, and set theory to give you a complete understanding of the method.

Programmers use this logic to check that software code works without mistakes. Engineers use it to prove that formulas for structural designs or machines are safe. This skill is vital for anyone in technology, finance, or data science because it makes logical thinking a clear, repeatable process. It removes guesswork and provides the certainty needed for professional work in any technical field.

You will learn the three-step induction method to solve different kinds of mathematical proofs. You will prove formulas for series, check if expressions are divisible, and handle difficult inequalities. You will also find general formulas for repeating sequences and solve problems involving matrices and sets. By the end, you will write clear, logical proofs that are required for university mathematics examinations.

This course is for university students starting science or engineering degrees and senior secondary school students preparing for higher education. It is also helpful for workers who want to improve their reasoning and problem-solving. Even those not studying mathematics will benefit from the clear way of thinking this course teaches. It provides the basic skills needed for any career that requires logic and proof.

mathematical-induction-mathematics-undergraduate

Mathematical Induction - Mathematics (Undergraduate Foundation)

Stop counting one by one. This course provides the mathematical tools to calculate arrangements and selections with speed. You will master the fundamental counting rules including product, addition, subtraction, and division. The curriculum covers linear and cyclic permutations, identical objects, and restricted placements where items must be together or apart. We conclude with combinations, derangements, and the calculation of shapes within geometric frameworks.

Counting is the engine of probability and modern computing. These skills are vital for cryptography, software development, and statistical analysis. You will apply these methods to calculate network paths, secure passwords, and optimise logistics. In any technical career, the ability to quantify possibilities is the difference between guessing and knowing.

You will solve complex arrangement problems using standard formulas and logical shortcuts. You will handle specific constraints like fixed positions or items that cannot be next to each other. You will learn to distinguish between permutations and combinations in practical scenarios. You will also calculate the number of lines, triangles, and diagonals in geometric figures using combinatorial principles.

This foundation is for undergraduate students and secondary school leavers aiming for high scores in competitive exams. It is also essential for professionals in engineering, finance, and data science who require a refresher on discrete mathematics. Anyone seeking to improve their logical deduction and analytical speed will find value here.

permutation-and-combination-mathematics-undergraduate

Permutation and Combination - Mathematics (Undergraduate Foundation)

Stop manually multiplying brackets. This course teaches the systematic expansion of binomial expressions using Pascal's triangle and the formal Binomial Theorem. We cover the fundamental proof for positive integers before moving to individual term identification and the general expansion for negative or fractional powers. You will master the mechanics of series expansion from simple squares to complex infinite series.

The Binomial Theorem is a core tool in probability, statistics, and financial engineering. It allows for the approximation of complex functions and the calculation of compounding interest or risk factors. Engineers and data scientists use these principles to manage error margins and optimise algorithms. Understanding these patterns is essential for any career involving quantitative analysis or technical forecasting.

You will expand binomials to any power and identify specific terms within a series without full expansion. You will demonstrate the theorem's proof and apply Pascal's triangle for rapid computation. You will also calculate expansions for non-integer indices and determine the range of validity for these series. These skills enable the simplification of advanced algebraic expressions.

This curriculum is for undergraduate students and secondary school leavers entering science or technology tracks. It provides the necessary foundation for engineering, physics, and economics degrees. Professionals needing a mathematical refresher for data analysis will find the direct approach efficient. Any learner requiring precise algebraic tools for higher education will gain immediate value.

binomial-theorem-mathematics-undergraduate-foundation

Binomial Theorem - Mathematics (Undergraduate Foundation)

Master the algebraic rules governing ordered lists of numbers and their total sums. This course establishes a solid foundation in the mechanics of sequences and series. We investigate precise definitions for arithmetic and geometric progressions; use formal notation for general terms; and handle finite and infinite series using sigma notation. The curriculum focuses on the structural properties required for university-level mathematical analysis.

Knowing how to handle numerical patterns is vital for many modern careers. Financial analysts use geometric series to calculate compound interest, loan repayments, and annuities. Computer scientists use sequence structures to organise data sets and analyse computer loops. This knowledge is necessary for measuring growth, decay, and accumulation in business and science with absolute accuracy.

You will learn to identify and define sequences using general terms and recurrence formulas. You will calculate the nth term and the sum of terms for arithmetic, geometric, and harmonic progressions. You will master sigma notation; determine when infinite series converge; convert recurring decimals into fractions; and use formulas to sum natural numbers, squares, and cubes.

This course is for students entering university foundation programmes in mathematics, finance, or computer science. It serves as an intensive refresher for professionals returning to academia or shifting into roles that demand precise numerical work. Even those outside these fields will benefit from the sharp logical thinking and problem-solving speed developed through pattern analysis.

sequences-and-series-mathematics-undergraduate-foundation-2

Sequences and Series - Mathematics (Undergraduate Foundation)

Quadratic equations are the bedrock of advanced algebra and the starting point for mastering non-linear mathematical models. This course provides a rigorous analysis of these equations, covering standard forms, solving methods like factorisation and completing the square, and the critical use of the discriminant to determine root nature. You will study turning points for optimisation, solve complex quadratic inequalities, and master the relationship between roots and coefficients to build equations from scratch.

Mastering these models is essential for careers in engineering, physics, and finance where trajectories and profit levels must be calculated precisely. You will use these principles to describe projectile motion, design parabolic structures, and identify boundary limits in economic models. This is the mathematics of optimisation, providing the necessary tools to find the highest or lowest possible values in any system governed by second-degree polynomials.

By the end of this course, you will solve any quadratic equation using multiple methods; use the discriminant to identify real, identical, or imaginary roots; and determine the location and value of turning points. You will master solving quadratic inequalities; identifying valid ranges for rational expressions; and using symmetric identities to evaluate root properties without solving the original equation. These skills form the essential foundation for calculus and mechanics.

This course is built for first-year university students in mathematics, physics, engineering, and economics who need a solid algebraic foundation. It also serves secondary school leavers preparing for advanced entrance exams or technical professionals looking to refresh their analytical skills. Even those in data science or basic programming will benefit from the logical structuring and problem-solving techniques required to handle non-linear variables.

theory-of-quadratic-equations-mathematics-undergraduate

Theory of Quadratic Equations - Mathematics (Undergraduate Foundation)

Standard numbers cannot solve every square root. This course teaches you to use complex numbers for such problems. You will learn number systems, algebra, and how to use the Argand plane. Lessons cover polar forms, De Moivre's theorem, and finding roots. You will also study sine, cosine, and log functions through many worked examples.

These methods are vital for electrical engineering, physics, and signal processing. You need these skills to calculate electricity flow and wave behaviour. Engineers use these tools to build machines and structures. Mastering this allows you to solve the difficult maths used in modern technology and research. It provides the logic needed for all advanced technical work.

You will learn to add, multiply, and divide complex numbers. You will switch between rectangular, polar, and exponential forms using Taylor series. You will gain the skill to find Nth roots of unity and solve hyperbolic equations. You will also learn to draw complex equations on a graph accurately. By the end, you will handle advanced mathematical expressions without errors.

This course is for university students in engineering or maths who must pass advanced modules. It also serves technical workers who need to refresh their skills. The step-by-step examples make the topics easy to follow for anyone starting out. This knowledge is a requirement for anyone pursuing a career in high-level science or technology.

complex-numbers-mathematical-methods-undergraduate

Mathematical Methods

Complex Numbers - Mathematical Methods (Undergraduate Advanced)

Mathematics begins with sets. This course covers everything from basic definitions and membership notations to complex set algebra and De Morgan's laws. You will master cardinality, power sets, and the classification of number systems including rational, irrational, and complex numbers. The curriculum moves from simple operations like union and intersection into element-wise proofs, Cartesian products, and the mechanics of relations and functions.

Set theory is the language of modern data and logic. These concepts are essential for computer programming, database management, and statistical analysis. Understanding functions and mappings allows you to model real-world dependencies in engineering, economics, and the sciences. Mastering these foundations provides the exact logical framework needed to solve complex problems in technology and research.

Upon completion, you will be able to simplify set expressions and solve grouping problems using Venn diagrams and the inclusion-exclusion principle. You will know how to perform element-wise proofs and calculate set cardinalities. You will also gain the ability to evaluate composite functions and prove whether a mapping is one-to-one, onto, or bijective.

This course is designed for undergraduate students and secondary school leavers entering STEM disciplines. It provides a necessary logical foundation for anyone moving into calculus, data science, or advanced mathematics. The clear, direct instruction ensures that any student can develop the systematic thinking required for professional technical roles.

set-theory-mathematics-undergraduate-foundation

Set Theory - Mathematics (Undergraduate Foundation)

This course provides a complete guide to trigonometry, from the principles of circular measure to functions of any angle. It covers the unit circle definitions and culminates in a full treatment of the addition and factor formulae. This is the mathematical language of cycles, waves, and angles.

A command of trigonometry is essential for any field that models periodic or geometric systems. It is used extensively in physics to analyse waves and oscillations, in engineering for structural analysis and signal processing, and in computer graphics for rotations and 3D modelling.

By the end of this course, you will be able to convert between degrees and radians, define the six trigonometric functions for any angle using the unit circle, and apply the addition and factor formulae to manipulate and simplify trigonometric expressions and solve equations.

This course is a mandatory prerequisite for any student of mathematics, physics, or engineering. It provides the necessary foundation for the study of calculus, complex numbers, and vector analysis.

trigonometry-mathematics-undergraduate-foundation

Trigonometry - Mathematics (Undergraduate Foundation)

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings.

This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction.

You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Basic Mathematics

AMS 102: Basic Mathematics

Carbon is the backbone of life and modern technology, yet most students struggle to visualise how its atoms connect. This course strips away the confusion surrounding organic chemistry by focusing on the fundamental rules that govern carbon behaviour. You will move from the basic history of the subject to the precise electronic arrangements that allow carbon to form millions of compounds. We cover hybridisation, bonding types, and molecular geometry with clarity. You will also explore the various forms of carbon, from diamond and graphite to advanced nanostructures like graphene and carbon nanotubes. This foundation is critical for understanding any advanced topic in chemistry or related sciences.

Understanding these concepts is not just about passing exams; it is about grasping the material world. Knowledge of bonding and polarity helps you predict how drugs interact with the body, how plastics are formed, and why certain materials conduct electricity while others do not. Engineers use these principles to design stronger composites; medical students need them to understand biochemistry; and industrial chemists rely on them to create new products. By mastering the structure of carbon allotropes and nanostructures, you gain insight into the technologies driving the future, from battery storage to nanomedicine. This knowledge turns abstract symbols into tangible tools for problem-solving in real-world scenarios.

By the end of this course, you will be able to determine the hybridisation state of any carbon atom and predict the three-dimensional shape of molecules. You will calculate formal charges, draw accurate resonance structures, and assess molecular polarity using electronegativity values. You will distinguish between the different allotropes of carbon and explain their unique physical properties based on their atomic arrangement. You will also understand the basic principles of nanochemistry and the significance of graphene and carbon nanotubes. These skills provide the necessary toolkit for tackling reaction mechanisms and spectroscopy in higher-level courses.

This course is built for first-year university students in chemistry, engineering, pharmacy, and medicine who need a solid start in organic chemistry. It is also ideal for advanced secondary school students preparing for university entrance exams or those who found their previous chemistry classes confusing. Even if you are not pursuing a science degree, this course offers a clear window into the molecular basis of life and technology. The explanations are direct and free of unnecessary jargon, making complex ideas accessible to anyone with a basic understanding of general chemistry. If you want to stop memorising and start understanding, this is the place to begin.

introduction-to-organic-chemistry-undergraduate-foundation

Chemistry

Introduction to Organic Chemistry (Undergraduate Foundation)

Organic chemistry starts with how electrons move and hold atoms together. This course explains electronic theory, covering how bonds form and why electrons sit in specific places within a molecule. You will learn to isolate pure substances from mixtures using standard laboratory methods. We also cover how to identify what is inside a compound and calculate its exact chemical formula through qualitative and quantitative analysis.

Knowing how to purify chemicals is vital for making medicines, refining oil, and ensuring food safety. If you cannot separate a target substance from waste, you cannot manufacture a useful product. These techniques are the same ones used by forensic scientists to solve crimes and by engineers to develop new materials. Mastering these basics allows you to work accurately in any professional science lab or industrial setting.

By the end of this course, you will understand inductive effects, resonance, and how electron distribution dictates chemical reactions. You will be able to perform solvent extraction, chromatography, and distillation to get pure samples. You will also know how to test for specific elements like nitrogen or halogens and use mass data to determine empirical and molecular formulas. These skills ensure your laboratory results are reliable and scientifically sound.

This course is for first-year university students and science enthusiasts who want to move beyond textbook theory into practical lab work. It provides a solid base for anyone entering pharmacy, chemical engineering, or medical sciences. Even if you are just starting out, these lessons simplify complex ideas into clear steps, making it easier to grasp how modern science identifies the invisible components of the world around us.

electronic-theory-and-purification-techniques-chemistry

Electronic Theory and Purification Techniques - Chemistry (Undergraduate Foundation)

Chemical names follow strict laws. This course teaches IUPAC rules for naming organic compounds and how functional groups define their nature. You will learn to identify molecules by their structures and understand 3D spatial arrangements. We cover optical and geometric isomerism to show how identical formulas can have different shapes.

Doctors and pharmacists use these rules to identify drugs. In a lab, naming a substance wrongly can cause dangerous accidents. Knowing how atoms sit in space helps you understand how medicines fit into the human body. This knowledge is the base for making new materials, fuels, and life-saving treatments.

You will name complex organic molecules using standard IUPAC Systems. You will categorise compounds by their functional groups and predict their chemical behaviour. You will also identify different types of isomers and draw 3D structures accurately. By the end, you can explain how molecular shape affects biological function.

This course is for first-year university students in chemistry, pharmacy, and engineering. It also helps secondary school leavers preparing for advanced science exams. Even if you are not a science major, understanding these basics helps you read product labels and understand the chemicals in your daily life.

organic-nomenclature-and-stereochemistry-undergraduate

Organic Nomenclature and Stereochemistry (Undergraduate Foundation)

Organic reactions follow specific pathways called mechanisms rather than happening by chance. This course covers how molecules break and form bonds through step-by-step pathways and measured reaction rates. You will learn to track electron movement, identify intermediates, and understand the kinetics governing reaction speed. Studying these mechanisms allows you to predict how organic systems behave using fundamental chemical principles instead of simple memorisation.

Understanding these mechanisms is vital for industries like pharmacy, oil and gas, and food processing. Knowing how a reaction works allows you to control it to produce better medicines or stronger materials. These skills apply directly to laboratory research, chemical manufacturing, and quality control. Mastering reaction kinetics enables the optimisation of industrial processes, which saves time and reduces waste in commercial production.

You will gain the ability to draw reaction mechanisms using curly arrows to show electron flow and calculate reaction rates. The course teaches how temperature and catalysts change reaction speeds and helps you predict the final products of organic reactions. You will explain why specific pathways are preferred over others and master the relationship between energy changes and reaction timing in organic synthesis.

This course is for undergraduate chemistry and engineering students needing a solid foundation in organic chemistry. It also suits science teachers or laboratory assistants wanting to refresh their knowledge of reaction pathways. Even those new to the subject will benefit from clear explanations of bond-breaking and bond-making as a core part of chemical science. Any student preparing for advanced exams will find these logical steps useful for solving complex chemical problems.

organic-reaction-mechanisms-and-kinetics-chemistry

Organic Reaction Mechanisms and Kinetics - Chemistry (Undergraduate Foundation)

Organic chemistry is the study of carbon compounds, and functional groups are the specific clusters of atoms that decide how these molecules behave. This course focuses on the properties and reactions of alkanes, alkenes, and alkynes, alongside the chemistry of alcohols, ethers, amines, and alkyl halides. You will also study the structure and reactivity of nitriles, aldehydes, ketones, and carboxylic acids to understand how millions of different molecules are organised into manageable families.

Understanding these groups is essential for producing everyday items like medicines, plastics, fuels, and soaps. This knowledge allows you to predict how chemicals will react in a lab, a factory, or inside the human body, making it vital for anyone pursuing a career in pharmacy, chemical engineering, or medicine. You will learn to identify these reactive parts and use them to solve practical problems in manufacturing and research.

By the end of this course, you will be able to name organic compounds using standard rules and predict the products of their chemical reactions. You will gain the skill to distinguish between different families of compounds based on their chemical tests and physical properties. You will also understand the mechanisms behind how these molecules transform into new substances, providing a solid foundation for advanced laboratory work and industrial applications.

This course is built for undergraduate students starting their journey in chemistry or related sciences like biochemistry and engineering. It is also useful for secondary school leavers preparing for university entrance exams who want a head start on complex topics. Even professionals in the health and manufacturing sectors will find this a useful refresher to better understand the chemical basis of the products they handle daily.

chemistry-of-functional-groups-undergraduate-foundation

Chemistry of Functional Groups (Undergraduate Foundation)

Periodic table mastery starts here. You will compare Group 1A, 2A, and 4A elements to see how their electron setups dictate chemical habits. The course connects these main groups to transition metals, focusing on how d-block metals form complex coordination compounds.  This knowledge bridges the gap between organic and inorganic chemistry.

These principles drive industries from medicine to mining. You will understand how metals like iron and copper work in biological systems and industrial catalysts. Knowledge of coordination compounds is vital for purifying metals and creating new materials. This foundation helps you predict how substances react in a laboratory or a manufacturing plant.

You will learn to write electronic configurations for transition metals and explain the trends in Groups 1A, 2A, and 4A. You will identify the parts of coordination compounds, including ligands and central atoms, and calculate their oxidation states. By the end, you will be able to predict chemical properties based on an element's position in the periodic table.

This course suits undergraduate science and engineering students needing a solid chemistry base. It also helps secondary school graduates preparing for university entrance exams. Even those in related fields like pharmacy or metallurgy will find the clear breakdown of metal behaviour useful for their professional work.

main-group-and-transition-metal-chemistry-undergraduate

Main Group and Transition Metal Chemistry (Undergraduate Foundation)

Excel in your CHM 102 exams and build a professional career in the global science and engineering sectors. This track follows the NUC CCMAS syllabus, covering carbon bonding, molecular structures, and metal chemistry. You will learn how atoms form fuels and medicines, how to identify pure substances, and why molecular shapes affect biological systems. This programme provides the scientific foundation needed for roles in the oil, gas, and pharmaceutical industries.

This track is for first-year university students in chemistry, engineering, medicine, or pharmacy. It also serves secondary school leavers preparing for university entrance or technical workers needing a refresher on laboratory methods. Anyone starting a science-based degree will find these lessons essential for their academic progress.

You will gain the ability to name organic compounds using IUPAC rules, predict reaction outcomes, and use lab techniques like chromatography and distillation. You will understand how to calculate chemical formulas and explain the behaviour of transition metals. Finishing this programme prepares you for advanced research, quality control roles, and industrial manufacturing.

Olanrewaju Owoyomi

A passionate teacher of Chemistry who is not just interested in teaching but has a strong desire in seeing students enjoying the beauty of the subject 

General Chemistry II

CHM 102: General Chemistry II

Chemistry is the science of matter. This course provides a rigorous introduction to its fundamental principles, moving from the definition of matter and its states to the atomic and molecular structures that govern its behaviour. We will classify matter into elements, compounds, and mixtures, and establish the critical distinction between physical and chemical changes.

A command of chemistry is essential for any quantitative science. The principles covered here are foundational to medicine, engineering, environmental science, and materials development. Understanding how matter is structured and how it transforms is the basis for creating new materials, developing pharmaceuticals, and managing industrial chemical processes safely and efficiently.

Upon completion, you will possess a clear conceptual framework for chemistry. You will be able to classify different types of matter, distinguish between physical and chemical changes, and define elements, compounds, and mixtures. You will also be able to identify the fundamental roles of atoms, molecules, and ions in chemical reactions.

This course is designed for first-year university students beginning their studies in any scientific or engineering discipline. It serves as a mandatory prerequisite for further study in chemistry, chemical engineering, biology, and medicine. It is also suitable for anyone requiring a concise and formal review of foundational chemical concepts.

introduction-to-chemistry-undergraduate-foundation

Introduction to Chemistry (Undergraduate Foundation)

This course provides a complete guide to the modern theory of the atom. It traces the historical development of atomic models, from Dalton's foundational theory to the modern understanding of electronic structure. The material covers subatomic particles, the contributions of Thomson and Rutherford, the Bohr model, wave-particle duality, and culminates in a full treatment of electronic configuration and its direct relationship to the periodic trends of the elements.

A command of atomic theory is the absolute foundation of modern chemistry. The electronic structure of the atom dictates all chemical properties and bonding behaviour. This knowledge is essential for understanding the periodic table, predicting chemical reactions, and is the prerequisite for the study of spectroscopy, materials science, and quantum mechanics.

By the end of this course, you will be able to describe the historical evolution of atomic theory. You will also be able to explain the atom's structure, including the roles of protons, neutrons, and electrons. You will determine the electronic configuration of any element and use periodic trends to predict and justify atomic properties like size, ionisation potential, and electronegativity.

This course is for students who have completed an introductory chemistry course. It is a mandatory prerequisite for any student pursuing a degree in chemistry, chemical engineering, materials science, or physics.

atomic-structure-and-periodicity-of-elements-chemistry

Atomic Structure and Periodicity of Elements - Chemistry (Undergraduate Foundation)

The shape of a molecule dictates its function. This course provides a practical, foundational treatment of chemical bonding and molecular geometry - the principles governing how atoms connect to form substances. It covers ionic and covalent bonding, the drawing of Lewis structures, and methods for determining molecular shape using VSEPR theory and orbital hybridisation. Finally, we examine intermolecular forces that control a substance's physical properties.

A command of this material is essential for molecular design. Knowledge of bonding and geometry dictates the properties of everything from pharmaceuticals, where shape governs drug-receptor specificity, to new materials like polymers and catalysts. Mastery of this foundational knowledge is the starting point for developing or synthesising any new chemical compound. Our system uses comprehensive videos and allows you to ask questions directly, making it fully online and easy to master at your pace.

By the end of this course, you will be able to draw correct Lewis structures for any molecule, predict its three-dimensional geometry and polarity using VSEPR theory, determine the central atom's hybridisation and bond types, and identify the various intermolecular forces present in a substance.

This course is mandatory for all undergraduate students of chemistry, biochemistry, and materials science, and is a direct prerequisite for studying organic chemistry. It benefits anyone needing a rigorous, structured, student-centred refresher or initial exposure to this critical subject, assuming a complete understanding of atomic theory and electronic configuration.

chemical-bonding-and-shapes-of-molecules-chemistry

Chemical Bonding and Shapes of Molecules - Chemistry (Undergraduate Foundation)

This course provides a rigorous treatment of the Kinetic Theory and the Gas Laws, explaining the physical principles that control the behaviour of solids, liquids, and gases. We move from the foundational kinetic postulates to the precise mathematical relationships required to model matter's response to energy, pressure, and temperature.

These principles dictate real-world engineering, not just textbook theory. You will apply this knowledge to model atmospheric dynamics, design efficient chemical reactors, and optimise engine performance. A command of these laws allows you to quantify substance behaviour under varying conditions, solving the calculation pain points often faced in process engineering and physical science.

By the end of this course, you will confidently apply Boyle's, Charles's, Avogadro's, and the Combined Gas Laws to determine unknown state variables. You will derive and utilize the Ideal Gas Equation, PV = nRT, and explain gas properties using kinetic theory postulates. Additionally, you will analyse the structure of solids and calculate gas density. 

This is a mandatory foundation for Chemistry and Chemical Engineering undergraduates and a prerequisite for thermodynamics. It is intended for learners with a grasp of chemical bonding who require a structured, student-centred alternative to disjointed free resources.

kinetic-theory-of-matter-and-gas-laws-chemistry

Kinetic Theory of Matter and Gas Laws - Chemistry (Undergraduate Foundation)

Grasp the fundamental language of chemistry through Stoichiometry of Composition. This concise undergraduate-foundation course systematically establishes core quantitative concepts essential for all subsequent chemistry studies. We will precisely define and calculate relative atomic mass, master the critical mole concept to transition between the microscopic and macroscopic worlds, determine molar masses, and then apply these principles to calculate percent composition and accurately derive both empirical and molecular formulae from experimental data. The content is structured for immediate application, moving from foundational definitions to complex problem-solving.

Quantitative chemistry is not abstract theory; it is the practical basis for chemical synthesis and analysis across science and industry. Learners will develop the ability to accurately predict reactant and product ratios in chemical reactions, interpret laboratory data for compound identification, and correctly formulate materials in fields such as chemical engineering, pharmaceuticals, and materials science. Mastery of these stoichiometric calculations is non-negotiable for success in laboratory work and industrial scale-up.

Upon completion, you will be able to calculate and interpret relative atomic and molecular masses; confidently apply the mole concept to interconvert mass, moles, and number of particles; calculate the molar mass of any compound; precisely determine the percent composition of a substance; and successfully solve multi-step problems to deduce a compound's empirical and molecular formulae. The course culminates in extensive practice to secure computational fluency.

This course is essential for undergraduate students beginning any science or engineering programme that requires a solid foundation in Chemistry, particularly those preparing for university-level coursework. It also serves as an intensive, structured refresher for advanced students, technical professionals needing to reinforce core computational skills, and anyone using UniDrills to self-study for competitive professional examinations.

stoichiometry-i-mole-and-chemical-formulae-chemistry

Stoichiometry of Composition - Chemistry (Undergraduate Foundation)

Master the quantitative prediction of chemical change with Stoichiometry of Reactions. This undergraduate foundation course focuses on transforming conceptual chemical reactions into balanced, calculable equations. We begin by applying the conservation of mass principle to balance equations through inspection, the algebraic method, and the oxidation number change method. Next, we simplify reactions in solution by deriving total and net ionic equations, rigorously defining redox reactions, and teaching the precise assignment of oxidation numbers. The final section culminates in balancing complex redox equations using the half-reaction (electron transfer) method in both acidic and basic media.

Accurate reaction stoichiometry is the cornerstone of chemical processing, environmental analysis, and energy generation. Learners will gain the necessary computational skills to predict theoretical yields, determine limiting reagents in industrial synthesis, and analyse electrochemical processes like batteries and corrosion. Correctly balancing and interpreting chemical equations ensures laboratory safety, validates experimental results, and underpins quantitative decision-making in chemical engineering, materials science, and biochemistry.

After completing this course, you will be proficient in balancing any chemical equation based on the conservation of mass; accurately converting molecular equations into total and net ionic forms; defining and identifying oxidation and reduction processes, including their agents; assigning oxidation numbers to elements in compounds; and confidently balancing complicated redox reactions in both acidic and basic solutions. The course concludes with comprehensive practice problems to cement computational accuracy in reaction stoichiometry.

This course is specifically designed for undergraduate students beginning foundational Chemistry or related programmes, including Chemical Engineering, Pharmacy, and pure Sciences, where proficiency in calculating reaction quantities is mandatory. It is also an ideal, focused resource for pre-university students seeking an advanced start, or for any professional needing a rapid, expert-led review of fundamental reaction stoichiometry principles for accreditation or further study.

stoichiometry-ii-chemical-equations-and-redox-reactions

Stoichiometry of Reactions - Chemistry (Undergraduate Foundation)

Precision in volumetric analysis is the difference between experimental success and catastrophic failure in the laboratory. This course provides a rigorous mathematical framework for quantifying dissolved substances, beginning with fundamental concentration units like molarity and mass concentration before progressing to the principles of dilution and standard solution preparation. You will master the stoichiometric requirements of complex chemical interactions, including precipitation, acid-base neutralisation, and redox reactions, through a series of intensive worked examples covering advanced techniques such as back-titration and standardisation.

Quantitative titration skills are the industrial standard for quality control and analytical research. Proficiency in solution stoichiometry allows for the exact determination of drug purity in pharmaceuticals, contaminant levels in environmental monitoring, and reactant concentrations in industrial chemical synthesis. Mastering these computational methods ensures the accuracy required for professional competency in any clinical or academic laboratory setting.

By the conclusion of this course, you will be able to calculate precise concentrations from raw experimental data across multiple reaction types. You will acquire the technical ability to prepare primary standard solutions, apply dilution laws to reach target molarities, resolve limiting reagent problems in aqueous phases, and execute complex multi-step stoichiometric calculations for redox and back-titration scenarios. These skills are essential for converting laboratory observations into reportable analytical results.

This course is a mandatory requirement for undergraduate students in Chemistry, Pharmacy, Biochemistry, and Chemical Engineering. It also serves as a critical computational review for laboratory technicians and research assistants preparing for technical certification or professional exams. Even for those in peripheral scientific fields, the rigorous logic and mathematical precision developed here provide a necessary foundation for any discipline requiring core analytical data processing.

stoichiometry-iii-volumetric-analysis-chemistry

Stoichiometry of Solutions - Chemistry (Undergraduate Foundation)

This course provides a complete guide to chemical equilibria, the state where the rates of forward and reverse reactions are equal. It covers the law of mass action, the definition and calculation of the equilibrium constant, and the factors that can cause a shift in the equilibrium position. The course then applies these principles to the study of aqueous equilibria, including the properties of acids, bases, and salts, and the calculation of pH.

The principles of equilibrium govern the outcomes of all reversible reactions, from industrial synthesis to biological processes. A command of this topic is essential for chemists and chemical engineers to maximise the yield of a desired product, for environmental scientists to understand natural water systems, and for biochemists to analyse metabolic pathways.

By the end of this course, you will be able to write the expression for the equilibrium constant for any reversible reaction, use Le Chatelier's principle to predict how a system at equilibrium will respond to changes in concentration, pressure, or temperature, and perform calculations involving the pH of acidic and basic solutions.

This course is for students who have a solid foundation in stoichiometry. It is a mandatory course for all students of chemistry and chemical engineering and is a direct prerequisite for the study of analytical chemistry, biochemistry, and environmental science.

chemical-equilibria-and-acid-base-chemistry-undergraduate

Chemical Equilibria and Acid-Base Chemistry (Undergraduate Foundation)

Energy drives every chemical change in our universe. This course explains how heat, work, and internal energy dictate the behaviour of matter from simple phase changes to complex chemical reactions. You will master the laws of thermodynamics, enthalpy calculations, entropy changes, and the ultimate predictor of spontaneity, Gibbs free energy.

These principles are the backbone of modern industry. Chemical engineers use them to design efficient industrial reactors and cooling systems. Materials scientists apply them to develop better batteries and energy sources, while biochemists use these same laws to understand the energy flow within living cells. Mastering these concepts is essential for anyone aiming to solve energy-related problems in the real world.

By the end of this course, you will be able to distinguish between open, closed, and isolated systems and calculate heat changes using specific heat capacities. You will apply Hess’s law and bond energies to find reaction enthalpies and use the second law of thermodynamics to predict disorder through entropy. Finally, you will calculate Gibbs free energy to determine exactly if and when a reaction will occur naturally under various temperatures.

This course is built for undergraduate students in chemistry, chemical engineering, and materials science who need a solid foundation in physical chemistry. It also benefits secondary school leavers preparing for university-level science and professionals looking to refresh their technical knowledge of energy systems. Even those outside these fields will gain a logical framework for understanding how energy and disorder shape the physical world.

chemical-thermodynamics-chemistry-undergraduate-foundation

Chemical Thermodynamics - Chemistry (Undergraduate Foundation)

Chemical kinetics determines how fast a reaction occurs and why. This course builds a rigorous foundation in reaction rates, rate laws, integrated kinetics, and the influence of temperature and catalysts on molecular transformations. You will move from basic rate definitions to solving complex problems involving zero, first, and second-order reactions using the Arrhenius equation and experimental data analysis.

Understanding reaction kinetics is essential for industrial process control and chemical engineering. Mastery of this subject allows you to predict how changes in concentration, temperature, or the presence of catalysts will impact manufacturing yields, energy consumption, and safety protocols. These principles are the backbone of chemical production, pharmacology, and environmental monitoring, providing the technical basis for optimising output in real-world systems.

Upon completion, you will possess the analytical ability to calculate reaction rates, derive rate laws from empirical data, and determine half-life values for various reaction orders. You will be able to apply the collision model to predict reaction behaviour and manipulate the Arrhenius equation to solve for activation energy. These technical skills will enable you to interpret experimental kinetic studies and apply theoretical models to solve practical chemical problems with precision.

This course is for undergraduate students building a foundation in chemistry. It is equally valuable for professionals in pharmaceutical, petrochemical, or environmental sectors who require a refresher on kinetic principles to improve efficiency in their daily operations. Even if you are not a chemistry major, the logical framework developed here enhances your quantitative reasoning and problem-solving capabilities, offering a clear advantage in any science or engineering discipline.

chemical-kinetics-chemistry-undergraduate-foundation

Chemical Kinetics - Chemistry (Undergraduate Foundation)

Electrochemistry bridges chemical reactions and electrical energy. This course examines the mechanics of electron transfer. You will study galvanic cells that generate power and electrolytic cells that consume it. The curriculum covers cell structure, standard notation, and the role of inert electrodes.

This science drives portable energy and industrial manufacturing. You apply these principles when working with batteries, fuel cells, and corrosion prevention. Industrial applications rely heavily on this knowledge for metal extraction, electroplating, and purifying elements like aluminium and copper. Mastering this connects theoretical chemistry to practical engineering.

You will learn to identify cell components and write precise cell notations. You will calculate standard cell potentials, determine reaction spontaneity using Gibbs free energy, and apply the Nernst equation to non-standard conditions. You will also use Faraday's laws to compute mass deposited, time taken, and current passed during electrolysis.

This course is built for undergraduate foundation students in chemistry and chemical engineering. It is also directly useful for recent secondary school leavers preparing for university admissions. Engineering and materials science students will find this material essential for understanding thermodynamics and electrical systems.

electrochemistry-undergraduate-foundation

Electrochemistry (Undergraduate Foundation)

Radioactivity powers our world, from nuclear energy plants to cancer treatment centres. This course reveals the invisible forces inside atomic nuclei that drive these technologies. You will explore radioactive decay, nuclear reactions, and the principles that govern how unstable atoms transform over time.

This knowledge applies directly to medicine, energy production, and environmental science. Nuclear engineers use these principles to design safe reactors. Medical professionals apply radioisotopes for imaging and cancer therapy. Archaeologists rely on carbon dating to determine the age of ancient artifacts. Understanding radioactivity opens doors to careers in nuclear engineering, health physics, radiology, and industrial safety.

By the end of this course, you will describe radioactive disintegration and identify alpha, beta, and gamma radiation; calculate half-life and decay rates for practical problems; explain nuclear fission and fusion processes; balance nuclear equations accurately; and recognise the applications of radioisotopes in medicine and industry. These skills form the foundation for advanced study in nuclear chemistry and related fields.

This course targets undergraduate students in chemistry, physics, medicine, and engineering programmes. It suits secondary school leavers preparing for university entrance exams and professionals needing a refresher on nuclear concepts. Even if you do not specialise in science, this knowledge helps you understand radiation safety, medical procedures, and energy debates that affect daily life in Nigeria and beyond.

radioactivity-chemistry-undergraduate-foundation

Radioactivity - Chemistry (Undergraduate Foundation)

This learning track delivers the complete NUC CCMAS curriculum for General Chemistry I. It is a comprehensive programme designed to build a robust, university-level foundation in modern chemistry. The track systematically covers all essential topics, from atomic theory, chemical bonding, and the states of matter, to the quantitative principles of stoichiometry, equilibrium, thermodynamics, and kinetics.

This programme is for first-year undergraduates in science, technology, engineering, and mathematics (STEM) faculties who are required to take CHM 101. It is also essential for any student or professional globally who needs a rigorous and complete foundation in first-year university chemistry for further study or career development.

This track delivers a full skill set in chemical theory and quantitative problem-solving. Graduates will be able to determine molecular structures, calculate reaction quantities, analyse the energetics and rates of reactions, and solve complex equilibrium problems. This programme provides the non-negotiable prerequisite knowledge for all subsequent chemistry courses and for any degree in the physical sciences, engineering, or medicine.

General Chemistry I

CHM 101: General Chemistry I

Master advanced matrix algebra and linear systems through rigorous technical training. This course covers matrix definitions; algebraic operations; transpositions; and elementary row transformations. You will investigate determinants; matrix inverses using the adjoint method; and the structural properties of similar matrices. Computational methods using MS-Excel or Google Sheets are included to handle large-scale data sets efficiently.

These mathematical structures are the engines behind modern engineering and data science. Structural engineers use matrices to calculate stress in bridges; computer scientists use them to render 3D graphics; and economists use linear systems to model market equilibrium. Mastering these tools allows you to solve multi-variable problems that are impossible to handle manually.

By the end, you will possess the skills to execute matrix additions; multiplications; and scalar operations with absolute precision. You will demonstrate competence in reducing matrices to row echelon form; calculating rank and nullity; and evaluating determinants of any order. Furthermore, you will command the ability to solve complex systems of linear equations using Cramer's rule or matrix inversion; identify special matrix types like orthogonal or symmetric; and automate these calculations using software.

This curriculum is built for undergraduate students in engineering; mathematics; and physics requiring a high-level command of linear algebra. Professionals in data science or finance will find the content vital for understanding the algorithms governing their software. Even those in general sciences will benefit from the structured logical thinking and numerical methods required to manage complex variables in any technical field.

matrices-determinants-and-systems-of-linear-equations

Linear Algebra

Matrices, Determinants, and Systems of Linear Equations - Linear Algebra (Undergraduate Advanced)

Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science.

This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions.

Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Elementary Mathematics I

Algebra and Trigonometry

MTH 101: Elementary Mathematics I - Algebra and Trigonometry

Physics is not a collection of facts; it is a quantitative language. This course establishes that language. We cover the formal system of measurement and units, the rigorous method of dimensional analysis, the complete framework of vector algebra, and the use of calculus to describe how vector quantities change. This is the essential grammar of science.

The tools in this course have immediate, practical applications. Correct dimensional analysis is a critical technique for verifying equations and preventing catastrophic errors in any technical calculation. Vectors are the required language for describing forces, displacements, velocities, and fields in any engineering or scientific discipline. Mastering this material is the first step to becoming a competent technical professional.

Upon completion, you will command the mathematical toolkit for physics. You will perform dimensional analysis to validate equations. You will resolve vectors into components, calculate vector sums and products, and differentiate vector functions to analyse rates of change, such as deriving velocity from a position vector.

This course is the mandatory starting point for first-year university students of engineering, physics, computer science, and related disciplines. A firm command of secondary school algebra, geometry, and trigonometry is a prerequisite. It is also suitable for professionals who require a rigorous and efficient refresher on the foundational mathematical tools of science.

introduction-to-physics-undergraduate-foundation

Introduction to Physics (Undergraduate Foundation)

Motion is the most fundamental concept in physics. This course provides the mathematical framework to describe it with quantitative precision. We will systematically analyse motion in one, two, and three dimensions, progressing from motion along a straight line to the vector analysis of projectiles and general spatial motion. This requires a full command of both vector algebra and introductory calculus.

The principles of kinematics are the bedrock of physical analysis, engineering design, and biomechanics. This knowledge is required to analyse everything from vehicle performance and projectile trajectories to the movement of organisms and robotic motion. A command of this material is essential for any work involving the dynamics of moving systems, providing the tools to predict and control motion in the real world.

Upon completion, you will be able to analyse motion in multiple dimensions. You will solve one-dimensional problems using the standard kinematic equations for constant acceleration. You will analyse two-dimensional projectile motion by resolving vectors into independent components. Critically, you will use vector calculus to describe the general case of motion with variable acceleration.

This course is designed for first-year university students of the physical, biological, and medical sciences, as well as engineering and computer science. A firm command of vector algebra and introductory calculus (differentiation and integration) is a mandatory prerequisite. This material is the necessary foundation for the subsequent study of Newtonian dynamics and biomechanics.

vectors-and-kinematics-of-motion-physics-undergraduate

Kinematics: Motion in One and Two Dimensions - Physics (Undergraduate Foundation)

Dynamics explains why objects move, and Newton's laws provide the exact mathematical rules for this movement. This course transitions from basic motion to the rigorous use of force vectors, inertia, and action-reaction pairs. You will learn to handle gravity, tension, and springs while solving resistive problems involving static, kinetic, and fluid friction. We build from first principles to complex systems used in modern machinery.

Every machine and structure operates under these principles. Understanding these forces is required to predict when a system will fail, how to build safe cars, and how to design efficient engines. These analytical tools allow you to solve real problems in construction, manufacturing, and transport. This knowledge is the foundation for anyone building or maintaining physical systems.

After this course, you will construct precise free-body diagrams to isolate objects from their surroundings.  You will acquire the technical skill to calculate acceleration in systems with multiple forces, find centripetal force for circular motion, and use equilibrium laws to find unknown force values. You will master the mathematics of friction on ramps, calculate terminal velocity in fluids, and solve for tension in connected pulley systems.

This course is for first-year university engineering and physics students. It also helps technicians who need a refresher and secondary school leavers who want to prepare for undergraduate work. Anyone interested in how things work will find these structured methods useful for clear thinking and scientific problem-solving.

force-and-motion-newtons-laws-physics-undergraduate

Force and Motion: Newton's Laws - Physics (Undergraduate Foundation)

Master the laws that govern how everything moves, from a simple football to a space rocket. This course teaches you to solve complex physics problems by tracking energy and momentum instead of just forces. You will learn to calculate work, power, and efficiency; use the work-energy theorem to predict speeds; apply conservation laws to collisions; and find the balance point of complex objects using centre of mass principles.

Understanding energy and momentum is the backbone of engineering and modern technology. These principles are used to design safe cars with crash zones, build efficient engines, and calculate rocket trajectories for space exploration. Mastering these concepts allows you to predict the outcome of physical events with high accuracy, making it an essential skill for anyone looking to build machines, design structures, or solve real-world technical problems.

By the end of this course, you will be able to calculate work done by constant and variable forces; apply the principles of kinetic and potential energy to find the velocity of moving objects; and use the law of conservation of energy to solve systems with springs and weights. You will also learn to analyse elastic and inelastic collisions using momentum; calculate impulse and impact forces; and determine the centre of mass for composite shapes and moving systems.

This course is specifically for first-year university students of physics and engineering who need a solid foundation in mechanics. It is also highly beneficial for secondary school leavers preparing for advanced placement exams or those entering technical fields who want to understand the physical laws behind machines and motion. Even those not pursuing a degree will gain a sharp, logical approach to solving problems by learning how energy and matter interact in the physical world.

work-energy-and-momentum-physics-undergraduate

Work, Energy, and Momentum - Physics (Undergraduate Foundation)

Everything in the universe from car wheels to distant planets follows the laws of rotational motion. This course explains how objects spin and move in circles by breaking down the physics of torque, angular momentum, and inertia. You will learn to calculate how much force is needed to start a rotation, how energy is stored in spinning flywheels, and why objects like gyroscopes resist falling. We cover the transition from simple circular movement to complex rolling and the conservation laws that govern every rotating system.

Mastering these principles is essential for any career in mechanical, civil, or aerospace engineering. You will use this knowledge to design efficient engines, stabilising systems for ships, and better vehicle parts. Understanding how torque and power relate allows you to analyse machine performance and industrial turbines. These tools are also the foundation for tracking satellite paths and managing the stability of aircraft in flight.

By the end of this course, you will be able to calculate angular displacement, velocity, and acceleration; determine the moment of inertia for various shapes; and apply Newton's second law to rotational systems. You will master solving problems involving rotational kinetic energy and work; linking linear and angular variables for rolling objects; and using the conservation of angular momentum to predict the behaviour of spinning systems. These skills allow you to model and solve real-world dynamics problems with precision.

This course is built for first-year university students of physics and engineering who need a solid foundation in mechanics. It is a mandatory requirement for those moving into advanced robotics, automotive design, or space science. Even if you are not an engineering student, these lessons help anyone interested in the logic of how machines work or those preparing for technical entrance exams. The material is presented simply to ensure any learner with a basic understanding of mathematics can follow and apply these laws.

rotational-motion-and-angular-momentum-physics

Rotational Motion and Angular Momentum - Physics (Undergraduate Foundation)

This course provides a complete treatment of Newton's law of universal gravitation. It covers the principles governing the attractive force between masses, the concepts of gravitational fields and potential energy, and culminates in the application of these laws to the orbital mechanics of planets and satellites.

The law of gravitation is a fundamental principle of the cosmos. It is essential for understanding the motion of celestial bodies, launching and maintaining artificial satellites for communications and Earth observation, and for calculating interplanetary trajectories. This is the physics that governs the structure of the solar system and the universe.

By the end of this course, you will be able to apply Newton's law of universal gravitation to calculate the force between two masses, determine the gravitational potential energy of a system, explain Kepler's laws of planetary motion, and solve problems involving the orbital velocity and period of satellites.

This course is a mandatory part of the curriculum for first-year university students of physics and engineering. It directly builds upon the principles of rotational motion and dynamics and is a critical prerequisite for the study of astrophysics and celestial mechanics.

gravitation-physics-undergraduate-foundation

Gravitation - Physics (Undergraduate Foundation)

This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering.

The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics.

This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

General Physics I

Mechanics

PHY 101: General Physics I - Mechanics

Build the mathematical foundation required to excel in social science degrees and data-driven careers. This track follows the official NUC syllabus for DSS 103 to teach sets, number operations, counting methods, logical proofs, binomial expansions, complex numbers, and trigonometry. Each topic connects directly to the quantitative skills you need for statistics, research methods, and economic analysis.

This programme is for first-year university students studying economics, sociology, political science, psychology, geography, or other social science disciplines. It is also for secondary school leavers preparing for university entry and professionals who must strengthen their maths for postgraduate study or analytical roles in government, NGOs, or private sector research.

After completing this track, you will solve equations, handle algebraic proofs, manipulate trigonometric formulas, and apply counting principles to real-world data problems. These skills prepare you for advanced coursework in econometrics, statistical analysis, social research, and policy evaluation. You will have the confidence to tackle quantitative modules and compete for roles in banking, public service, consulting, and development work.

Mathematics for Social Scientists I

DSS 103: Mathematics for Social Scientists I - Algebra and Trigonometry

Tutorials for 100-level students, based on NUC CCMAS, institution-specific and general syllabuses.

Find Your Classes

100-Level University Classes

MTH 102: Elementary Mathematics II - Calculus

PHY 102: General Physics II - Electricity and Magnetism

AMS 102: Basic Mathematics

CHM 102: General Chemistry II

CHM 101: General Chemistry I

MTH 101: Elementary Mathematics I - Algebra and Trigonometry

PHY 101: General Physics I - Mechanics

DSS 103: Mathematics for Social Scientists I - Algebra and Trigonometry

All Active Classes

Exam. Prep. (8)

University (22)

Professional (2)