# P3 Flashcards Preview

## Edexcel A-level maths P3&P4 > P3 > Flashcards

Flashcards in P3 Deck (17)
1
Q

Types of mapping?

A

One-to-one, many-to-one, one-to-many

2
Q

relationship between f(x) and f-1(x) in terms of domain and range?

A

f(x) domain = f-1(x) range
f-1(x) domain = f(x) range

3
Q

Inverse function only exist for ______?

A

one-to-one function

4
Q

sec x= _____
cosec x= ______
cot x= _____

A

1/cos x
1/sin x
1/tan x

5
Q

Trigonometric identities?

A

sin^2x+cos^2x=1
1+cot^2x=cosec^2x
1+tan^2x=sec^2x

6
Q

A

sin(A±B)=sinAcosB±cosAsinB
cos(A±B)=cosAcosB-+sinAsinB

7
Q

Double-angle formula

A

sin(2A)=2sinAcosA
cos(2A)=cos^2(A)-sin^2(A)=1-2sin^2(A)=2cos^2(A)-1

8
Q

algorithm of ln?

A

lna+lnb=ln(ab)
lna-lnb=ln(a/b)
klna=ln(a^k)
ln(e^x)=e^(lnx)=x

9
Q

Common differentiation:
x^n
sinx
cosx
e^x
a^x
lnx

A

nx^(n-1)
cosx
-sinx
e^x
a^(x)·lna
1/x

10
Q

Differentiation Chain rule?

A

Used in composite function

11
Q

Differentiation Product rule?

A

f(x)=uv
f’(x)=uv’+vu’

12
Q

Differentiation quotient rule?

A

f(x)=u/v
f’(x)=(vu’-uv’)/v^2

13
Q

Common Integration:
x^n
sinx
cosx
1/x
a^x
e^x
sec^2x

A

x^(n+1)/n+1
-cosx
sinx
ln|x|
(a^x)/lna
e^x
tanx

14
Q

∫f’(ax+b)dx=?

A

1/af(ax+b)+c

15
Q

Integration Reverse chain rule?

A

1) k∫[f(x)^n·f’(x)]dx=?
Try y=[f(x)]^n+1
2) k∫f’(x)/f(x)dx=?
Try y=ln[f(x)]

16
Q

How to determine if f(x) has one root?

A

If the function f(x) is continuous on the interval [a, b], f(a) and f(b) have opposite signs, then f(x) has at least one root, x, which satisfies a

17
Q

Iterative formula?

A

xn+1=g(xn)