Edexcel A-level Mathematics 'Core Mathematics 4 (C4)' 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 Core Mathematics 4 (C4).

Pages in this set

Page 1

Preview of page 1
Core Mathematics 4
Formulae Sequences and
Series
·(
nr

)=
r!(n-r)! n!

· an [(1 +
ba

x)
n

] = an [1 +
n1

(
ba

x) + +
n(n-1)...(n-r-1) 1×2×...×r

(
ba

x)
r

+ ],|x| <
ab

,n R
Differentiation
· y = f(y)
dy dx

·…

Page 2

Preview of page 2
xn+1 + C,(n -1)
· y = (ax + b)n ydx =
a(n+1) 1

(ax + b)n+1 + C
· y = e(ax+b) ydx =
a1
eax+b + C

·y=
ax+b 1

ydx =
a1

ln|ax + b| + C
· y = sin(ax + b) ydx = -
a1…

Page 3

Preview of page 3
· y = sec(ax + b) y dx =
a1

ln|sec(ax + b) + tan(ax + b)| + C
· y = cot(ax + b) ydx =
a1

ln|sin(ax + b)| + C
· y = cosec(ax + b) ydx = -
a1

ln|cosec(ax + b) + cot(ax + b)|…

Page 4

Preview of page 4
du

· u
dx dv

dx = uv - v
dx

dx
·A=ab
y
dx
·A=ab
y
dx dt

dt
· V = a b
y2

dx
· V = a b
y2
dx dt

dt
·h=
b-a n
·ab

y
dx
h2

[y
0

+ 2(y
1

+y
2…

Page 5

Preview of page 5
·
dy dx

= f(x)g(y)
g(y) 1

dy = f(x)dx
Vectors · u =
|a| a

· |a| = x2 + y2 + z2
· |AB | = (x
2

)2 + (y
2

)2 + (z
2
)2

·a·b=x
1

-x
1

-y
1

-z
1x
2

+y
1…

Page 6

Preview of page 6
· a · a = |a|2
+ + y
n-1

)+y
n

Page 7

Preview of page 7
Notes Tips Algebra and Functions
·
... (ax-b)(... )
A ax+b

· To split improper fractions:
· Use algebraic division
· To split proper fractions:
· Use substitution
· Use comparing coefficients
·
Use substitution x = 0 Sequences and Series
·(
=
+
·
... (ax-b)2(...)

=
ax-b A…

Page 8

Preview of page 8
n

] = an [1 +
n1

(
ba

x) + +
n(n-1)...(n-r-1) 1×2×...×r
ba
r

+ ],|x| <
ab

· To find an approximation for ( m c )
n

:
· Use given substitution (
x)
,n R
· Use substitution x =
c-a b

· To find…

Page 9

Preview of page 9
dy Differentiation
· y = f(y)
dx
dy dx

· Remember to include the differential
· y = af(x)
·
= f(y)
dy dx

= f(x)af(x) lna
... dx

·
dy dx

=
dy ...

×
dy dx

= k(...); directly proportional increase
·
dy dx

= -k(...); directly proportional…

Comments

No comments have yet been made

Similar Mathematics resources:

See all Mathematics resources »

Edexcel A-level Mathematics 'Core Mathematics 4 (C4)' 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 Core Mathematics 4 (C4).

Pages in this set

Page 1

Preview of page 1
Core Mathematics 4
Formulae Sequences and
Series
·(
nr

)=
r!(n-r)! n!

· an [(1 +
ba

x)
n

] = an [1 +
n1

(
ba

x) + +
n(n-1)...(n-r-1) 1×2×...×r

(
ba

x)
r

+ ],|x| <
ab

,n R
Differentiation
· y = f(y)
dy dx

·…

Page 2

Preview of page 2
xn+1 + C,(n -1)
· y = (ax + b)n ydx =
a(n+1) 1

(ax + b)n+1 + C
· y = e(ax+b) ydx =
a1
eax+b + C

·y=
ax+b 1

ydx =
a1

ln|ax + b| + C
· y = sin(ax + b) ydx = -
a1…

Page 3

Preview of page 3
· y = sec(ax + b) y dx =
a1

ln|sec(ax + b) + tan(ax + b)| + C
· y = cot(ax + b) ydx =
a1

ln|sin(ax + b)| + C
· y = cosec(ax + b) ydx = -
a1

ln|cosec(ax + b) + cot(ax + b)|…

Page 4

Preview of page 4
du

· u
dx dv

dx = uv - v
dx

dx
·A=ab
y
dx
·A=ab
y
dx dt

dt
· V = a b
y2

dx
· V = a b
y2
dx dt

dt
·h=
b-a n
·ab

y
dx
h2

[y
0

+ 2(y
1

+y
2…

Page 5

Preview of page 5
·
dy dx

= f(x)g(y)
g(y) 1

dy = f(x)dx
Vectors · u =
|a| a

· |a| = x2 + y2 + z2
· |AB | = (x
2

)2 + (y
2

)2 + (z
2
)2

·a·b=x
1

-x
1

-y
1

-z
1x
2

+y
1…

Page 6

Preview of page 6
· a · a = |a|2
+ + y
n-1

)+y
n

Page 7

Preview of page 7
Notes Tips Algebra and Functions
·
... (ax-b)(... )
A ax+b

· To split improper fractions:
· Use algebraic division
· To split proper fractions:
· Use substitution
· Use comparing coefficients
·
Use substitution x = 0 Sequences and Series
·(
=
+
·
... (ax-b)2(...)

=
ax-b A…

Page 8

Preview of page 8
n

] = an [1 +
n1

(
ba

x) + +
n(n-1)...(n-r-1) 1×2×...×r
ba
r

+ ],|x| <
ab

· To find an approximation for ( m c )
n

:
· Use given substitution (
x)
,n R
· Use substitution x =
c-a b

· To find…

Page 9

Preview of page 9
dy Differentiation
· y = f(y)
dx
dy dx

· Remember to include the differential
· y = af(x)
·
= f(y)
dy dx

= f(x)af(x) lna
... dx

·
dy dx

=
dy ...

×
dy dx

= k(...); directly proportional increase
·
dy dx

= -k(...); directly proportional…

Comments

No comments have yet been made