THIS ARTICLE IS FOR THE STUDENTS WHO ARE IN LAST MINUTE PREPARATION.

It is very difficult to mention important questions in mathematics. Because the direct questions what everybody list as important questions in other subjects will not appear in mathematics.

But patron of the questions will be same as in previous year question papers. practicing problems of previous year questions is enough to prepare for Mathematics.

If u are selecting, complete the following areas:

**ALGEBRA**

**Matrices and determinants: **

a)Solving the simultaneous equation by cramer’s rule and matrix method

b)Statement of cayley Hamilton theorem and finding inverse of matrix and verifying cayley Hamilton theorem

**Vectors**

a)Application of vectors like: proving sine rule, projection rule, cosine rule, compound angle formulae, angle in a semicircle is right angle by vector method

b)Problems on scalar triple product and vector triple product.(standard problems)

c)Find the projection of one vector to another vector , find the sine or cosine of angle between the vectors, unit vector in the direction of vector,

**Groups**

a)Proving a particular set forms an abelian group like Show that a*b=a+b-ab forms an abelian group, Show that G={5^n, (integral multiples of 5) } forms an abelian group etc refer topic wise questions in mathematics in this website.

**Elements of Number theory :**

**a)F**inding GCD of two numbers and representing them as a linear combination of x and y and showing x and y is not unique

b)Find the number and sum of divisors

c)Finding the last digit or unit digit, solving linear congruence.

**TRIGONOMETRY**

** **

**INVERSE TRIGONOMETRIC FUNCTIONS:**

a)problems on use of formula tan^-1 x + tan^1 y= tan^1(x+y/1-xy) etc

**GENEREAL SOLUTION OF TRIGONOMETRIC EQUATION**

a)GS of trignometric equation of the form acosx+bsinx=c

b)GS by using FORMULA OF CONVERTING sum of trigonometric functions into product or product into sum

C**OMPLEX NUMBERS**

a)State and prove Demoivre’s theorem

b)problems on this, see topic wise questions in this website.

**CIRCLES**

a)all derivations: equation of tangent, condition of orthogonality, finding length of tangent, condition for the line y=mx+c to be tangent to to circle x^2+y^2 =a^2

b)problems on orthoganal circles, and finding equation of circle by finding g, f and c using conditions in the given problem.

**CONIC SECTION:**

a) all derivations: Derivation of parabola, ellipse and Hyperbola

b)problems on finding centre , focus, directrix and ends of Latus rectum of parabola , ellipse and Hyperbola,

c)Definition of rectangular hyperbola, director circle, auxilary circle and its equations

**DIFFERENTIATION:**

a)problems on differentiation from first principles: no need to solve differentiation of inverse trigonometric function by first principles and some problems like root sinx, sinrootx etc.

b)problem on successive differentiation, logarithmic differentiation , parametric differentiation

implicit differentiation (refer topic wise questions- it contains limited number of questions).

**APPLICATION OF DERIVATIVES**

a)Problems on Derivative as a rate measure, problems on finding maxima and minima involving 2 dimensions figure only( Don’t go for problems on finding maxima and minima involving figures like , sphere, cylinder, etc)

b)Angle of intersection between two curves: like: If ax^2+by^2=1 and Ax^2+By^2=1 cut each other orthogonally , show that 1/a-1/b=1/A-1/B

I**NDEFINITE INTEGRAL:**

a)problems on forms of integral, all types

**DEFINITE INTEGRAL**

Proving some properties of definite integral, and problems using definite integral.

**AREA UNDER A CURVE**

See topic wise questions in this website.

**DIFFERENTIAL EQUATION**

a)Finding order and degree of Differential equation.

b)Solving Differential equations by variable separable method (see topic wise questions)

**At last:**

Finding GCD of two numbers, and representing them as linear combination or finding sum and number of divisors 5 MARKS

Solving simultaneous linear equations by matrix method, cramer’s rule, finding inverse and verifying matrix by using cayley Hamilton theorem. 5 marks

Groups : Showing a set forms a group : 5 marks

**Definition of ellipse , hyperbola, parabola as a locus and Derivation of parabola, ellipse , hyperbola in standard form in conic section ** (Important) or all derivations in conic section like condition for the line y =mx+c to be tangent to parabola, ellipse, hyperbola including problem etc 6 marks

Problems on differentiation from first principles: 3 marks

Complex numbers: problems on demovires theorem

and its proof : 6 marks

Vectors: Application of vectors or problems 4 marks

Problems on Derivative as a rate measure , angle of intersection between two curves, maximal and minima (application of derivative problems) : 6 marks

Finding Area under a curve 5 marks

Proving some important properties of Definite integral and problem on this 6 marks

And so on……………………………………………………………………..

Count the marks you will get more than 35 marks

So it is easy to prepare for mathematics examination .

Excuse for spelling and grammatical mistakes

so

BEST OF LUCK .

FROM

VASUDEVA KH

VYBHAV G.R.