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