The English System of MeasurementThe English system of measurement grew out of the creative way that people measured for themselves. Familiar objects and parts of the body were used as measuring devices. For example, people measured shorter distances on …

Trigonometry: Solving for a SideThe word ‘trigonometry’ is derived from the Greek words ‘tri’(meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Trigonometry is the study of relationships between the sides and angles of a triangle. Ap…

Reference Table for Areas“(The universe) is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is impossible to understand a single word of it; without these, one is wandering …

Number Of Tangents From A Point On A Circle(i) There is no tangent passing through a point lying inside the circle. (ii) There is one and only one tangent passing through a point lying on a circle. (iii) There are exactly two tangents through a point lyi…

How To Find The Area Of A Sector Of A Circle If the arc subtends an angle of θ at the centre, then its arc length is \( \frac{\text{ }\!\!\theta\!\!\text{ }}{\text{180}}\text{ }\!\!\times\!\!\text{ }\!\!\pi\!\!\text{ r} \) Hence, the arc length ‘l’ of a…

Pair Of Linear Equations In Two Variables A statement of equality of two algebraic expressions, which involve one or more unknown quantities is known as an equation. If there are two unknown quantities then equation is called linear equation in two vari…

Working with Sets and Venn DiagramsSets are simply collections of items. A set may contain your favorite even numbers, the days of the week, or the names of your brothers and sisters. The items contained within a set are called elements, and elements in…

Pythagorean Theorem in AlgebraOver 2,500 years ago, a Greek mathematician named Pythagoras popularized the concept that a relationship exists between the hypotenuse and the legs of right triangles and that this relationship is true for all right triangle…

Areas Of Parallelograms And TrianglesParallelograms on the same base and between the same parallels are equal in area.Area of a parallelogram is the product of its any side and the corresponding altitude.Parallelogram on the same base and having equal ar…

Solving A Quadratic Equation By Factoring Since, 3x2 – 5x + 2 is a quadratic polynomial; 3x2 – 5x + 2 = 0 is a quadratic equation. Also, 3x2 – 5x + 2 = 3x2 – 3x – 2x + 2 [Factorising] = 3x (x – 1) – 2(x – 1) = (x – 1) (3x – 2) In the same way : 3x2 – 5…