Here areĀ Mathematics revision sheet for class 11 and class 12 physics

**Differentiation**

We have two quantities x and y such that where is some function of x.We may be interested in finding followings things

1.

2. Maximum and Minimum values of y.It can be find with the method of Maxima and Minima

is the called the derivative of y w.r.t to x

It is defined as

Some commonly known functions and their derivatives are:-

Some important and useful rules for finding derivatives of composite functions

1. where c is constant

2. where a and b are function of x

3.

4.

5.

6.

**Maximum and Minimum values of y**

**Step 1:**

fine the derivative of y w.r.t x

**Step2:**

Equate

Solve the equation to find out the values of x

**Step3:**

find the second derivative of y w.r.t x and calculate the values of

for the values of x from step2

if then the value of x corresponds to mimina of y then can be find out by putting this value of x

if then the value of x corresponds to maxima of y then can be find out by putting this value of x

**Integration**

It reads as integration of function f(x) w.r.t. x within the limits from x=a to x=b.

Integration of some important functions are

Useful rules for integration are

**Trigonometry**

Properties of trigonometric functions

**1. Pythagorean identity**

**2. Periodic function**

**3.Even-Odd Identities**

**4. Quotient identities**

**5. Co-function identities**

**6. Sum difference formulas**

**7. Double angle formulas**

**8. Product to sum formulas**

**9. Power reducing formulas**

*10. reciprocal identities*

**Binomial Theorem**

From the binomial formula, if we let a = 1 and b = x, we can also obtain the binomial series which is valid for any real number n if |x| < 1.

(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+………..

**Geometric Series**

where q is not equal to 0, q is the common ratio and a is a scale factor.Formula for the sum of the first n numbers of geometric progression

**Infinite geometric series where |q| < 1**

If |q| < 1 then , when n -> infinity So the sum S of such a infinite geometric progression is:

which is valid only for |x|

**Arithmetic Progression**

The sum S of the first n values of a finite sequence is given by the formula:

**Quadratic Formul**a

then

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Mathematics revision sheet for class 11 and class 12 physics part 2 (48.0 KiB)

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