Edexcel A-level Further Mathematics 'Further Pure Mathematics 2 (FP2)' Revision

Contains a list of all the formulae you need for the exam, as well as further notes and tips on the Edexcel specification of Further Pure Mathematics 2 (FP2).

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Page 1

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Further Pure Mathematics 2
Formulae Coordinate
Systems · x = r cos rcos = x
· y = rsin r sin = y
· r = x2 + y2 r2 = x2 + y2
· = arctan
yx
yx

·A=
tan =
12


r2

d
·A=
12

r2
·A=
12…

Page 2

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· = argz = arctan(
yx

) tan =
yx

, - <
· z = a + bi z = a - bi, a R,b R
· z = r(cos() + i sin()), - <
· z = rei, - <
·z
1

(cos(
1

) + isin(
1…

Page 3

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1

-
2

) + i sin(
1

-
2

))
· |z
1

| = |z
1

||z
2

|
·|
z
2z
1
|z z
2

|=
1
| |z
2
|

· arg(z
1

) = arg(z
1

) + arg(z
2

)
· arg(

Page 4

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z
2z
1z
2

) = arg(z
1

) - arg(z
2

)
· z = ei = cos + isin; Euler's relation

Page 5

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1

·
z

= e-i = cos - i sin; Euler's relation
·z+
1z

= 2cos
· · z zn -
=1z

(rei) = 2isin
n

= rnein = [r(cos + isin)]n = rn(cosn + isinn); de Moivre's theorem
· zn +
zn 1

= 2cosn
· zn -
zn…

Page 6

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d dx2 2
y

+b
dy dx

+ cy = f(x) y = C.F.+P. I.
· am2 + bm + c = 0; auxiliary equation
· y = Aex + Bex; complementary function 1
· y = (A + Bx)ex; complementary function 2
· y = Aeqix + Be-qix y…

Page 7

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+ ...; Taylor series

Page 8

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r(a)

· f(x) = f(a) + f(a)(x - a) +
f
(a)
2!

(x - a)2 + +
f
r!

(x - a)r + ; Taylor series
· sinx = x -
x 3! 3

+
x 5! 5

+ + (-1)r
(2r+1)!
x
2r+1

,xR
· cosx = 1…

Page 9

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2
2

+
x
3
3

+ + (-1)r-1
x
r
r

+ , -1 < x 1
· (1 + x)n = 1 + nx +
n(n-1) 2!

x2 + +
n(n-1)...(n-r+1) r!

xr + , -1 < x < 1
·y=y
0

+x(
dy dx

)
x
0…

Page 10

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+ (x - x
0

)(
dy dx

)
x
0

+
(x-x 2!
0
)2

(
d dx2 2
y

)
x
0

+
Series
·
... (ax-b)(... )

=
ax+b A

+
·
... (ax-b)2(...)

=
ax-b A

+
(ax-b)2 B

+
·
... (ax2+bx+c)(... )

=

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Edexcel A-level Further Mathematics 'Further Pure Mathematics 2 (FP2)' Revision

Contains a list of all the formulae you need for the exam, as well as further notes and tips on the Edexcel specification of Further Pure Mathematics 2 (FP2).

Pages in this set

Page 1

Preview of page 1
Further Pure Mathematics 2
Formulae Coordinate
Systems · x = r cos rcos = x
· y = rsin r sin = y
· r = x2 + y2 r2 = x2 + y2
· = arctan
yx
yx

·A=
tan =
12


r2

d
·A=
12

r2
·A=
12…

Page 2

Preview of page 2
· = argz = arctan(
yx

) tan =
yx

, - <
· z = a + bi z = a - bi, a R,b R
· z = r(cos() + i sin()), - <
· z = rei, - <
·z
1

(cos(
1

) + isin(
1…

Page 3

Preview of page 3
1

-
2

) + i sin(
1

-
2

))
· |z
1

| = |z
1

||z
2

|
·|
z
2z
1
|z z
2

|=
1
| |z
2
|

· arg(z
1

) = arg(z
1

) + arg(z
2

)
· arg(

Page 4

Preview of page 4
z
2z
1z
2

) = arg(z
1

) - arg(z
2

)
· z = ei = cos + isin; Euler's relation

Page 5

Preview of page 5
1

·
z

= e-i = cos - i sin; Euler's relation
·z+
1z

= 2cos
· · z zn -
=1z

(rei) = 2isin
n

= rnein = [r(cos + isin)]n = rn(cosn + isinn); de Moivre's theorem
· zn +
zn 1

= 2cosn
· zn -
zn…

Page 6

Preview of page 6
d dx2 2
y

+b
dy dx

+ cy = f(x) y = C.F.+P. I.
· am2 + bm + c = 0; auxiliary equation
· y = Aex + Bex; complementary function 1
· y = (A + Bx)ex; complementary function 2
· y = Aeqix + Be-qix y…

Page 7

Preview of page 7
+ ...; Taylor series

Page 8

Preview of page 8
r(a)

· f(x) = f(a) + f(a)(x - a) +
f
(a)
2!

(x - a)2 + +
f
r!

(x - a)r + ; Taylor series
· sinx = x -
x 3! 3

+
x 5! 5

+ + (-1)r
(2r+1)!
x
2r+1

,xR
· cosx = 1…

Page 9

Preview of page 9
2
2

+
x
3
3

+ + (-1)r-1
x
r
r

+ , -1 < x 1
· (1 + x)n = 1 + nx +
n(n-1) 2!

x2 + +
n(n-1)...(n-r+1) r!

xr + , -1 < x < 1
·y=y
0

+x(
dy dx

)
x
0…

Page 10

Preview of page 10
+ (x - x
0

)(
dy dx

)
x
0

+
(x-x 2!
0
)2

(
d dx2 2
y

)
x
0

+
Series
·
... (ax-b)(... )

=
ax+b A

+
·
... (ax-b)2(...)

=
ax-b A

+
(ax-b)2 B

+
·
... (ax2+bx+c)(... )

=

Comments

No comments have yet been made