Mathematical Tool

Question 1

What is a function?

Answer 1

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

Question 2

Domain and range ?

Answer 2

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

Question 3

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

Answer 3

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

Question 4

X radian how many degrees?

Answer 4

X radian = 180/pi * x

Question 5

X degrees = how many radians

Answer 5

X degrees = pi/180 * x radians

Question 6

Sin 37, cos37 , tan37

Answer 6

3/5 , 4/5 , 3/4

Question 7

Sin 53, cos 53, tan 53 ?

Answer 7

4/5 , 3/5, 4/3

Question 8

C A S T rule

Answer 8

Revise from copy [NOW]

Question 9

Sin(A+B)

Answer 9

SinA cosB +Cos A. Sin B

Question 10

Sin (A-B)

Answer 10

Sin A cos B - Cos A sin B

Question 11

Cos (A+B)

Answer 11

Cos A Cos B - sin A sin B

Question 12

Cos (A - B)

Answer 12

Cos A Cos b + Sin A sin B

Question 13

Tan (a+b)

Answer 13

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

Question 14

Tan (a-b)

Answer 14

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

Question 15

sin 2ø

Answer 15

2 Cosø sinø

Question 16

cos 2ø

Answer 16

2 cos^2 ø - 1

Question 17

cos ^ 2 ø =

Answer 17

1+cos 2ø/2

Question 18

sin ^2 ø =

Answer 18

1-cos 2ø/2

Question 19

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

Answer 19

√a^2 + b^2

Question 20

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

Answer 20

a/sin1 = b/sin2 = c/sin3

Question 21

when ø is small then ø ≈ ?

Answer 21

ø ≈ tan ø ≈ sin ø

Question 22

differentiation of y wrt x =

Answer 22

Lim ∆x –> 0 ∆y/∆x = dy/dx

Question 23

secant in a curve is?

Answer 23

line joining any two points on a curve

Question 24

tangent on a curve is ?

Answer 24

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

Question 25

y = 5, dy/dx = ?

Answer 25

0

Question 26

y = mx, dy/dx = ?

Answer 26

m

Question 27

y = x^n , dy/dx = ?

Answer 27

nx ^ n-1

Question 28

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

Answer 28

C x d(f(x))/dx

Question 29

d/dx(sinx) = ?

Answer 29

cos x

Question 30

d/dx(cosx) = ?

Answer 30

-sinx

Question 31

d/dx(e^x)

Answer 31

e^x

Question 32

d/dx(lnx) = ?

Answer 32

1/x

Question 33

d/dx[f(x) ± g(x)] = ?

Answer 33

d/dx(f(x)) ± d/dx(g(x))

Question 34

(uv)’

multiplication rule?

Answer 34

u’v + v’u

read from copy

Question 35

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

from copy before quotient rule

Answer 35

a’ * b * c + a * b’ * c + a * b * c’

first differentiation of a, then b, then c

Question 36

quotient rule

(u/v)’ = ?

Answer 36

vu’ - uv’/ v^2

read from notes

Question 37

d/dx(tanx) = ?

Answer 37

sec^2 x

Question 38

d/dx(cotx) = ?

Answer 38

-cosec^2 x

Question 39

d/dx(secx) = ?

Answer 39

tan x . sec x

Question 40

d/dx(cosecx) = ?

Answer 40

• cot x cosec x

Question 41

chain rule

Answer 41

copy revision

Question 42

dy^2/dx = ?

Answer 42

2y . dy/dx

Question 43

dy^5 /dx = ?

Answer 43

5y^4 dy/dx

Question 44

steps for point of maxima?

Answer 44

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

revise graph from copy

Question 45

steps for point of minima?

Answer 45

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

revise graph from copy

Question 46

∫x^n dx = ?

Answer 46

x^n+1/n+1 + c

Question 47

∫1/x dx = ?

Answer 47

lnx + c

Question 48

∫sinx dx = ?

Answer 48

-cos x + c

Question 49

∫cosx dx = ?

Answer 49

sinx + c

Question 50

∫sec^2 x dx

Answer 50

tan x + c

Question 51

∫tanx secx dx = ?

Answer 51

secx + c

Question 52

∫ cot x cosec x = ?

Answer 52

-cosecx + c

Question 53

∫cosec ^2 x dx = ?

Answer 53

-cot x + c

Question 54

∫e^x dx = ?

Answer 54

e^x + c

Question 55

∫lnx dx = ?

Answer 55

xlnx -x

Question 56

∫ a^x dx = ?

Answer 56

a^x / lna

Question 57

∫ {f(x) ± g(x)} dx = ?

addition rule

Answer 57

∫f(x) dx ± ∫g(x) dx

Question 58

integration by substitution

Answer 58

read in copy

Question 59

some more formulas

after substitution (there are so many)

Answer 59

read in copy

Question 60

definite integration and average

Answer 60

read in copy