Blog topic
Math articles
Step-by-step guides to linear equations, percentages, fractions, slope, the quadratic formula, areas and circumference, ratios, probability, standard deviation and more. Each one works a full example, names the usual mistake, and gives a quick check so you can tell when an answer is wrong.
35 explainers, newest first. Each one ends with real questions from the unit that teaches it, so you can read the explanation and then check whether it stuck.
These are the readable companion to the Math track, which holds 18 units and 2,161 practice questions. If you are starting the subject rather than looking something up, the study guide is the better place to begin.
What Is Trigonometry? Triangles, Circles and the Waves in Everything
Trigonometry began as the study of triangles and became the maths of anything that repeats. What sine, cosine and tangent are, and why they describe waves.
September 15, 20265 min readWhat Is Statistics? Making Sense of Data When No Single Measurement Can Be Trusted
Statistics is the science of drawing conclusions from data that vary. What averages hide, why samples work, what a p-value does not say, and how numbers lie.
September 15, 20265 min readWhat Is Algebra? Letters for Numbers and the Art of the Unknown
Algebra is arithmetic done with symbols that stand for any number, turning particular sums into general rules. Where it came from, and why the letters matter.
September 15, 20265 min readWhat Is Geometry? From Measuring Fields to the Shape of Space
Geometry began as the measuring of land and became the study of shape and space. Euclid's system, the geometries that broke his fifth rule, and where it went.
September 15, 20265 min readWhat Is a Vector? Arrows, Coordinates and the Mathematics of Direction
A vector is a quantity with both size and direction, drawn as an arrow and written as a list of numbers. How they add, and why physics and computing use them.
September 15, 20265 min readWhat Is a Matrix? Grids of Numbers That Rotate, Solve and Rank
A matrix is a grid of numbers that acts on vectors, the machine behind graphics, search rankings and neural networks. How they multiply, and why.
September 15, 20265 min readWhat Is Pi and Why Does It Turn Up Everywhere?
Pi is the ratio of a circle's circumference to its diameter, about 3.14159, and it goes on forever without repeating.
September 14, 20264 min readWhat Is a Prime Number? The Atoms of Arithmetic
A prime number has exactly two divisors, itself and one. Why primes are the building blocks of arithmetic, how they are found, and why they guard bank cards.
September 14, 20265 min readWhat Is Zero? The Number That Took Centuries to Accept
Zero is both a placeholder that makes positional notation work and a number in its own right. Where it was invented, why the Greeks lacked it, and what it does.
September 14, 20265 min readWhat Is Infinity? Why Some Infinities Are Bigger Than Others
Infinity is not a very large number but a property of collections that never run out. How Cantor tamed it, and why the points on a line outnumber the integers.
September 14, 20265 min readWhat Is Calculus? The Mathematics of Change and Accumulation
Calculus is the mathematics of things that change continuously: speeds, slopes, areas and totals. What its two halves do, and why they are one subject.
September 14, 20265 min readWhat Is a Logarithm? The Scale That Turns Multiplication Into Addition
A logarithm is the power a base must be raised to in order to give a number. Why that turns multiplying into adding, and where log scales hide in daily life.
September 14, 20265 min readWhat Is the Fibonacci Sequence?
How the pattern works, where it genuinely appears in nature, and which famous claims about it are overstated.
August 28, 20265 min readHow to Factor Quadratics Step by Step
Learn how to factor quadratics by finding number pairs, using the product-sum method, checking your brackets, and spotting cases that need other methods.
August 17, 20266 min readHow to Calculate Standard Deviation Step by Step
Learn how to calculate standard deviation by finding the mean, measuring each value's distance from it, calculating variance, and taking the square root.
August 17, 20266 min readHow to Find Percentage Change Step by Step
Learn how to find percentage change by comparing the difference with the original value, then turning the result into a percentage with clear examples.
August 17, 20265 min readHow to Calculate Volume of a Cylinder Step by Step
Learn how to calculate volume of a cylinder using pi, radius, and height, with a clear formula, worked example, unit checks, and common mistakes.
August 17, 20265 min readHow to Find the Area of a Trapezoid Step by Step
Learn how to find the area of a trapezoid using the two parallel sides and perpendicular height, with a clear formula, example, and common error checks.
August 17, 20265 min readHow to Find Slope: A Step-by-Step Math Guide
How to find slope becomes simple with rise over run. Learn the slope formula, positive and negative slopes, graphs, points, and common mistakes.
August 14, 20265 min readHow to Add Fractions: A Simple Step-by-Step Guide
How to add fractions starts with a common denominator. Learn the method for like and unlike denominators, simplify answers, and avoid common errors.
August 14, 20265 min readHow to Divide Fractions: A Simple Step-by-Step Guide
How to divide fractions uses one reliable method. Learn when to flip the second fraction, multiply, simplify, and check whether your answer makes sense.
August 14, 20265 min readQuadratic Formula: How to Solve Quadratic Equations
The quadratic formula gives you a reliable way to solve equations in standard form. Learn each part, avoid sign errors, and see what the discriminant tells you.
August 14, 20266 min readArea of a Circle: How to Use Pi Times Radius Squared
The area of a circle is found with pi times radius squared. Learn why the radius is squared, how to use diameter, and how to avoid common unit mistakes.
August 14, 20265 min readHow to Solve Simultaneous Equations Step by Step
How to solve simultaneous equations becomes easier with elimination or substitution. Learn both methods, check solutions, and avoid common sign errors.
August 14, 20266 min readArea of a Triangle: How to Use Base Times Height
The area of a triangle is half the base times the perpendicular height. Learn how to choose the right height, handle units, and check your answer.
August 14, 20266 min readHow to Calculate Probability: A Simple Step-by-Step Guide
How to calculate probability becomes easier when you count possible outcomes carefully. Learn basic fractions, complements, and independent events.
August 14, 20266 min readCircumference of a Circle: How to Use Pi, Radius, and Diameter
The circumference of a circle is the distance around it. Learn the formulas using pi, radius, and diameter, plus simple checks that prevent common mistakes.
August 14, 20266 min readHow to Multiply Fractions Step by Step
How to multiply fractions is simple once you multiply numerators and denominators, simplify the result, and handle whole or mixed numbers carefully.
August 14, 20266 min readHow to Calculate Ratios and Simplify Them Step by Step
How to calculate ratios becomes easier when you compare quantities in the same units, simplify with common factors, and keep the order of terms clear.
August 14, 20266 min readHow to Solve Inequalities Step by Step
How to solve inequalities becomes easier when you isolate the variable, track the inequality sign, and reverse it after multiplying or dividing by a negative.
August 14, 20266 min readHow to Solve Linear Equations Step by Step
Learn how to solve linear equations by keeping both sides balanced, undoing operations in order, and checking your answer with simple examples.
August 13, 20265 min readPythagorean Theorem: How to Use It and When It Works
The Pythagorean theorem links the three sides of a right triangle. Learn the formula, identify the hypotenuse, and solve missing-side problems clearly.
August 13, 20265 min readHow to Calculate Percentages Step by Step
Learn how to calculate percentages using simple formulas for finding a percent of a number, finding the percentage, and working backward from a result.
August 13, 20265 min readMean, Median, Mode and Range: How to Find Each One
Mean, median, mode and range describe a data set in different ways. Learn how to calculate each measure and how outliers can change what the results show.
August 13, 20265 min readBeat Math Fear: A Kinder Way to Learn Numbers
Math anxiety is common, and it is not a sign you are bad at math. Here is how to calm the fear, build up slowly, and treat mistakes as a normal part of learning.
December 3, 20255 min read