SSC CGL 2014 praparation

Algebra,Trigonometry and Number systems are very important part of SSC CGL Math Section. In recent paper of SSC  conventional questions from ratio-proportion, basic maths, time-speed-work are asked for namesake only.Students preparing for SSC often face difficulties while solving the problems on Algebra,Trigonometry and Number systems.Earlier, they used to ask mostly area-volume-perimeter type questions from Geometry segment. You just had to plug-in values into the formulas and get the answer. So You Need To prepare these topics before exam. Merely knowing the concepts or formulas won’t help. Because unless you practice different variety of questions, you won’t become proficient in applying those concepts flawlessly in the actual-exam. 
If you have already prepared for any competitive exam, then you can directly start your preparation. I mean you can directly start picking topics, learning and practicing them according to your schedule. But if you are new to this competitive exam world, then you need some warm up sessions before starting your actual practice. For 4 to 7 days, you should spend memorizing basic Math Tables, Formulas, Squares and Cubes upto 15, Place Values of Alphabets, Synonyms and Antonyms lists. Once you are comfortable with these topics, you can go for the actual practice. Basically Algebra problem divided into two parts
  1. Linear equation
  2. Quadratic equations, Polynomials 
You can view TIME and SPEED problem and Percentage shortcut in older post.  In this post I try to solve  linear equation by tricks and shortcut. In linear algebra question asked in word like
  1. Lukas was 50 years old when his grand daughter was born. Now he is 2 years more than 4 times his grand daughter's age. How old is his grand daughter?
  2. Kevin is 31 years younger than Monique. 2 years ago, Monique's age was 2 times Kevin's age. How old is Kevin now?
  3. What is the sum of the multiples of 7 from 14 to 700, inclusive?
You can solve this type of question very easily. Just follow these step
  • Read the question. In any Math problem, there is a paramount need to read the question carefully, from beginning to end.
    •    List information and the variables you identify Attach units of measure to the variables (gallons, miles, inches, etc.)
  • Set up easily solvable equations. After reading the question you should be able to translate all the given data into mathematical equations.
  • Think of useful shortcuts. Any formula or procedure that could shorten the solution is a shortcut. 
  • Simplify and factor as much as possible. Simplifying fractions into lowest terms and rationalizing radical expressions can make your numbers on paper more organized and easier to handle arithmetically.
Now its time to salve a question lets take an example.

The ratio of the present ages of Anju and Sandhya is 13:17 respectively. Four years ago the ratio of their respective ages was 11:15. What will be the respective ratio of their ages six years

Let the present ages of Anju and Sandhya be 13x and 17x years respectively. 
   
   ∴         3x-4⁄17x-4 =11⁄15 
            =>      187x-44=195x-60
            =>      195x-187x=60-40
            =>      x=2
            ∴       Required ratio= (13×2+6):(17×2+6)
            =4:5

Basic Formula

a^2-b^2 = (a+b)\times (a-b)
a^2+b^2 = (a+b)^2-2ab=(a-b)^2+2ab
(a+b)^2 = a^2+2ab+b^2 = (a-b)^2+4ab
(a-b)^2 = a^2-2ab+b^2 = (a+b)^2-4ab
a^3+b^3 = (a+b) \times (a^2-ab+b^2) = (a+b)^3-3ab \times (a+b)
a^3-b^3 = (a-b) \times (a^2+ab+b^2) = (a-b)^3+3ab \times (a-b)
(a+b)^3 = a^3+3a^2b+3ab^2+b^3 = a^3+b^3+3ab \times (a+b)
(a-b)^3 = a^3-3a^2b+3ab^2-b^3 = a^3-b^3-3ab \times (a+b)
(x+a) \times (x+b) = x^2+x \times (a+b)+ab
(x-a) \times (x+b) = x^2+x \times (b-a)-ab
(x-a) \times (x-b) = x^2-x \times (a+b)+ab
(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ac
(a+b+c)^3 = a^3+b^3+c^3+3(a+b)(b+c)(c+a)
a^4-b^4 = (a-b) \times (a+b) \times (a^2+b^2)
a^6-b^6 = (a+b) \times (a^2-ab+b^2) \times (a-b) \times (a^2+ab+b^2)
a^6+b^6 = (a^2+b^2) \times (a^4-a^2b^2+b^4)
a^4+a^2b^2+b^4 = (a^2-ab+b^2) \times (a^2+ab+b^2)
(a-b-c)^2 = a^2+b^2+c^2-2ab+2bc-2ac
a^3+b^3+c^3-3abc = (a+b+c) \times (a^2+b^2+c^2-ab-bc-ac)

Indices Formulas:

The formulas involving relations between variables and their powers or powers and indices are:
x^m \times x^n = x^{m+n}
and
x^m \times x^n \times \ldots \times x^p = x^{m+n+ \ldots +p}
x^m \div x^n = x^{m-n}
and
x^m \div x^n \div \ldots \div x^p = x^{m-n- \ldots -p}
(x^m)^n = x^{m \times n}
and
((x^m)^n)^o) = x^{m \times n \times o}
x^0 = 1
x^{-m} = \dfrac{1}{x^m}
and
x^{m} = \dfrac{1}{x^{-m}}
x^{\frac{m}{n}} = \sqrt[n]{x^m}

\left( \dfrac{x^a}{y^b} \right)^c = \dfrac{x^{ac}}{y^{bc}}

\dfrac{x^m}{y^m} = \left( \dfrac{x}{y} \right)^m

\sqrt[m]{\dfrac{x^a}{y^b}} = \dfrac{x^{\frac{a}{m}}}{y^{\frac{b}{m}}}

x^{\frac{p}{q}} = \sqrt[q]{x^p} = \left(\sqrt[q]{x}\right)^p

\sqrt[m]{\dfrac{x}{y}} = \dfrac{\sqrt[m]{x}}{\sqrt[m]{y}}

\sqrt{a} \times \sqrt {b} = \sqrt{a \times b}    provided that a , b and a*b are not negative numbers.

If, a^x = a^y then , x=y. ( Provided That : 0 < a\text{ and }a \ne 1 )

If, a^x = b^x then , a=b.  ( Provided That : 0 < a , b \text{ and }a , b \ne 1 



Degree of a Polynomial

The exponent of the highest degree term in a polynomial is known as its degree.

Linear Polynomial

A polynomial of degree one is called a linear polynomials. In general f(x) = ax + b, where a ¹ 0 is a linear polynomial.

Quadratic Polynomials

A polynomial of degree two is called a quadratic polynomials. In general f(x) = ax2 + bx + c, where a ¹ 0 is a quadratic polynomial.

Cubic Polynomial

A polynomial of degree 3 is called a cubic polynomial in general.

f(x) = ax3 + bx3 + cx + d, a ¹ 0 is a cubic polynomial.

Biquadratic Polynomial

A fourth degree polynomial is called a biquadratic polynomial in general.

f(x) = ax4 + bx3 + cx2 + dx + e, a ¹ 0 is a bi quadratic polynomial.

Zero of a Polynomial

A real number a is a zero (or root) of a polynomial f(x), if f (a) = 0

Remainder Theorem

Let f(x) be a polynomial of a degree greater than or equal to one and a be any real number, if f(x) is divisible by (x – a), then the remainder is equal to f(a) .

Factor Theorem

Let f(x) be a polynomial of degree greater than or equal to one and a be any real number such that f(a) = 0, then (x – a) is a factor of f(x).

Conversely, if (x – a) is a factor of f(x), then f(a) = 0.

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