Bhanzu Blog — Sparking Math Curiosity

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Expert guides for parents, students and math enthusiasts. Algebra to Olympiads — we've got you covered.

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Algebra

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.
Bhanzu Team
Jul 20, 2026
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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, and the mistakes to avoid. Bhanzu Team
Jul 20, 2026
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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.
Bhanzu Team
Jul 20, 2026
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Geometry

Midsegment of a Triangle - Definition, Theorem, and Examples
The midsegment of a triangle is the segment joining the midpoints of two sides. By the midsegment theorem it is parallel to the third side and exactly half its length. This article defines the midsegment, proves the theorem, works through examples, and clarifies how the midsegment relates to (and differs from) the midpoint theorem.
Bhanzu Team
Jul 22, 2026
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Types of Quadrilaterals: Definition and Classification
A quadrilateral is any four-sided closed shape whose interior angles sum to , and the main types of quadrilaterals are the parallelogram, rectangle, square, rhombus, trapezoid, and kite. This article defines each type, shows how they nest in one family tree, and works through examples of classifying a shape from its sides, angles, and diagonals.
Bhanzu Team
Jul 22, 2026
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Vertex of an Ellipse: Definition, Formula & Examples
The vertices of an ellipse are the two endpoints of the major axis - the farthest points from the center - located a distance from the center along the longer axis. The endpoints of the shorter (minor) axis are the co-vertices, at distance . This article defines both, gives the formulas for finding them from an ellipse's equation, and works through examples.
Bhanzu Team
Jul 22, 2026
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Trigonometry

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.
Bhanzu Team
Jul 16, 2026
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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.
Bhanzu Team
Jul 16, 2026
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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.
Bhanzu Team
Jul 16, 2026
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Parenting

Vedic Maths Multiplication: The Real Methods, Explained
Vedic maths multiplication is a set of pattern-based shortcuts that make specific multiplications fast — multiplying by 11, numbers near a power of ten, and a general cross-pattern — and they genuinely work for the patterns they fit. This guide teaches the real methods with worked examples, names what they're good for, shows where they break on unfamiliar problems, and shows how to build the understanding that makes the speed transfer to algebra and beyond.
Bhanzu Team
Jul 22, 2026
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Math Formulas

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.
Bhanzu Team
Jun 22, 2026
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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.
Bhanzu Team
Jun 22, 2026
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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.
Bhanzu Team
Jun 22, 2026
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Math Terms

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.
Bhanzu Team
Jun 22, 2026
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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.
Bhanzu Team
Jun 22, 2026
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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.
Bhanzu Team
Jun 17, 2026
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