Maths : Tips & Tricks

Some Critical Tips :
 * 1) If certain conditions are given, look for the options that satisfy the condition.
 * 2) If an equation is asked then substitute the values in the option in the equation.
 * 3) Use Trial and Error Method / Elimination method.
 * 4) For co-ordinate geometry, draw graphs according to equations given and predict the answer.
 * 5) The first step in Mathematics is mostly crucial and may require Simplification . Here are techniques of SImplifications that you should try : 1. Rationalizing 2. Plus & Minus 3. Multiplying and Dividing 4. Dividing Throughout by 5.Splitting the Numerator 6. Squaring on Both Sides.

Sets, Relations and Functions
1) For functions, try to plot graphs . So learn more different kinds of functions and their graphs , or else derive the graph using x-y method.

2) For Set theory draw venn diagrams for better understanding of the question.

Theory of Equations

 * 1) For Analyzing an equation, remember :
 * 2) If ∆ = 0 ; then there will be infinite solutions if  ∆x,∆y,∆z = 0 . And there will b no solution otherwise.
 * 3) If ∆ =/= 0 ; then there will be an unique solution.
 * 4) If ∆ = 0 ; then equations will have nontrivial solution
 * 5) For an equation to have  no solution, the ratios of co-efficients of x , y and constant will be equal to each other.
 * 6) A Monotonic Function (Increasing/Decreasing) has only one root.

Complex Numbers

 * 1) In order to get rid of i term, you can rationalize the question to convert i into i2 . Prefer to reach i2 .
 * 2) Use Geometrical interpretation of Complex Numbers along with De Moivre's Theorem for solving geometry based questions.

Sequences and Series

 * 1) For Infinite Series, first find the equation of the series in general terms . Then use the Sum of /infite Series Formulae.
 * 2) For AP, GP and HP ; trying out the 4 options can be helpful.

Trigonometry

 * 1) For General Solution, bring the equation in one of the sandard forms . This can be done by using factorization formulae (i.e. to convert from addition to multiplication).
 * 2) For Solutions of Triangle problems, the following techniques should be used :
 * 3) sin
 * 4) a2, b2,c2
 * 5) A  + B + C = 180
 * 6) Half Angle
 * 7) Factorization formulae

Circle & Conics

 * 1) Draw a graph with the help of given equations, to predict the answer.

Limits

 * 1) If the Question is of the form 0/0, then apply L' Hospitals Rule.

Differentiation and Application

 * 1) For Implicit, use shortcut.

Integral Calculus and Area under Curve

 * 1) For Indefinite Integration ; Differentiate the options to reach the Question.
 * 2) For u.v ; use the shortcut

Matrices

 * 1) Do Adjoint first or transpose/square/other operation first, the answer is same.
 * 2) Try to use the options for finding the answer, rather than solving the entire sum.
 * 3) Use properties of determinants to simplify a given matrix.

3 Dimensional Geometry

 * 1) In formulas dealing with ratios (e.g. cartesian equation of line, condition for parallel and perpendicular lines) direction ratios can be replaced with direction cosines.