Maths

A Theoretical Approach * Experimental probability is based on the observations of an experiment. * Experimental probability gets closer to the theoretical probability as the number of observations increases. * Theoretical probability of an event E, P(E) = \frac{Number \thinspace \thinspace of \thinspace \thinspace outcomes \thinspace\thinspace \thinspace favourable \thinspace \thinspace to \thinspace \thinspace E}{Total \thinspace ... Read more

Mean of Grouped Data Mean of given set of data is given by the sum of values of all the given observations divided by the number of observations. The three ways of finding the mean of grouped data are: * Direct Method * Assumed Mean Method * Step-Deviation Method Class Mark ( X_{i} ) = \frac{( upper ... Read more

Surface Areas and Volumes of Combinations of Solids * Complex solid shapes are composed of fundamental solid shapes. * By summing the surface areas of the simpler shapes that compose a complex shape, you can calculate a area of a complex shape. * By summing the volumes of the simpler shapes that compose a complex ... Read more

Areas of Sector and Segment of Circle * Circumference of a circle of radius r is 2πr * Area of circle is πr². * Length of the arc of a sector of a angle θ is \frac{θ}{360} × 2πr * Area of a sector of angle θ is \frac{θ}{360} × πr² * Area of a ... Read more

Constructions Construction to draw a triangle APQ similar to a given triangle ABC as per given scale factor.  

Tangents to a Circle * A line that touches a circle at only one point is called a tangent to the circle. * The point where a tangent touches a circle is called its point of contact. * Only one tangent can be drawn at any given point on a circle. * The tangent at ... Read more

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