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A-level Mathematics/OCR/C4/Formulae
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A-level Mathematics
|
OCR
|
C4
Contents
1
Formulae
1.1
Differentiation
1.2
Integration
1.3
Vectors
Formulae
edit
By the end of this module you will be expected to have learnt the following formulae:
Differentiation
edit
If
y
=
sin
k
x
,
{\displaystyle y=\sin kx,\,}
then
d
y
d
x
=
k
cos
k
x
{\displaystyle {\frac {dy}{dx}}=k\cos kx}
.
If
y
=
cos
k
x
,
{\displaystyle y=\cos kx,\,}
then
d
y
d
x
=
−
k
sin
k
x
{\displaystyle {\frac {dy}{dx}}=-k\sin kx}
.
Integration
edit
∫
cos
k
x
d
x
=
1
k
sin
k
x
+
c
{\displaystyle \int \cos kx\,dx={\frac {1}{k}}\sin kx+c}
∫
sin
k
x
d
x
=
−
1
k
cos
k
x
+
c
{\displaystyle \int \sin kx\,dx=-{\frac {1}{k}}\cos kx+c}
∫
f
′
[
g
(
x
)
]
.
g
′
(
x
)
d
x
=
f
[
g
(
x
)
]
+
c
{\displaystyle \int f^{'}[g(x)].g^{'}(x)\,dx=f[g(x)]+c}
Vectors
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|
x
i
+
y
j
+
z
k
|
=
x
2
+
y
2
+
z
2
{\displaystyle \left|x\mathbf {i} +y\mathbf {j} +z\mathbf {k} \right|={\sqrt {x^{2}+y^{2}+z^{2}}}}
(
a
i
+
b
j
+
c
k
)
⋅
(
x
i
+
y
j
+
z
k
)
=
a
x
+
b
y
+
c
z
{\displaystyle (a\mathbf {i} +b\mathbf {j} +c\mathbf {k} )\cdot (x\mathbf {i} +y\mathbf {j} +z\mathbf {k} )=ax+by+cz}
a
⋅
b
=
|
a
|
|
b
|
cos
θ
{\displaystyle \mathbf {a} \cdot \mathbf {b} =\left|\mathbf {a} \right|\left|\mathbf {b} \right|\cos \theta }
The vector equation of a line through point
a
{\displaystyle \mathbf {a} }
with direction
b
{\displaystyle \mathbf {b} }
is
r
=
a
+
t
b
{\displaystyle \mathbf {r} =\mathbf {a} +t\mathbf {b} }
![{\displaystyle \int f^{'}[g(x)].g^{'}(x)\,dx=f[g(x)]+c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ae7f26f064c993232fdfbaf7b92fa54fbf983a4)
