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Math Formulas: Complete List by Topic, With Examples
Stationary Points: Maxima, Minima & Inflection
Standard Limits: Formulas, Proofs & Examples
Separable Differential Equations: Solve Step By Step
Second Derivative Test: Rules, Examples & When It Fails
Math Terms A to Z: 1,400+ Definitions Explained Simply
Second Derivative: Concavity & Acceleration Explained
Root Test: Statement, Examples & When To Use It
Removable Discontinuity: Definition & How To Find It
Related Rates: Method, Formulas & Worked Examples
Ratio Test: Convergence Of Series Explained
Radius of Convergence: Formula, Examples & Interval
Properties Of Definite Integrals: Rules & Examples
Ordinary Differential Equations: Order, Degree & Solutions
Order and Degree of a Differential Equation
Optimization Problems in Calculus: Steps & Examples
Math Formulas: Complete List by Topic, With Examples
Stationary Points: Maxima, Minima & Inflection
Standard Limits: Formulas, Proofs & Examples
Separable Differential Equations: Solve Step By Step
Second Derivative Test: Rules, Examples & When It Fails
Math Terms A to Z: 1,400+ Definitions Explained Simply
Second Derivative: Concavity & Acceleration Explained
Root Test: Statement, Examples & When To Use It
Removable Discontinuity: Definition & How To Find It
Related Rates: Method, Formulas & Worked Examples
Ratio Test: Convergence Of Series Explained
Radius of Convergence: Formula, Examples & Interval
Properties Of Definite Integrals: Rules & Examples
Ordinary Differential Equations: Order, Degree & Solutions
Order and Degree of a Differential Equation
Optimization Problems in Calculus: Steps & Examples
The goal was never to make kids faster at math — it was to make them fall in love with it. Speed is a byproduct of genuine understanding.
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Algebra
Variables, equations, and the language of math
Coefficient - Definition, Types, and Math Examples
A coefficient is the number that multiplies a variable in an algebraic expression — in 3x, the coefficient is 3. This article covers the formal definition, the four types of coefficients, how to identify them in any expression, the rule for variables with no visible number, and the most common mistakes when picking out the coefficient.
Properties of Logarithms - Laws, Formulas, Proofs
The properties of logarithms are seven identities that simplify logarithmic expressions: the product rule (log b(xy) = log b x + log b y), quotient rule (log b(x/y) = log b x - log b y), power rule (log b(xⁿ) = n log b x), change-of-base formula, and three special values (log b 1 = 0, log b b = 1, log b bⁿ = n).
Roots In Polynomial Expressions: Full Guide
Roots in polynomial expressions are the values of x that make the polynomial equal zero, so a root of P(x) is any x with P(x) = 0. A number r is a root exactly when (x - r) is a factor, and by the Fundamental Theorem of Algebra a degree-n polynomial has exactly n roots when you count multiplicity and allow complex numbers.
Geometry
Shapes, proofs, and spatial thinking
Collinear Vectors — Definition, Conditions, Examples
Collinear vectors are vectors that lie along the same line — which means one is always a scalar multiple of the other, a = k,b. This article covers the three tests for collinearity (scalar multiple, equal coordinate ratios, zero cross product), how collinear differs from parallel and coplanar, and worked examples.
Rotational Symmetry - Order & Angle of Rotation
Rotational symmetry means a shape maps exactly onto itself when turned about its centre by some angle smaller than a full turn. The order counts how many times it matches in one 360° rotation, and the angle of rotation is 360°/(order); this guide gives the definitions, six worked examples, and the traps that produce a wrong order.
Basic Proportionality Theorem: Statement, Proof & Examples
The Basic Proportionality Theorem (BPT), also called Thales' theorem, says that if a line is drawn parallel to one side of a triangle and cuts the other two sides, it divides those two sides in the same ratio: for DE ∥ BC, AD/DB = AE/EC. This guide gives the statement, the area-based proof, the converse, six worked examples, and the ratio-matching mistake that trips most students.
Trigonometry
Angles, waves, and circular harmony
Tan 7pi/6 : Exact Value 1/√3 Explained
The value of tan 7π/6 is exactly 1/(√3), or in rationalised form (√3)/3, which is about 0.5774. This article shows why the answer is positive (the angle lands in the third quadrant), how the reference angle (π)/6 produces the value, and how the unit circle confirms it, with a tangent table, worked examples, and the mistakes to sidestep.
Sin A Cos B Formula : Derivation & Examples
Sin A cos B equals 1/2[sin(A+B) + sin(A-B)], a product-to-sum identity that turns a product of a sine and a cosine into a sum of two sines. This article covers the formula, its derivation from the angle-sum and angle-difference identities, six worked examples, the mistakes students make, and why the identity matters for integration.
Sin Double Angle Formula : Derivation, Identities, and Examples
The sin double angle formula is sin 2x = 2sin x cos x, which rewrites the sine of a doubled angle using the sine and cosine of the original angle. This article covers the formula, its derivation from the angle-sum identity, the tangent form, six worked examples, the mistakes to avoid, and where doubling an angle actually matters.
Parenting
Raising confident, curious young mathematicians
Math Formulas
Every essential formula, explained and derived
Percentile Formula – Definition, Calculation, Examples
The percentile formula tells you where a value stands in a dataset: P = (number of values below x)/N × 100. This article covers both directions — finding the percentile of a value, and finding the value at a given percentile — with worked examples, the percentile-versus-percentage distinction, and the mistakes that trip students up.
Maths Formulas for Class 10 — Chapter-Wise List
The maths formulas for class 10 span the full board syllabus — real numbers, polynomials, linear and quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry, circles, mensuration, statistics, and probability. This hub lists every formula by chapter, explains where each one comes from, and works one example per cluster so the formulas connect instead of floating loose.
nPr Formula — Permutations, Derivation, Examples
The nPr formula counts how many ordered arrangements of r objects you can make from n distinct objects: ⁿP r = (n!)/((n-r)!). This article derives that formula from the counting principle, defines every symbol, shows where order makes a permutation different from a combination, and works six examples from a simple line-up to a locked-position arrangement.
Math Terms
Crystal-clear definitions with worked examples
Radius of a Circle: Definition, Formula, Examples
The radius of a circle is the distance from its centre to any point on the boundary, and it is exactly half the diameter. This article covers the definition, the three formulas for finding the radius, how it ties to the circle equation, six worked examples, and the common mistakes.
CP Formula — How to Find Cost Price, Examples
The CP formula recovers the cost price of an item from its selling price and a profit or loss: CP = SP - profit, CP = SP + loss, and from a percentage, CP = 100/(100 + profit%) × SP or 100/(100 - loss%) × SP. This article derives all four forms, defines every term, and works six examples plus the percentage mistakes that flip answers.
Isosceles Triangle Formula — Area, Perimeter, Height
The isosceles triangle formula set is: area = 1/2bh (or b/2√(a² - (b²)/4) from the equal side a and base b), perimeter = 2a + b, and height = √(a² - (b²)/4). This article gives each formula, derives the height and area straight from the Pythagorean theorem, works six examples from one-step to a word problem, and clears up the mistakes that cost the most marks.
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