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.
 Figures with one Line of Symmetry
 Figures with two Line of Symmetry
 Figures with more Line of Symmetry
Definition
 Line Symmetry: A figure has line symmetry if a line can be drawn dividing the figure into two symmetrical parts. The line is called a line of symmetry.
Notes
Line Symmetry:
A figure has line symmetry if a line can be drawn dividing the figure into two symmetrical parts. The line is called a line of symmetry.
A figure can have any number of lines of symmetry passing through it. Some can have one, two, or even multiple lines of symmetry.
1. Figures with one Line of Symmetry:
A figure has line symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.
2. Figures with two Lines of Symmetry:
Example of two lines of symmetry: A rectangle.
 Take a rectangular sheet (like a postcard).
 Fold it once lengthwise so that onehalf fits exactly over the other half.
 Open it up now and again fold on its width in the same way.
 After opening it, we get two lines of symmetry of the rectangular sheet.
Construction of figure with two Lines of Symmetry:
We can also learn to construct figures with two lines of symmetry starting from a small part.
1. Let us have a figure as shown alongside.
2. We want to complete it so that we get a figure with two lines of symmetry. Let the two lines of symmetry be L and M.
3. We draw the part as shown to get a figure having line L as a line of symmetry.
4. To complete the figure we need it to be symmetrical about line M also. Draw the remaining part of the figure as shown. This figure has two lines of symmetry i.e. line Land line M.
3. Figures with multiple Lines of Symmetry:
Example of multiple lines of symmetry (two or more)
 Take a square piece of paper. Fold it into half vertically, fold it again into half horizontally. (i.e. you have to fold it twice).
 Now open out the folds and again fold the square into half (for a third time now), but this time along a diagonal.
 Again open it and fold it into half (for the fourth time), but this time along the other diagonal.
 When you will open the paper you will see four imaginary lines and these lines are the lines of symmetry.
Some more images with more than two lines of symmetry:

The equilateral triangle will have three lines of symmetry.

Square will have four lines of symmetry.

The regular pentagon will have five lines of symmetry.

Regular hexagon will have six lines of symmetry.