Topics
Commercial Mathematics
Co-ordinate Geometry Distance and Section Formula
- Co-ordinates Expressed as (x,y)
- Distance Formula
- Section Formula
- The Mid-point of a Line Segment (Mid-point 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 3-years
- 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 Semi-circle 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 2-D 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, Semi-Inter 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.
Co-ordinate 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 y-intercept 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 Co-ordinate Geometry.
Definition
- Sales tax (ST): Sales tax (ST) is charged by the government on the sale of an item.
- Value-added tax: A value-added tax, known in some countries as a goods and services tax, is a type of tax that is assessed incrementally. It is levied on the price of a product or service at each stage of production, distribution, or sale to the end consumer, except a business is the end consumer which will reclaim this input value.
- Goods and Services Tax (GST): Goods and Services Tax is an indirect tax used in India on the supply of goods and services.
Formula
- Sales tax = Tax % of Bill Amount
Notes
Sales Tax, Value-added tax, Goods and Services Tax:
-
Sales tax (ST) is charged by the government on the sale of an item. It is collected by the shopkeeper from the customer and given to the government. This is, therefore, always on the selling price of an item and is added to the value of the bill.
Sales tax = Tax % of Bill Amount -
A value-added tax, known in some countries as a goods and services tax, is a type of tax that is assessed incrementally. It is levied on the price of a product or service at each stage of production, distribution, or sale to the end consumer, except a business is the end consumer which will reclaim this input value. It is similar to and is often compared to a sales tax.
- Goods and Services Tax (GST) is an indirect tax used in India on the supply of goods and services. Goods and services are divided into five different tax slabs for collection of tax - 0%, 5%, 12%, 18% and 28%. However, petroleum products, alcoholic drinks, and electricity are not taxed under GST and instead are taxed separately by the individual state governments, as per the previous tax system. From July 1, 2017, the Government of India introduced GST. The tax came into effect from 1 July 2017 through the implementation of the One Hundred and First Amendment of the Constitution of India by the Indian government. The GST replaced existing multiple taxes levied by the central and state governments. The tax rates, rules, and regulations are governed by the GST Council which consists of the finance ministers of the central government and all the states.
Example
The cost of a pair of roller skates at a shop was Rs. 450. The sales tax charged was
5%. Find the bill amount.
On ₹ 100, the tax paid was ₹ 5.
On ₹ 450, the tax paid would be = ₹ `5/100 xx 450` = ₹ 22.50
Bill amount = Cost of item + Sales tax
= ₹ 450 + ₹ 22.50
= ₹ 472.50.
Example
Waheeda bought an air cooler for ₹ 3300 including a tax of 10%. Find the price of the air cooler before VAT was added.
The price includes the VAT, i.e., the value-added tax. Thus, a 10% VAT means if the price without VAT is ₹ 100 then the price including VAT is ₹ 110.
Now, when price including VAT is ₹ 110, original price is ₹ 100.
Hence when price including tax is ₹ 3300, the original price
= ₹ `100/110 xx 3300`
= ₹ 3000.
Example
Salim bought an article for ₹ 784 which included GST of 12%. What is the price of the article before GST was added?
Let the original price of the article be ₹ 100. GST = 12%.
Price after GST is included = ₹ (100 + 12) = ₹ 112
When the selling price is ₹ 112 than the original price = ₹ 100.
When the selling price is ₹ 784, then the original price
= ₹ `100/112 xx 784`
= ₹ 700.
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