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Zeros of a Polynomial — Definition & Examples
Synthetic Division of a Polynomial — Steps and Examples
Sum of Odd Numbers — Formula, Proof & Examples
Squaring a Trinomial: Formula and Examples
Square Root of 4900 — Value, Steps, and Why It Is 70
Square Root of 640 — Value, Simplification, and Steps
Square Root of 567 — Value, Simplification, and Steps
Square Root of 384: Value and Simplification
Square Root of 340 — Value, Simplification, Steps
Square Root of 255 — Value, Simplification, and Steps
Square Root of 245 — Value, Simplification, Steps
Square Root of 157 — Value and How to Find It
Square Root of 153 — Value, Simplification, and Steps
Square Root of 115 — Value, Simplification, and Steps
Square Root of 105 — Value and How to Find It
Square Root of 47 — Value, Simplification, and Steps
Zeros of a Polynomial — Definition & Examples
Synthetic Division of a Polynomial — Steps and Examples
Sum of Odd Numbers — Formula, Proof & Examples
Squaring a Trinomial: Formula and Examples
Square Root of 4900 — Value, Steps, and Why It Is 70
Square Root of 640 — Value, Simplification, and Steps
Square Root of 567 — Value, Simplification, and Steps
Square Root of 384: Value and Simplification
Square Root of 340 — Value, Simplification, Steps
Square Root of 255 — Value, Simplification, and Steps
Square Root of 245 — Value, Simplification, Steps
Square Root of 157 — Value and How to Find It
Square Root of 153 — Value, Simplification, and Steps
Square Root of 115 — Value, Simplification, and Steps
Square Root of 105 — Value and How to Find It
Square Root of 47 — Value, Simplification, and Steps
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
Objective Function — Definition, Formula, and Examples
The objective function is the linear expression a linear programming problem sets out to maximize or minimize — usually written , where and are decision variables. This article defines it, shows the form, works six examples, and separates it clearly from the constraints.
Scalar Triple Product — Definition, Formula, Example
The scalar triple product of three vectors is , a single number equal to the signed volume of the parallelepiped built on those vectors. This article covers the definition, the determinant formula, six worked examples, why a zero result means the vectors are coplanar, and the mistakes to avoid
Square Root 1 to 25 — Values, Chart & Examples
The square root 1 to 25 chart gives through , where five values () are exact whole numbers and the other twenty are irrational, rounded here to three decimals. This article gives the full table, marks rational versus irrational, and shows how to read and rebuild it.
Geometry
Shapes, proofs, and spatial thinking
Corresponding Sides in Geometry - Definition, Examples
Corresponding sides are sides in the same relative position in two figures that are either similar or congruent. In congruent figures corresponding sides are equal; in similar figures they are proportional - their ratio is constant. This article shows how to match them from vertex order, how to use the ratio to find a missing length, and the mistakes to avoid
Convex Shape - Definition, Properties & Examples
A convex shape is a shape where the straight line joining any two points inside it stays completely inside - equivalently, every interior angle of a convex polygon is less than . This guide gives the one-line test, the properties, six worked examples, and the mistakes that make students misclassify a shape.
Angles of a Quadrilateral - Formula and Examples
The four interior angles of a quadrilateral always add up to 360°, because any four-sided figure splits into two triangles of 180° each. This article shows why the rule holds, how to find a missing angle, the exterior-angle and cyclic-quadrilateral cases, and the mistakes to avoid.
Trigonometry
Angles, waves, and circular harmony
Trigonometric Ratios of Specific Angles — Table & Values
The trigonometric ratios of specific angles are the exact values of sin, cos, tan, csc, sec, and cot at and — five angles whose ratios come out as clean surds, not decimals. This article gives the full values table, shows where each number comes from (the -- and -- triangles plus the unit circle), explains why entries like are undefined, and works through six examples.
Trigonometric Ratios of Complementary Angles
Two angles are complementary when they add to , and the trigonometric ratio of an angle equals the co-ratio of its complement — so , , and . This article gives all six complementary-angle identities, proves them from a right triangle, explains why the "co-" in cosine means complement, and works through six examples — including the classic problem.
Trigonometric Ratios in Radians - Values & Examples
Trigonometric ratios in radians are the same six ratios — sin, cos, tan, csc, sec, cot — measured with the angle written in radians instead of degrees, where a full circle is radians rather than . This article gives the standard-angle table (), how to convert, why radians exist, six worked examples, and the mistakes that cost marks.
Parenting
Raising confident, curious young mathematicians
Math Formulas
Every essential formula, explained and derived
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 objects you can make from distinct objects: . 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.
Sum of Arithmetic Sequence Formula — Proof, Examples
The sum of arithmetic sequence formula adds the first terms of an arithmetic progression: . This article derives both forms by the pairing trick, defines every variable, works through six examples from one-step sums to finding from a known total, and clears up the mistakes that cost the most marks.
Math Terms
Crystal-clear definitions with worked examples
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: , , and from a percentage, or . 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 (or from the equal side and base ), perimeter , and height . 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.
What Is a Chord? Definition, Properties & Examples
A chord is a straight line segment whose two endpoints both lie on a curve — most often a circle. This article defines the term, gives the chord-length formulas, lays out the key chord properties, works six examples, and clears up the chord-versus-diameter mix-up that trips students.
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