Topics
Commercial Mathematics
Coordinate Geometry Distance and Section Formula
 Coordinates Expressed as (x,y)
 Distance Formula
 Section Formula
 The Midpoint of a Line Segment (Midpoint Formula)
Compound Interest
 Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
 Use of Compound Interest in Computing Amount Over a Period of 2 Or 3years
 Use of Formula
 Finding CI from the Relation CI = A – P
Loci
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
Shares and Dividends
Algebra
Quadratic Equations
Banking
Geometry
Factorization
 Factor Theorem
 Remainder Theorem
 Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem
Constructions
 Circumscribing and Inscribing a Circle on a Regular Hexagon
 Circumscribing and Inscribing a Circle on a Triangle
 Construction of Tangents to a Circle
 Circumference of a Circle
 Circumscribing and Inscribing Circle on a Quadrilateral
Ratio and Proportion
 Concept of Ratio
 Concept of Proportion
 Componendo and Dividendo Properties
 Alternendo and Invertendo Properties
 Direct Applications
 Concept of Ratio
Mensuration
 Circumference of a Circle
 Surface Area of a Right Circular Cone
 Surface Area of a Sphere
 Circle  Direct Application Problems Including Inner and Outer Area
 Surface Area of a Right Circular Cone
 Surface Area of a Sphere
 Volume of a Cylinder
 Volume of a Combination of Solids
 Surface Area of Cylinder
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
 Trigonometric Ratios of Complementary Angles
 Trigonometric Identities
 Heights and Distances  Solving 2D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
 Trigonometry
Similarity
 Similarity of Triangles
 Similarity of Triangles
 Axioms of Similarity of Triangles
 Areas of Similar Triangles Are Proportional to the Squares on Corresponding Sides
Linear Inequations
 Linear Inequations in One Variable
 Solving Algebraically and Writing the Solution in Set Notation Form
 Representation of Solution on the Number Line
Arithmetic Progression
 Arithmetic Progression  Finding Their General Term
 Sum of First ‘n’ Terms of an Arithmetic Progressions
 Simple Applications of 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
 Geometric Progression  Finding Their General Term.
 Geometric Progression  Finding Sum of Their First ‘N’ Terms
 Simple Applications  Geometric Progression
Matrices
Reflection
 Reflection Examples
 Reflection Concept
 Reflection of a Point in a Line
 Reflection of a Point in the Origin.
 Invariant Points.
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.
Definition
Ratio: The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. This method is known as ratio.
Notes
Ratio:
i) Comparison by taking difference:
In our daily life, many times we compare two quantities of the same type. If the height of Rahim is 150 cm and that of Avnee is 140 cm then, we may say that the height of Rahim is 150 cm – 140 cm = 10 cm more than Avnee. This is one way of comparison by taking the difference.
ii) Comparison by division:
Consider an example. The cost of a car is 2,50,000 and that of a motorbike is 50,000. If we calculate the difference between the costs, it is 2,00,000 and if we compare by division; i.e. `(2,50, 000)/(50, 000)` = 5: 1.
Thus, in certain situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio.
 The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. This method is known as ratio.

Mathematical numbers used in comparing two things that are similar to each other in terms of units are ratios.

We denote ratio using symbol ‘:’

A ratio can be written in three different ways viz, m to n, m: n, and mn but read as the ratio of m is to n. Example: 2: 3 = ratio of 2 is to 3.

Note that the ratio 3: 2 is different from 2: 3. Thus, the order in which quantities are taken to express their ratio is important.

For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.

A ratio may be treated as a fraction, thus the ratio 10 : 3 may be treated as `10/3`.

A ratio can be expressed in its lowest form. For example, ratio 50: 15 is treated as `50/15`; in its lowest form `50/15 = 10/3`. Hence, the lowest form of ratio 50: 15 is 10: 3.
Same ratio in different situations:
Ratios can remain the same in different situations.

The length of a room is 30 m and its breadth is 20 m.
So, the ratio of the length of the room to the breadth of the room =`30/20=3/2`=3: 2.

There are 24 girls and 16 boys going for a picnic. The ratio of the number of girls to the number of boys = `24/16=3/2`= 3: 2
The ratio in both examples is 3: 2.
Example
Distance from Mary’s home to school (in km.)

10  4  
Distance from John’s home to school (in km.)

5  4  3  1 
Distance from Mary’s home to school (in km.)

10  8  4  6  2 
Distance from John’s home to school (in km.)

5  4  2  3  1 
Example
Find the ratio of 90 cm to 1.5 m.