Friday, June 8, 2012

A-Z of Economic and Banking Terms


 Here comes the list.
Absolute Advantage:
Country ‘A’ has an absolute advantage over country ‘B’ if the output per unit of input of A is higher than that of B.
Accelerator Principle:
Accelerator Principle of a company is the growth in ouput of the company that would induce a continuation in net investment.
Ad Valorem Tax:
It is a tax based on the value of the property.
Aggregate Demand:
It is the total of all the demand in a country. It can also be expressed as
Total Exports of a country – Total imports of the country.
Aggregate Supply:
Total value of good and services produced in an economy + {Imports-Exports}
Asset:
Any item of monetary value like bank accounts, real estate property, stocks,..etc
Barter System:
Trade which doesnt involve the exchange of money
Bretton-Woods:
It is a monetary system that existed from the year 1946-1973. In this monetary system the value of dollar was calculated using gold reserves and every other country held it’s currency at an exchange rate with US dollars.
Budget Deficit:
Budget Deficit = Goverment Expenditure- Goverment Revenues.
Call Money Market:
It is the market in which the Dealers and brokers locate and borrow money to satisfy their investment needs.
Capital Gains Tax:
Tax paid for the profit made through the sale of an asset.
Cash Reserve Ratio{CRR}:
It is determined by the RBI and is the minimum reserves each bank must hold to customer deposits and notes..
Both CRR and Statutory Liquidity Ratio{SLR} are used to combat inflation. Higher CRR and SLR decrease the money supply thereby combating inflation.
Centrally planned economy:
An economic system where the production & pricing of goods and services are determined by the goverment
Classical Economics:
The theory emphasizes the fact that free market can regulate themselves. This theory was framed by Adam Smith, David Ricardo, Thomas Malthus and John Stuart Mill
Closed economy:
The economy is closed and doesnt have any contact with the rest of the world
Consumer Price Index:
It is the measure of the average price of consumer goods and services purchased by households. It is measured with 1982 as it’s base year.


Countervailing Duties:
These are the duties that are imposed by a country on Foreign producers in order to neutralize the negative effects of other duties.
Currency Appreciation:
Increase in the value of a currency over the other. It takes place when the market exchange rates change.
Current Account Deficit:
Current account deficit= Export-Import
Current GDP:
Current GDP is GDP expressed in the current prices of the period being measured
Customs Duty:
Duty levied on imports.
Deflation:
An economy is said to be in deflation when there is a fall in the prices of the commodities.
Direct Tax:
These are the taxes that are levied on us directly. Taxes on Corporate Income, Capital Gains tax, Personal Income tax and Fringe benefit tax fall under this category.
Dividends:
It is the portion of the profits made by a company that is paid to the share holders.
Exchange rate:
Also called as Foreign Exchange Rates or FOREX of a country specifies how much the country’s currency is worth in terms of the other currency.
Fiscal Deficit:
Fiscal Deficit= Goverment Expenditure in the current fiscal year- Goverment Revenues in the fiscal year.
Fiscal Policy:
It is the use of goverment revenue to influence the country’s economic situation.
Foreign Direct Investment:
It is the investment made by a company in one country on building a factory in another country.
Foreign Institutional Investor:
Investor from a foreign country.
Free Trade:
In this type of trade there is no tariffs to the imported or exported goods between two countries.
Fringe Benefit:
These are the benefits that are offered to employees in addition to their salaries like lunch coupons, cars, free petrol etc.
GATT:
The General Agreement on Tariffs and Trade{GATT} was created in 1947 as a replacement to International Trade Organization (ITO). GATT was replaced by World Trade Organization in the year 1995.
GDP {Gross Domestic Product}:
Expenditure method:
GDP = consumption + gross investment + government spending + (exports – imports)
Note: GNP is similar to GDP except for the fact that GNP takes the country’s localities into account
Income method:
The formula for GDP measured using the income approach, called GDP(I), is:
GDP = Compensation of employees + Gross operating surplus + Gross mixed income + Taxes less subsidies on production and imports
GDP per capita:
GDP per capita is the contribution of every citizen of the country to the total GDP
Giffen goods:
These are the goods which people consume more as prices increase thereby violation law of demand. {Usually people purchase less as the prices increase}
Government Securities {G-Secs}
These are issued by the RBI on behalf of the market borrowing programme. It includes State Government Securities, Central Government Securities and Treasury Bills.
Human development Index
Measurement based on GDP per capita, life expectancy and education
Inflation:
An economy is said to be in inflation when there is a rise in the price of the commodities.
Indirect Tax:
These are the taxes that we don’t pay directly. It includes Excise Duty, Customs Duty, Service tax and Securities Transaction Tax.
Insurance Regulatory & Development Authority (IRDA):
It is based in Hyderabad and the Mission of IRDA as stated in the act is “to protect the interests of the policyholders, to regulate, promote and ensure orderly growth of the insurance industry and for matters connected therewith or incidental thereto.”
Insurance Regulatory and Development Authority Act in 1999
This act allowed private companies into the insurance sector. It also increased the cap on FDI in insurance sector to 26 percent.
International Labour Organization{ILO}
Was established in 1919 and is a specialized UN agency that deals with labour issues.
Internation Monetary Fund:
It is an organization of 186 countries that aims at stabilizing foreign exchange rates and assisting the reconstruction of the international payment system. It was established in 1944.
International Poverty Line:
It is the minimum money expressed in dollars that an individual needs to achieve an adequate standard of living. For some years this Internation Poverty Line has been roughly around one dollar a day.
Macro-economics:
As the word suggests, it deals with the economic behaviour and performance of an entire country.
Microcredit
It is the provision of credit, parsimony, and other financial services and products of very small amount to the poor in semi-urban, rural and urban areas. It is to enable them to raise their income levels and improve their living standards.
Micro-economics:
This deals with studying how firms and households make decisions to allocate resources in markets. Market analysis is the main concept of Microeconomics.
Monetary Policy:
The policy through which the RBI controls the supply, availability and cost of money {Interset rate} in order to attain economic goals.
Net Domestic Product:
NDP= GDP-depreciation of capital goods in that country.
All are measured using Purchasing Power Parity
Nominal GDP:
Nominal GDP growth is GDP growth in nominal prices (unadjusted for price changes).
Parallel economy:
Alternative term for black economy, shadow economy and underground economy.
Politically Exposed Persons PEPs
Politically Exposed Persons are individuals who are or have been entrusted with prominent public functions in a foreign country.
Purchasing power parity:
Using market exchange values to equalize their purchasing power.
Quasi Money:
Also called as Near Money. These are the assets that can be easily converted to money without no loss in value.
Real GDP:
Real GDP growth is GDP growth adjusted for price changes(using ppp).
Repo rate:
The rates at which banks borrow money from RBI.
Reverse repo rate:
The rates at which RBI borrows money from the Banks.
Securities:
It is an instrument that has a financial value. It can be classified as debt securites{Bank notes(currency), bonds} and equity securities{Stocks}.
Statutory Liquidity Ratio
It is determined by the RBI and is the minimum amount that a bank must hold in the form of gold, cash and government securities.
Subsidy:
It is the payment given to the producers and distributors in a particular sector to prevent the downfall of that sector. For example goverment providers subsidies to small scale industry owners in order to prevent the downfall of small scale industries in the country.
The Wealth of Nations:
It is the famous book written by Adam Smith {Renowned economist}
Treasury Bills:
These are short term borrowing instruments that are issued by RBI. They are issued at discount to face value and on attaining maturity the maturity value is paid to the holder. The minimum amount in treasury bills is 25,000 Rs and thereafter they are available in multiples of 25,000.
Wholesale price Index:
Wholesale price Index is used to measure the inflation in our country and is the price of a basket of wholesale goods with it’s base year as 1993-94.
World Bank:
It is an international financial institution that was established in the year 1945. It provides loans to poor countries in order to reduce poverty.
World Trade Organization:
Was established in the year 1995 in order to supervise international capital trade.

Bank PO Study Notes



Directions—(Q. 1–12) Read the following passage carefully and answer the questions given below it.Certain words have been printed in bold to help you locate them while answering some of the questions.

Keshava, the washerman had a donkey. They worked together all day, and Keshava would pour outhis heart to the doneky. One day, Keshava was walking home with the donkey when he felt tired. He tied the donkey to a tree and sat down to rest for a while, near a school. A window was open, and through it, a teacher could be heard scolding the students. ‘Here I am, trying to turn you donkeys into human beings, but you just won’t study !’ As soon as Keshava heard these words, his ears pricked up.

A man who could actually turn donkeys into humans ! This was the answer to his prayers. Impatiently, he waited for school to be over that day. when everyone had gone home, and only the teacher remained behind to check some papers, Keshava entered the classroom. ‘How can I help you ?’ asked the teacher. Keshava scratched his head and said, ‘I heard what you said to the children. This donkey is my companion. If you made it human, we could have such good times together.’ The teacher decided to trickKeshava. He pretended to think for a while and then said, ‘Give
me six months and it will cost you a thousand rupees.’ The washerman agreed and rushed home to get the money. He then left the donkey in the teacher’s care.
After the six months were up, Keshava went to the teacher. The teacher had been using the donkey for his own work. Not wanting to give it up, he said, ‘Oh, your donkey became so clever that it ran away. He is the headman of the next village.’ When Keshava reached the next village he found the village elders sitting under a tree, discussing serious problems. How surprised they were when Keshava marched up to the headman, grabbed his arm and said, ‘How dare you ? You think you are so clever that you ran away ? Come home at once !’

The headman understood someone had played a trick on Keshava. ‘I am not your donkey !’ he said. ‘Go find the sage in the forest.’ Keshava found the sage sitting under a tree with his eyes closed, deep in meditation. He crept up and grabbed the sage’s beard. ‘Come back home now !’ he shouted. The startled sage somehow calmed Keshava. When he heard what had happened, he had a good laugh. Then he told the washerman kindly, ‘The teacher made a fool of you. Your donkey must be still with him. Go and take it back from him. Try to make some real friends, who will talk with you
and share your troubles. A donkey will never be able to do that !’ Keshava returned home later that day with his donkey, sadder and wiser.

1. Which of the following can be said about the teacher ?
(A) He had the ability to transform animals into human beings
(B) He took advantage of Keshava’s simple nature
(C) He had plotted with the village headman to cheat Keshava
(D) He enjoyed teaching children though he was poorly paid
(E) He was honest and used Keshava’s money to care for the donkey
Ans : (B)

2. Why did Keshava talk to his donkey while working ?
(A) He wanted to practise his communication skills because he wanted to make friends
(B) To entertain himself because he found his work monotonous
(C) The donkey helped him to find answers to his problems
(D) He regarded the doneky as his friend and confided in him
(E) He believed the donkey to be a human being in disguise
Ans : (E)

3. How did Keshava get his donkey back ?
(A) He threatened to take the teacher to the village elders
(B) The sage forced the teacher to release the donkey
(C) He asked the village headman for help
(D) The teacher returned it on learning that Keshava had learnt his lesson
(E) None of these
Ans : (E)

4. Which of the following is NOT true in the context of the passage?
(a) The donkey was over burdened by the teacher.
(b) The teacher was cunning by nature.
(c) The sage laughed at Keshava and treated him unkindly.
(A) Both (a) & (c)
(B) Both (b) & (c)
(C) Only (b)
(D) All (a), (b) & (c)
(E) None of these
Ans : (A)

5. Why was Keshava keen to meet the teacher one day ?
(A) Keshava wanted to ask the teacher how to make his donkey a better companion
(B) He wanted to learn more prayers as he was devout
(C) He had been reliably informed that the teacher had changed donkeys into human beings
(D) He heeded the teacher’s words of advice and wanted to study
(E) None of these
Ans : (A)

6. Why did Keshava interrupt the discussion among the village elders ?
(A) He did not agree with their views on different issues
(B) To confront the headman who had cheated him out of one thousand rupees
(C) He wanted them to get justice for him
(D) He was looking for the donkey and wanted to ask for directions
(E) None of these
Ans : (E)

7. What made Keshava pull the sage’s beard ?
(A) He wanted to wake up the sage who was a sleep under the tree
(B) The headman requested him to move the sage from under the tree
(C) He wanted the sage to explain what had happened to the donkey
(D) He misunderstood the village headman and took the sage to be his donkey
(E) None of these
Ans : (D)

8. Why did the teacher ask Keshava to leave the donkey with him for six months ?
(a) He realised that the donkey would require a lot of training.
(b) To reduce Keshava’s dependence on the donkey.
(c) He wanted to rescue the donkey from Keshava who did not know to treat the donkey properly.
(A) None
(B) Only (b)
(C) Both (a) & (b)
(D) Only (c)
(E) None of these
Ans : (A)
What does Base rate mean?
It was in July last year that RBI made it mandatory for all the banks to move to the Base rate regime from BPLR {Benchmark prime lending rate}. So, what exactly is this base rate all about? And why is it so important that RBI made it compulsory for all banks to migrate to the base rate.

Firstly, let me explain what base rate is. To be short, it is the minimum rate below which the bank cant lend to any customer. Earlier, there was a similar rate called the BPLR {Benchmark Prime Lending Rate}, but most of the lending took place below this BPLR. Let me cite an example here, the base rate in SBI is 9.25% and the BPLR in SBI used to be 14%. During the pre-base rate period, banks usually lent out money at rates less than the BPLR. The prime reason for migrating to this base rate mechanism is the transparent lending mechanism. Earlier banks used to lend big companies at rates far less than they lend to an average customer. The base rate mechanism means that SBI can never lend below 9.25% {except for priority sectors like agriculture, govt sponsored schemes, etc} for any customer.

This base rate also results in better implementation of the economic policies. For example, if RBI hikes lending rates in order to contain inflation then the banks have no other go than to increase their base rates as well. At present the base rate of all the banks in India varies between 9% to 11%.
Know your customer- KYC?
KYC stands for “know your customerr” and this is one important policy followed by all the finance institutions in our country especially after the Sep 11th attack on the world trade center. During the pre-world trade center attacks era, the banks never insisted customers to submit their address or identity proofs for opening an account. All they needed was an introducer and some cash for opening the account. It is believed that the RBI had paid a hefty sum as fine for not providing the customer details of the certain transactions when asked by the FBI who were investigating on the September 11 attacks.

From then on RBI made it mandatory for the banks to collect the customer’s valid address and identification proofs before opening a bank account or investing in mutual fund or for doing anything related to banking activities. Usually banks accept ration cards as a proof of address. For proof of identity, banks usually accept voter id, passports, driving licenses and employee ID Cards.
What is financial inclusion?
Despite being the home to almost 1.3 billion people, less than 40% of the people in India come under the financial system in one way or the other. For example, if you hold an account with a bank or have borrowed money from a Micro Finance Institution then you will come under the financial system.

Bringing the entire population inside the financial system is the ultimate aim of our government as it will help in better implementation of economic policies which in turn plays an important role in overall economic growth of the country. Government is taking a lot of steps to achieve this target, with opening ‘No-Frills‘ account using Business correspondents being the numero Uno technique. Government is also encouraging banks to start a number of rural branches in order to bring more people from the rural areas into the financial system.
Term of the day: – Inflation
Most of us are familiar with the term I guess. In short, inflation can be termed as the Rise in price.
How is inflation measured?

Inflation can be measured using two methods

Cost price Index method (CPI)

Whole sale price Index method  (WPI)

In India inflation is measured using WPI method and critics term this measurement technique to be ineffective. Lets see in detailed about this CPI and WPI tomorrow.


Monday, June 4, 2012

EXAM PREPARATIONS BANK,MAT,CAT FREE MATERIAL


  • Quadrilateral

A quadrilateral is a polygon with four sides (edges) and four vertices (corners). The word quadrilateral is made of the words quad (meaning four) and lateral (meaning sides). So, quadrilateral is simply a four sided figure.
The sum of interior angles for all quadrilaterals must be equal to 360 degrees.

Types of Quadrilaterals

  1. Square
  2. Rectangle
  3. Parallelogram
  4. Rhombus
  5. Trapezoid
quadrilaterals

  • Quadrilateral: Square & Rectangle

Square: A square has four equal sides and four equal angles (90-degree angles or right angles).
square

Perimeter of Square

Perimeter of the square is 4 times the length of the side. For a square of length L, perimeter = 4 * L

Area of Square

Area of square is the square of length of the side. Area = L * L

Properties of Square

  • The diagonals of a square bisect each other and meet at right angles (90 degrees)
  • The diagonals of a square bisect its angles
  • The diagonals of a square are perpendicular
  • Opposite sides of a square are both parallel and equal in length
  • All four angles of a square are equal. (every angle of a square is a right angle)
  • The diagonals of a square are equal.
Rectangle: A rectangle is a quadrilateral with 4 right angles. It is similar to square except that its sides are not equal.
rectangle

Perimeter of Rectangle

Perimeter of the rectangle is sum of the length of its sides. Perimeter = 2 * (Length + Breadth)

Area of Rectangle

Area of rectangle is multiplication of its length and breadth. Area = Length * Breadth

Properties of Rectangle

  • All angles are right angles (90 degrees)
  • Opposite sides are parallel and equal.
  • Diagonals bisect each other.
  • Quadrilateral: Parallelogram
parallelogram is a quadrilateral with two pairs of parallel sides.
parallelogram

Properties of parallelogram

  • Each diagonal divides the quadrilateral into two congruent triangles with the same orientation.
  • The opposite sides are parallel and equal in length.
  • The diagonals bisect each other.
  • The opposite angles are equal in measure.
  • The sum of the squares of the sides equals the sum of the squares of the diagonals. (Parallelogram Law)
  • Adjacent angles are supplementary (180 degrees).
  • Square, Rectangle and Rhobus are special types of parallelograms.

Perimeter & Area of parallelogram

The perimeter of parallelogram is sum of the length of its sides. Perimeter = 2(L + B)
Area of parallelogram is multiplication of its longer side and distance between them. Area = L * H

Parallelogram Law

It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. If ABCD is parallelogram, then
2(AB)^2+2(BC)^2=(AC)^2+(BD)^2
In case of rectangle and square, this law reduces to pythagoras theorem.

  • Mensuration

Mensuration is the branch of mathematics which deals with the study of geometric shapes, their area, volume and different parameters in geometric objects.

Important Mensuration Formulae

1. Area of rectangle (A) = length(l) * Breath(b) A = l \times b
2. Perimeter of a rectangle (P) = 2 * (Length(l) + Breath(b)) P = 2 \times(l + b)
3. Area of a square (A) = Length (l) * Length (l) A = l \times l
4. Perimeter of a square (P) = 4 * Length (l) P = 4 \times l
5. Area of a parallelogram(A) = Length(l) * Height(h) A = l \times h
6. Perimeter of a parallelogram (P) = 2 * (length(l) + Breadth(b)) P = 2 \times (l + b)
7. Area of a triangle (A) = (Base(b) * Height(b)) / 2 A = \frac{1}{2} \times b \times h
Perimeter = (a + b + c)
Area of triangle = A = \sqrt{s(s-a)(s-b)(s-c)} [Hero’s formula]
8. Area of triangle (A) = \frac{1}{2} a \times b \times \angle C = \frac{1}{2} b \times c \times \angle A = \frac{1}{2} a \times c \times \angle B
9. Area of isosceles triangle = \frac{b}{4}\sqrt{4a^2 - b^2}
10. Area of trapezium (A) = \frac{1}{2} (a+b) \times h
11. Perimeter of a trapezium (P) = sum of all sides
12. Area of rhombus (A) =  Product of diagonals / 2
13. Perimeter of a rhombus (P) = 4 * length
14. Area of quadrilateral (A) = 1/2 * Diagonal * (Sum of offsets)
15.  Area of a Kite (A) = 1/2 * product of it’s diagonals
16. Perimeter of a Kite (A) = 2 * Sum on non-adjacent sides
17.  Area of a Circle (A) = \pi r^2 = \frac{\pi d^2}{4}
18. Circumference of a Circle = 2 \pi r = \pi d
19. Total surface area of cuboid = 2 (lb + bh + lh)
20. Total surface area of cuboid = 6 l^2
21. length of diagonal of cuboid = \sqrt{l^2+b^2+h^2}
22. length of diagonal of cube = \sqrt{3 l}
23. Volume of cuboid = l * b * h
24. Volume of cube = l * l * l
25. Area of base of a cone = \pi r^2
26.  Curved surface area of a cone = C = {tex inline}\pi r l{tex}
27. Total surface area of a cone = \pi r (r+l)
28. Volume of right circular cone = \frac{1}{3} \pi r^2 h
29. Surface area of triangular prism = (P * height) + (2 * area of triangle)
30. Surface area of polygonal prism = (Perimeter of base * height ) + (Polygonal base area * 2)
31. Lateral surface area of prism = Perimeter of base * height
32. Volume of  Triangular prism = Area of the triangular base * height
33. Curved surface area of  a cylinder = 2 \pi r h
34. Total surface area of a cylinder = 2 \pi r(r + h)
35. Volume of a cylinder = \pi r^2 h
36. Surface area of sphere = 4 \pi r^2 = \pi d^2
37. Volume of a sphere = \frac{4}{3} \pi r^3 = \frac{1}{6} \pi d^3
38. Volume of hollow cylinder = \pi r h(R^2-r^2)
39. Surface area of a right square pyramid = a \sqrt{4b^2 - a^2}
40. Volume of a right square pyramid = \frac{1}{2} \times base \, \, area \times height
41. Area of a regular hexagon = \frac{3\sqrt{3}a^2}{2}
42. area of equilateral triangle = \frac{\sqrt{3}}{4} a^2
43. Curved surface area of a Frustums = \pi h (r_1 + r_2)
44. Total surface area of a Frustums = \pi (r_1^2 + h(r_1+r_2) + r_2^2)
45. Curved surface area of a Hemisphere = 2 \pi r^2
46. Total surface area of a Hemisphere = 3 \pi r^2
47. Volume of a Hemisphere = \frac{2}{3} \pi r^3 = \frac{1}{12} \pi d^3
48. Area of sector of a circle = \frac{\theta r^2 \pi}{360}

  • Vedic Maths - Introduction

Vedic Mathematics is a system of mathematics consisting of a list of 16 basic sutras, or aphorisms. They were presented by a Hindu scholar and mathematician, Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century.
The calculation strategies provided by Vedic mathematics are said to be creative and useful, and can be applied in a number of ways to calculation methods in arithmetic and algebra.
16 Sutras translated in English (from Sanskrit) are:
  1. By one more than the one before
  2. All from 9 and the last from 10
  3. Vertically and Cross-wise
  4. Transpose and Apply
  5. If the Samuccaya is the Same it is Zero
  6. If One is in Ratio the Other is Zero
  7. By Addition and by Subtraction
  8. By the Completion or Non-Completion
  9. Differential Calculus
  10. By the Deficiency
  11. Specific and General
  12. The Remainders by the Last Digit
  13. The Ultimate and Twice the Penultimate
  14. By One Less than the One Before
  15. The Product of the Sums
  16. All the Multipliers
It is amazing that with the help of Vedic Mathematics, you will be able to solve or calculate complex mathematical problems mentally.

By one more than the previous one

1. Square of numbers ending in 5
65 x 65 = (6 x (6+1) ) 25 = (6x7) 25 = 4225
45 x 45 = (4 x (4+1) ) 25 = (4x5) 25 = 2025
105 x 105 = (10 x (10+1) 25 = (10 x 11) 25 = 11025
2. When sum of the last digits is the base(10) and previous parts are the same
44 x 46 = (4 x (4+1)) (4 x 6) = (4 x 5) (4 x 6) = 2024
37 x 33 = (3 x (3+1)) (7 x 3) = (3 x 4) (7 x 3) = 1221
11 x 19 = (1 x (1+1)) (1 x 9) = (1 x 2) (1 x 9) = 209

EXAM PREPARATIONS BANK,MAT,CAT FREE MATERIAL


  • Progressions

A Progression is a sequence of numbers which have some kinf of relation. This relation determines what kind of a progression is. Generally, there are two types of progressions:
  1. Arithmetic Progression (AP)
  2. Geometric Progression (GP)
Any progression (AP or GP) can be generally expressed as
a_1 + a_2 + a_3 +\dots+ a_{n-1} + a_n
Total Terms: n
First Term: a_1
Last Term: a_n

    Arithmetic Progression

    In AP, the relation amoung sequence of numbers is that the difference between any two successive numbers is same.
    Example: 3, 5, 7, 9, 11, 13, ... is an AP with difference 2. This difference is called common difference.
    a_n = a_1 + (n - 1)d
    S_n=\frac{n}{2}( a_1 + a_n)=\frac{n}{2}[ 2a_1 + (n-1)d]

    Geometric Progression

    In GP, each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. 
    Example: 2, 6, 18, 54, ...
    a + ar + ar^2 + ar^3 + ar^4 + \cdots
    a_n = a\,r^{n-1}

    • Functions

    A function is a rule which indicates an operation to perform.

    Graph Transformations

    1. y = f(x) + a is the same as the graph y = f(x), shifted upwards by a units.
    2. y = f(x - a) shifts the graph a units to the right.
    3. y = f(ax) is a stretch with scale factor 1/a parallel to the x-axis.
    4. y = a.f(x) is a stretch with scale factor a parallel to the y-axis.

    • Binomial Theorem

    Binomial Expression: An algebraic expression consisting of two terms with a positive or negative sign between themExample: (x+y)
    The expansion of binomial expression raised to power n is called Binomial Theorem.
    {(x + y)^n = x^n + ^nC_1x^{n-1}y + ^nC_2x^{n-2}y^2 + \dots + y^n}
    ^nC_1, ^nC_2, \dots , ^nC_n are Binomial Coefficients.
    Points to Note:
    1. There are total of (n+1) terms in the expansion.
    2. In each term, sum of the indices of x and y is equal to n.

    • Indices and Surds

    Laws of Indices

    a^m \times a^n = a^{m+n}
    a^m \div a^n = a^{m-n}
    (a^m)^n = a^{mn}
    a^{1 \over m} = \sqrt[m]{a}
    a^{-m} = \frac{1}{a^m}
    a^{\frac{m}{n}} = \sqrt[n]a^m
    a^0 = 1
    a^1 = 1

    • Logarithms

    Logarithmic Identities

    1. \log_b(xy) = \log_b(x) + \log_b(y)
    2. \log_b\!\left(\begin{matrix}\frac{x}{y}\end{matrix}\right) = \log_b(x) - \log_b(y)
    3. \log_b(x^d) = d \log_b(x)
    4. \log_b\!\left(\!\sqrt[y]{x}\right) = \begin{matrix}\frac{\log_b(x)}{y}\end{matrix}
    5. x^{\log_b(y)} = y^{\log_b(x)}
    6. c\log_b(x)+d\log_b(y) = \log_b(x^c y^d)
    7. \log_b(1) = 0
    1. \log_b(b) = 1
    2. b^{\log_b(x)} = x
    3. \log_b(b^x) = x
    4. \log_a b = {\log_c b \over \log_c a}

     

    • Permutation & Combination

     Combination & Permutation deals with arrangement of thing. If the order doesn't matter, then it is called Combination. If the order does matter, then it is a Permutation.
    In other words, Permutation is an ordered Combination.

    Permutation 

    {^nP_r} = {n! \over {(n-r)!}
    There are basically two types of permutation:
    1. When repetition is allowed
    2. No repetition
    1. Permutations with Repetition
    To choose r things from n when repetition is allowed, the permutations are:
    n × n × ... (r times) = nr
    (Because there are n possibilities for the first choice, then there are n possibilites for the second choice, and so on.)

    Combinations

    Number of ways objects can be selected from a group.
    {^nC_r} = {{^nP_r} \over r!}

    • Probability

    Probability is the likelihood or chance of an event occurring.
    Some Concepts
    • When we toss a coin, then either a Head (H) or a Tail (T) appears.
    • A dice is a solid cube ,having 6 faces,marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.
    • A pack of cards has 52 cards. It has 13 cards of each suit, namely spades, clubs, hearts and diamonds. Cards of spades and clubs are balck cards. Cards of hearts and diamonds are red cards. There are four honours of each suit. These are Aces, Kings, Queens and Jacks. These are called Face cards.
    The probability of a certain event occurring can be represented by P(A). The probability of a different event occurring can be written as P(B). Therefore, for two events A and B,
    \displaystyle P(A) + P(B) - P(A\cap B) = P(A\cup B)

    Mutually Exclusive Events

    Events A and B are mutually exclusive if they have no events in common. If two events are mutually exclusive,
    \displaystyle P(A) + P(B) = P(A\cup B)

    Independent Events

    Two events are independent if (and only if)
    \displaystyle P(A\cap B) = P(A)P(B)

    Conditional Probability

    Conditional probability is the probability of an event occurring, given that another event has occurred.
    \displaystyle P(A|B) means the probability of A occurring, given that B has occurred.
    For two events A and B,
    \displaystyle P(A\cap B) = P(A|B)P(B)
    \displaystyle P(A\cap B) = P(B|A)P(A)
    Triangles

    1. Sum of the angles of a triangle is 180 degrees.
    2. The sum of any two sides of a triangle is greater than third side.
    3. Pythagoras Theorem: In a right angled triangle (Hypotenuse)2 = (Base)2 + (Height)2
    4. The line joining the mid point of a side of a triangle to the opposite vertex is called the Median.
    5. The point where the three medians of a triangle meet, is called Centroid. The centroid divides each of the medians in the ratio 2:1.
    6. In an isosceles triangle, the altitude from the vertex bisects the base.
    7. The median of a triangle divides it into two triangles of the same area.
    8. The area of the triangle formed by joining the mid points of the sides of a given triangle is one-fourth of the area of the given triangle.
    Similar Triangles
    If the angles of one triangle are equal to the angles of another triangle, then the triangles are said to beEquiangular. Equiangular triangles have the same shape but may have different sizes. Therefore, equiangular triangles are also called Similar Triangles.
    Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional.
    similar_triangle

    {AB \over DE} = {BC \over EF} = {CA \over FD}
    \angle A = \angle D
    \angle B = \angle E
    \angle C = \angle F
    Properties
    1. The ratio of area of similar triangles is equal to the square of ratio of sides.
    2. If the ratio of corresponding sides equals to 1, then triangles become congruent.


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