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Physics Class 11 > Mathematical Tool > Flashcards

Mathematical Tool Flashcards

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1
Q

What is a function?

A

Relationship between 2 variables - dependent and independent [y = f(x)]

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2
Q

Domain and range ?

A

In [y = f(x)] All possible of x - domain, all possible value of y - range

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3
Q

In a linear function,f(x) = mx + c, slope and y intercept?

A

M = tan (theta) = slope , c - y intercept

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4
Q

X radian how many degrees?

A

X radian = 180/pi * x

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5
Q

X degrees = how many radians

A

X degrees = pi/180 * x radians

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6
Q

Sin 37, cos37 , tan37

A

3/5 , 4/5 , 3/4

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7
Q

Sin 53, cos 53, tan 53 ?

A

4/5 , 3/5, 4/3

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8
Q

C A S T rule

A

Revise from copy [NOW]

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9
Q

Sin(A+B)

A

SinA cosB +Cos A. Sin B

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10
Q

Sin (A-B)

A

Sin A cos B - Cos A sin B

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11
Q

Cos (A+B)

A

Cos A Cos B - sin A sin B

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12
Q

Cos (A - B)

A

Cos A Cos b + Sin A sin B

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13
Q

Tan (a+b)

A

tan a + tan B / 1- tan A tan B

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14
Q

Tan (a-b)

A

Tan A - tan B/ 1+tan A tan B

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15
Q

sin 2ø

A

2 Cosø sinø

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16
Q

cos 2ø

A

2 cos^2 ø - 1

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17
Q

cos ^ 2 ø =

A

1+cos 2ø/2

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18
Q

sin ^2 ø =

A

1-cos 2ø/2

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19
Q

f(ø) = A sinø + B cosø, then (f)max = ?

A

√a^2 + b^2

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20
Q

sine law? (side A opp to angle 1, side b opp to angle 2, side c = angle 3)

A

a/sin1 = b/sin2 = c/sin3

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21
Q

when ø is small then ø ≈ ?

A

ø ≈ tan ø ≈ sin ø

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22
Q

differentiation of y wrt x =

A

Lim ∆x –> 0 ∆y/∆x = dy/dx

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23
Q

secant in a curve is?

A

line joining any two points on a curve

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24
Q

tangent on a curve is ?

A

line just touching the curve, is a secant joining any nearby points.

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25
Q

y = 5, dy/dx = ?

A

0

26
Q

y = mx, dy/dx = ?

A

m

27
Q

y = x^n , dy/dx = ?

A

nx ^ n-1

28
Q

d/dx(c x f(x)) = ?

A

C x d(f(x))/dx

29
Q

d/dx(sinx) = ?

A

cos x

30
Q

d/dx(cosx) = ?

A

-sinx

31
Q

d/dx(e^x)

A

e^x

32
Q

d/dx(lnx) = ?

A

1/x

33
Q

d/dx[f(x) ± g(x)] = ?

A

d/dx(f(x)) ± d/dx(g(x))

34
Q

(uv)’

multiplication rule?

A

u’v + v’u

read from copy

35
Q

Trick f(x) = a , g(x) = b, u(x) = c
[a * b * c]’

from copy before quotient rule

A

a’ * b * c + a * b’ * c + a * b * c’

first differentiation of a, then b, then c

36
Q

quotient rule

(u/v)’ = ?

A

vu’ - uv’/ v^2

read from notes

37
Q

d/dx(tanx) = ?

A

sec^2 x

38
Q

d/dx(cotx) = ?

A

-cosec^2 x

39
Q

d/dx(secx) = ?

A

tan x . sec x

40
Q

d/dx(cosecx) = ?

A
  • cot x cosec x
41
Q

chain rule

A

copy revision

42
Q

dy^2/dx = ?

A

2y . dy/dx

43
Q

dy^5 /dx = ?

A

5y^4 dy/dx

44
Q

steps for point of maxima?

A

dy/dx = 0, d^2/dy = (-ve)

revise graph from copy

45
Q

steps for point of minima?

A

dy/dx = 0, d^y/dx^2 = (+ve)

revise graph from copy

46
Q

∫x^n dx = ?

A

x^n+1/n+1 + c

47
Q

∫1/x dx = ?

A

lnx + c

48
Q

∫sinx dx = ?

A

-cos x + c

49
Q

∫cosx dx = ?

A

sinx + c

50
Q

∫sec^2 x dx

A

tan x + c

51
Q

∫tanx secx dx = ?

A

secx + c

52
Q

∫ cot x cosec x = ?

A

-cosecx + c

53
Q

∫cosec ^2 x dx = ?

A

-cot x + c

54
Q

∫e^x dx = ?

A

e^x + c

55
Q

∫lnx dx = ?

A

xlnx -x

56
Q

∫ a^x dx = ?

A

a^x / lna

57
Q

∫ {f(x) ± g(x)} dx = ?

addition rule

A

∫f(x) dx ± ∫g(x) dx

58
Q

integration by substitution

A

read in copy

59
Q

some more formulas

after substitution (there are so many)

A

read in copy

60
Q

definite integration and average

A

read in copy

Physics Class 11 (1 decks)

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