Classes

Mathematical Tools for Class XI

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

1. Substitution method
2. Cross multiplication method
3. 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

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      x2 + 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

⇒ x2 + 6x + 8 = 0
⇒  x2 + 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 2x2 + 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

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

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  