Notes

Heights and Distances Line of sight: The line joining the observer’s eye and the object observed Angle of elevation: The angle between the horizontal line and the line of sight which is above the observer’s eye Angle of depression: The angle between the horizontal line and the line of sight which is below the observer’s ... Read more

Trigonometric Ratios and Angles * Trigonometry is the study of relationship between the angles and sides of triangles. * The ratios between the lengths of the sides of a right-angled triangle are relation with its acute angles is called trigonometric ratios. N a right-angled triangle ABC, if ∠A is an acute angle: * Sin ∠A ... Read more

Distance Formula * The distance between the points ( x_{1} y_{1} ) and ( x_{2} y_{2}  ) is given by : \sqrt{( x_{2} - x_{1} )² + ( y_{2} - y_{1} )²} * The distance of the point (x, y) from origin is given by : \sqrt{ x^{2} + y^{2} } * Three points A, ... Read more

Similarity of Triangles * Two triangles are similar, if their corresponding angles are equal and their corresponding sides are proportional or in the same ratio. * Basic proportionality Theorems: If a line is drawn parallel to one side of triangle to intersect the other two sides in distinct points, the other two sides are divided ... Read more

General terms * Arithmetic Progression (AP) is a sequence in which the difference between any two successive terms is constant, which is referred to as the Common Difference. * An AP either increases or decreases progressively. Common Difference = any term –Preceding term General term of an AP: t_{n} = a + (n – 1)d ... Read more

Quadratic Equation * The roots of a quadratic equation of the form ax² + bx + c = 0 can be calculated using the formula x = \frac{- b \pm \sqrt{ b^{2} - 4ac} }{2a} * The sum of roots of a quadratic equation is: α + β =  \frac{- b}{a} The product of roots ... Read more

Graphical Method of Solution * The general form of a pair of a linear equations in two variables x and y are: a_{1} x + b_{1} y + c_{1}  = 0 and a_{2} x + b_{2} y + c_{2} =0 a_{1}, a_{2}, b_{1} , b_{2} , c_{1} , c_{2} are all real numbers and a_{1}² ... Read more

Geometrical Meaning of the Zero Polynomial * The x-coordinate of the point, where the graph of a polynomial intersects the x-axis is called the zero of the polynomial. * An nth-degree polynomial intersects the x-axis at maximum of n points and therefore, has a maximum of n zeroes. In a quadratic polynomial ax²+ bx + ... Read more