Division Of A Line Segment Into A Given RatioGiven a line segment AB, we want to divide it in the ratio m : n, where both m and n are positive integers. To help you to understand it, we shall take m = 3 and n = 2. Steps of Construction: 1.  Draw any ray …

How To Construct A Tangent To A Circle From An External PointSteps of construction 1. Take given circle and a point P outside the circle. O is centre of the circle. 2. Joint OP. 3. Bisect OP and get its mid-point M. 4. Draw circle with centre M and radi…

Section FormulaLet A and B be two points in the plane of the paper as shown in fig. and P be a point on the segment joining A and B such that AP : BP = m : n. Then, the point P divides segment AB internally in the ratio m : n. If P is a point on AB prod…

OPERATIONS ON NUMBERSAdditionAddition of two or more numbers gives us another number. The numbers which are added are called addends and the new number thus obtained is called the sum. For example, 34670 + 12345 = 47015 Here, 34670 and 12345 are called …

Solving Quadratic Equations with Complex RootsWhen the roots of a quadratic equation are imaginary, they always occur in conjugate pairs.A root of an equation is a solution of that equation. If a quadratic equation with real-number coefficients has a neg…

Trigonometric Ratios Of Some Specific AnglesThe angles 0°, 30°, 45°, 60°, 90° are angles for which we have values of T.R.θ 0°30°45°60°90°Sin01/21/√2 √3/21 Cos1 √3/2 1/√21/20Tan 0 1/√31√3∞Cosec∞2√22/√31Sec12/√3 √22∞Cot∞√311/√30Trigonometric Ratios Of Some…

Review Factoring PolynomialsThis lesson will review the process of factoring, which is used when solving  equations and simplifying rational expressions.To factor polynomial expressions, there are several approaches that can be used to simplify the proce…

Solving Quadratic Equations by Completing the SquareSolving quadratic equations by completing the square is overpowered by an “offspring” of this process, namely, the quadratic formula. The quadratic formula was derived by completing the square on a qua…

Zeros Of A Polynomial FunctionIf for x = a, the value of the polynomial p(x) is 0 i.e., p(a) = 0; then x = a is a zero of the polynomial p(x).For Example: (i) For polynomial p(x) = x – 2; p(2) = 2 – 2 = 0 ∴ x = 2 or simply 2 is a zero of the polynomial p…

Types Of Polynomials(i) Based on degree : If degree of polynomial isExamples1.One  Linearx + 3, y – x + 2, √3x –32.TwoQuadratic2x2 –7, \(\frac{1}{3}{{\text{x}}^{2}}+{{\text{y}}^{2}}-2\text{xy}\), x2 +1+ 3y3.ThreeCubicx3 + 3x2 –7x+8, 2x2+5x3+7,4.Fourbi-qu…