### Class XII

#### Science Stream

##### Physics

##### Chemestry

##### Mathematics

##### Computer Science

##### English

##### Biology

#### Commerce Stream

##### Accountancy

##### Business Studies

##### Entrepreneurship

##### Economics

##### English

##### Informatics Prac

##### Banking

#### Art Stream

##### Geography

##### Mass Media Studies

##### Political Science

##### Economics

##### English

##### History

##### Psycology

##### Legal Studies

### Class XI

#### Science Stream

##### Physics

###### Basic Mathematics Required To Solve Physics

###### Algebra

## Mathematical Tools for Class XI

### Chapter 1

### Algebra

__Linear equations in two variables__

Algebra is essential for solving physics numerical problems . You have to learn basic algebra question which you already learn your previous classes i.e Class IX and X. Let us recall them

Solving the equations

For e.g

2x + 3y = 15 ——————- (eq 1)

5x + 2y = 10 ———————( eq 2)

Three ways to solve above question

- Substitution method
- Cross multiplication method
- Elimination method

In order to solve above question easily , I suggest you to choose elimination method

(2x + 3y = 15 )x 5 (5x + 2y = 10 )x 2 10x + 15y = 75 10x + 4y = 20 (-) (-)

11y = ∴ y = 5 Putting value of y in eq 1 or you can choose eq 2 it's your choice 2x + 3(5)= 15 On solving we will get X = 0

### Quadratic equations

Please try to use splitting the middle term method to solve quadratic equations because quadratic formula will take your more valuable time

For e.g x^{2} + 6x + 8 = 0

Now above equation factor of 8 is (8,1) and (4,2) also coefficient of x is 6 which can be obtaned by factor (4,2) i.e 6x = 4x +2x

⇒ x^{2} + 6x + 8 = 0

⇒ x^{2} + 4x+2x + 8 = 0

⇒ x(x +4) +2(x+4) = 0

⇒ (x+4)(x+2) = 0

x = -4 and -2

If splitting the middle term is not applied in any equation then quadratic formula is best option

For e.g

If the equation is 2x^{2} + 5x – 12 = 0 we cannot easily break it into splitting the middle term than use quadratic formula . Note that we can also use

splitting the middle term but for that you to use logically . In order to save time let us use quadratic equation

Using quadratic eq

** a = 2 ( coefficient of x2 )**

** b = 5 ( coefficient of x )**

** c = -12 ( constant term of equation)**

On Solving we

x = 3/2 , -4

Some book will ask you binomial theorem or permutation and combination but for class 11th or 12th physics , this topic are not essential so don’t

worry about them . Please try to solve question of basic algebra of class IX and X in your summer vacation that is essential for physics

###### Trigonometry

### Chapter 2

### Trigonometry

You should learn only basic trigonometric formulas as shown in below

Other most important formulas are as under for class XI and XII CBSE Physics

###### Differentiation

### Chapter 3

### Differentiation

You will learn about differentiation in details in class XII . You will learn basic differentiation in class XI mathematics but for physics you have to remember following formulas . Don’t worry about proof of formula because proof of these formulas you will learn in mathematics .

For example You learn use or application of pythagoras formula in class VII or VIII standard but proof of that formula is given in Class X.

**What is use of differentiation in physics or you can say application of differentiation in physics **

Since differentiation is rate of change of quantity with respect to another quantity is called derivative and the process of finding derivative is called **differentiation . **So while studying motion of object with respect to earth or another body you have to know differentiation . Also differentiation is used while finding object any any point at that instant of time . Not only in motion application of differentiation is also gravitation forces , electrostatic and magnetic particle and electricity etc . So don’t worry about this chapter because differentiation is quite easy to learn and in mathematics we will learn more about this in easiest way

Also these formulas are easy to remember . Blue colored formulae are most important formulas or backbone of differentiation formulae