MATHEMATICS 9

  Introduction to Probability Probability Probability is the measure of the likelihood of an event to occur. Events can’t be predicted with certainty but can be expressed as to how likely it can occur using the idea of probability. Probability can range between 0 and 1, where 0 probability means the event to be an impossible one and probability of 1 indicates a certain event. Experiment An experiment: is any procedure that can be infinitely repeated or any series of actions that have a well-defined set of possible outcomes. can either have only one or more than one possible outcomes. is also called the sample space. Trail A single event that is performed to determine the outcome is called a trial. All possible trials that constitute a well-defined set of possible outcomes are collectively called an experiment/sample space. Experimental Probability Experimental/Empirical Probability The empirical probability of an event that may happen is given by: Probability of event to happen...

  Introduction to Statistics – A study dealing with the collection, presentation and interpretation and analysis of data is called as statistics. Data Facts /figures numerical or otherwise collected for a definite purpose is called as data. data collected first-hand data:- Primary Secondary data: Data collected from a source that already had data stored Frequency – The number of times a particular instance occurs is called frequency in statistics. Ungrouped data Ungrouped data is data in its original or raw form. The observations are not classified in groups. Grouped data In grouped data, observations are organized in groups. Class Interval The size of the class into which a particular data is divided.    E.g divisions on a histogram or bar graph. Class width  = upper class limit – lower class limit Regular and Irregular class interval Regular class interval: When the class intervals are equal or of the same sizes. E.g 0-10, 10-20, 20-30….. 90-100 Irregular class int...

  The surface area and volume for class 9 notes are given here. In this article, the complete surface area and volume formulas for different three-dimensional shapes are discussed with the complete explanation. For any three-dimensional figures, the surface area can be broadly classified into Curved Surface Area(CSA), Lateral Surface Area (LSA), and Total Surface Area (TSA). These can be computed for 3d shapes such as a cube, cuboid, cone, cylinder and so on. Cuboid A cuboid is a three dimensional Shape. The cuboid is made from six rectangular faces, which are placed at right angles. The total surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Total Surface Area of a Cuboid Consider a cuboid whose length is “ l”  cm, breadth is  b  cm and height  h  cm. Area of face ABCD = Area of Face EFGH  =  ( l  ×  b )  c m 2 Area of face AEHD = Area of face BFGC  =  ( b  ×  h ) ...