Topics
Commercial Mathematics
Compound Interest
Coordinate Geometry Distance and Section Formula
Loci
Algebra
Shares and Dividends
Quadratic Equations
Circles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Areas of Sector and Segment of a Circle
 Tangent Properties  If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments
 Tangent Properties  If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection
 Tangent to a Circle
 Number of Tangents from a Point on a Circle
 Chord Properties  a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord
 Chord Properties  the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)
 Theorem: Equal chords of a circle are equidistant from the centre.
 Theorem : The Chords of a Circle Which Are Equidistant from the Centre Are Equal.
 Chord Properties  There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line
 Arc and Chord Properties  the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle
 Theorem: Angles in the Same Segment of a Circle Are Equal.
 Arc and Chord Properties  Angle in a Semicircle is a Right Angle
 Arc and Chord Properties  If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse
 Arc and Chord Properties  If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof)
 Arc and Chord Properties  If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal
 Cyclic Properties
 Tangent Properties  If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
Banking
Geometry
Factorization
Constructions
Ratio and Proportion
Mensuration
Gst (Goods and Services Tax)
 Sales Tax, Value Added Tax, and Good and Services Tax
 Computation of Tax
 Concept of Discount
 List Price
 Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
 Basic/Cost Price Including Inverse Cases.
 Selling Price
 Dealer
 Goods and Service Tax (Gst)
 Gst Tax Calculation
 Gst Tax Calculation
 Input Tax Credit (Itc)
Symmetry
Trigonometry
Similarity
Linear Inequations
Arithmetic Progression
Statistics
 Median of Grouped Data
 Graphical Representation of Data as Histograms
 Ogives (Cumulative Frequency Graphs)
 Concepts of Statistics
 Graphical Representation of Data as Histograms
 Graphical Representation of Ogives
 Finding the Mode from the Histogram
 Finding the Mode from the Upper Quartile
 Finding the Mode from the Lower Quartile
 Finding the Median, upper quartile, lower quartile from the Ogive
 Calculation of Lower, Upper, Inter, SemiInter Quartile Range
 Concept of Median
 Mean of Grouped Data
 Mean of Ungrouped Data
 Median of Ungrouped Data
 Mode of Ungrouped Data
 Mode of Grouped Data
 Mean of Continuous Distribution
Probability
Geometric Progression
Matrices
Reflection
Coordinate Geometry Equation of a Line
 Slope of a Line
 Concept of Slope
 Equation of a Line
 Various Forms of Straight Lines
 General Equation of a Line
 Slope – Intercept Form
 Two  Point Form
 Geometric Understanding of ‘m’ as Slope Or Gradient Or tanθ Where θ Is the Angle the Line Makes with the Positive Direction of the x Axis
 Geometric Understanding of c as the yintercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0
 Conditions for Two Lines to Be Parallel Or Perpendicular
 Simple Applications of All Coordinate Geometry.
description
 Construction of a histogram for continuous frequency distribution
 Construction of histogram for discontinuous frequency distribution.
definition
Histogram: Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
notes
Graphical Representation of Data as Histograms:

Grouped data can be presented using a histogram.

Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.

A Histogram is a bar graph that shows data in intervals. It has adjacent bars over the intervals.

This is a form of representation like the bar graph, but it is used for continuous class intervals.

There are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram, which is a graphical representation of a grouped frequency distribution with continuous classes.

Unlike a bar graph, the width of the bar plays a significant role in its construction. The widths of the rectangles are all equal and the lengths of the rectangles are proportional to the frequencies.
Construction of Histogram:
For instance, consider the frequency distribution Table, representing the weights of 36 students of a class:
Weights (in kg)  Number of students 
30.5  35.5  9 
35.5  40.5  6 
40.5  45.5  15 
45.5  50.5  3 
50.5  55.5  1 
55.5  60.5  2 
Total  36 
Let us represent the data given above graphically as follows:
(i) We represent the weights on the horizontal axis on a suitable scale. We can choose the scale as 1 cm = 5 kg. Also, since the first class interval is starting from 30.5 and not zero, we show it on the graph by marking a kink or a break on the axis.
(ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Since the maximum frequency is 15, we need to choose the scale to accommodate this maximum frequency.
(iii) We now draw rectangles (or rectangular bars) of width equal to the classsize and lengths according to the frequencies of the corresponding class intervals. For example, the rectangle for the class interval 30.5  35.5 will be of width 1 cm and length 4.5 cm.
Marks  Number of students 
0  20  7 
20  30  10 
30  40  10 
40  50  20 
50  60  20 
60  70  15 
70  above  8 
Total  90 
 Select a class interval with the minimum class size which is 10.
 The lengths of the rectangles are then modified to be proportionate to the classsize 10. For instance, when the classsize is 20, the length of the rectangle is 7.
So when the classsize is 10, the length of the rectangle will be `7/20 xx 10 = 3.5`.
Marks  Frequency  Width of the class  Length of the rectangle 
0  20  7  20  `7/20 xx 10` = 3.5 
20  30  10  10  `10/10 xx 10` = 10 
30  40  10  10  `10/10 xx 10` = 10 
40  50  20  10  `20/10 xx 10` = 20 
50  60  20  10  `20/10 xx 10` = 20 
60  70  15  10  `15/10 xx 10` = 15 
70  100  8  30  `8/30 xx 10` = 2.67 