Summary Edexcel A Level Maths Pure Maths Notes

Graph Transformations
=

Reciprocal graph



# u
=
> 0
↑ -
R
3
2




2012 ...




#
=

*
y

na8

2[2
at
Asymptotes < 8
0 G
x y
= =
,
< e g 1 2, 3
)
- - -
.
.
...

,




translates
a
y f(x) + a
=
cotranslations)

y
=
f(x + a) y =
f ((x))
- I
translation (a) Nauslation (g) ↳
Reflects the graph to the
right
↳ shift in of the
y axis in the
yaxis
↳ shift
.




in
left hand side
direction x direction Ignore the part of
y the graph



↳
a f(x)
stretch parallel to
f(as2]
↳
stretch parallel
y
=




↳
(f(x))
Reflects any part of
-Y the


yaxis, scalefactor = a
to
y axis , st = original f(x) graph that

was below the saxis in the



+ ( x)
-
-




f(x) X-axis


-reflection in ↳ reflection
yaXtS Mx
axis


a




menialsa b #
y
-
=




asymptote




#
Hal


#
=




Y =
-


(a) "

, differentiation
y =
Sind

Cur
y
length + sector area
=




d) Arc

y = cox 1 r0=
(arc length)
def -Sin
A
tri@ (seco area
=
-
=
dx




ex I
+ 4)
y= e
+ 4)
= f(x)e
x




/ fx

f x)
y = a




01
a
d + at
Yan
nue
P roduct ,
= UV' + NU




Quotientnul
(2)g(x) g'(x) +(x) -




Yes,
(g(x))
L




chainnle

=
OR
y = ((x))\
= =
nE)()" +'(x)
d)

. 0
when there is no subject (e g
= C + y" +
1)
&
.




implicit dy/dx

(yn) = nyn -


((y) x = +
y