Library
50 free math articles organised by category — algebra, geometry, trigonometry, statistics and more. From beginner to advanced level. No sign-up required.
When each number in a sequence is obtained by adding the same constant to the previous one, you have an arithmetic sequence. Learn how to find any term and calculate sums without listing every element.
A linear function describes any relationship that grows or decreases at a constant rate. Learn to identify the coefficients, draw the graph, and extract practical information such as the break-even point and zero of the function.
Learn to solve quadratic equations by the roots: identify the coefficients, calculate the discriminant, and apply the quadratic formula with confidence — or choose the fastest method for each case.
When two conditions must be satisfied simultaneously, we set up a system. Discover the most efficient methods for solving systems and understand what happens when there is no unique solution.
Addition and subtraction are inverse operations that form the backbone of arithmetic. In this article we explore the concepts, the carrying and borrowing algorithm, and mental calculation strategies for greater speed.
Why do some algorithms slow down with large data? Big-O notation describes how execution time grows with input size. Learn O(1), O(n), O(n²), and O(log n).
Angles measure rotations and the opening between lines. Mastering their classification and the relationships between parallel lines and transversals is the foundation for geometry, construction and design.
Area measures the surface; perimeter measures the boundary. Understanding this difference and mastering the formulas opens the way to solving flooring, painting and fencing problems.
Arrays group multiple values under a single name, accessible by index. Learn to create, iterate over, and operate on arrays and lists with practical examples.
Analytic geometry unites algebra and geometry on the Cartesian plane. With coordinates, you can calculate distances, find midpoints and describe lines with equations.
Probability quantifies uncertainty. Learn to calculate chances with dice, cards and everyday situations using the fundamental concepts.
Charts and tables turn numbers into understandable images. Learn how to choose the right type of visualization and how to avoid visual pitfalls.
A circle is the filled region; a circumference is the boundary curve. Understanding each element — radius, diameter, chord, arc — allows you to calculate lengths, areas and sectors precisely.
Commercial discount is calculated on the face value of the instrument, not on the present value. This detail completely changes the real cost of early collection.
In compound interest, each period's interest is added to the capital and generates even larger interest the next period. This exponential effect is the most powerful principle in finance.
Conditional statements allow a program to make decisions. Understand if, else, else-if, logical operators, and how to avoid the most common mistakes with conditionals.
Ice cream sales and drownings are positively correlated. Correlation measures the strength of linear relationships, but beware — it never proves cause and effect.
The number 0.75 represents the same quantity as 3/4 and 75%. Understanding decimals means understanding how fractions, percentages and measurements coexist in the same number system.
Functions are reusable blocks of code with their own name. Learn to create functions with parameters and return values, understand scope, and apply the DRY principle.
GCD simplifies fractions and divides objects into equal groups. LCM organises repeating cycles and resolves fraction addition. Each has its moment — knowing the difference is the key.
Comparing financial products requires understanding whether a rate is nominal or effective and whether it accounts for inflation. Converting correctly between periods avoids costly mistakes.
Understand what programming logic is, how algorithms show up in everyday life, and why learning to think in sequences of steps is essential in any field.
The Law of Cosines generalizes the Pythagorean Theorem to any triangle. See when to use it in SAS and SSS cases, how to calculate sides and angles, and practical applications.
The Law of Sines relates sides and opposite angles in any triangle. See when to apply it, how to handle the ambiguous case, and practical examples.
The metre, kilogram and second are the base units of the International System. Learn the metric prefixes, convert between units of length, mass and time, and avoid the most common mistakes.
Loops allow executing blocks of code multiple times without duplicating instructions. Learn about for, while, do-while, and best practices to avoid errors.
Learn to summarize data sets with mean, mode and median — and discover when each measure tells the most truthful story about your data.
Multiplication is accelerated addition, and division is its inverse. In this article you will understand the properties of these operations, learn the algorithms step by step, and discover why division by zero does not exist.
Natural numbers form the foundation of all mathematics. Understand how they are organized, which are even and odd, prime and composite, and how to use divisibility rules in everyday life.
The normal distribution is the most important in statistics. It describes heights, measurement errors and test scores — and has powerful mathematical properties.
Ordinal numbers indicate position, not quantity. First, second, third — we use ordinals for floors, rankings, calendars, and much more. Learn how to write, abbreviate, and use them correctly in English.
Exponentiation is repeated multiplication. Radicals are the inverse operation. Understanding the properties of exponents opens the door to algebra, geometry and physics.
Understanding the difference between revenue, cost and profit is the first step in running any business. Markup and margin are related concepts that are frequently confused.
The Pythagorean theorem relates the sides of any right triangle. Far beyond memorising a² + b² = c², you can understand why it works and where to use it.
Election polls interview 2,000 people to represent 150 million. Learn how sampling makes this possible and where distortions can arise.
Linear regression uses a line to predict values. Learn the equation ŷ = a + bx, what the slope and R² mean, with practical examples.
Understand why 30°, 45°, and 60° have exact values and how to derive the complete table from two simple triangles, without relying on rote memorization.
Two data sets can have the same mean and tell completely different stories. Standard deviation reveals how far data stray from the center.
The unit circle extends sine, cosine, and tangent to any real angle. Understand quadrants, signs, periodicity, and the fundamental identity.
Memorizing the times tables mechanically is less effective than understanding the patterns behind them. In this article we show the symmetry of the table, tricks for difficult facts, and how to use multiplication and division together.
Two triangles are similar when they have the same shape but different sizes. Understanding the similarity criteria opens the door to calculating heights, distances and scales.
Discover how sine, cosine, and tangent relate angles and sides of a right triangle, and how to use them to solve everyday problems.
Variables are the foundation of any program. Learn to declare, assign, and use variables with the correct data types to avoid common errors.
Volume measures how much space a solid occupies in three dimensions. Understanding the correct formulas and units solves everything from swimming-pool problems to packaging and tank calculations.
Understand the equilibrium principle behind every equation and solve any first-degree expression with confidence — no formulas to memorise.
A fraction is not a strange beast: it represents parts of a whole or a division between numbers. Understand the meaning before memorising the rules.
Trigonometry begins when you relate angles and sides of a right triangle. Understand the 'why' before memorising sin, cos and tan.
From store windows to credit card statements, percentages are everywhere. Understand the concept and stop relying on a calculator just to interpret the result.
The secret of the rule of three is not the cross-multiplication — it is correctly identifying whether the quantities grow together or in opposite directions.
When the rate is always applied to the original capital, growth happens in a straight line. Understand why this matters for your finances.