Boost your grades with these comprehensive OCR A-Level Pure Maths notes! Covering all key topics like differentiation, integration, algebra, and more, these notes simplify complex concepts and include essential formulas and exam techniques. Perfect for revising key OCR Maths A-Level topics, masteri...
9
midpoint :
( f(ax)Stretcha , Area of
Sector
Arc
length
O
factor a
by
·
t
Perpendiar 0
·
- Reflection factor
o M
,
by O
y= f) f(x) elei + ( x)
:reflectionis
-
Cone Volume
is
equation
m(x x) Sush
of y -y LOG LAWS
=
,
-
modulus
line
( 3)
y =) If(x))belowsup f(x) ·
everything easis In
109e
=
= =
ex +
o
o
Gradient ice
goes lett
loga1 = x va" =
Seg vences
AB
Vectors Factor Theorem
Insy
= (nx + my Binomial Expansion
b a If f(a) then (x-a)
= -
In-ly
In
= 0
arithmetic
=
157 ==
Fit !
,
Toeof Sequence
1d for f(x) and
Pale conditional
-
vica versa
arithmetic Sum Increasing seq
Inx" = Klux
(d)
+
S =
z(2a (n a =
1) b where I constant
( c)
is
·
- + -
inequalities
!
+ = 1 + nx
decreasing Seg In =
-
In
S= =
z(a 1) ,
+
It Unt & Un,
torade
magnitude
-
A
by negative
or X
=
xi +
y1 + zk
any - for(
Geometric Periodic Sequence the
= ↓) to <
Iv - =
(a bx))
181 m ubr Sukches
22 -
y2 Love
tum
+
+ =
Un = ark
-
1) If
Unti =
Un for all - (x a)+
Trigonometry
and its
period/order IS K
Gordi
um
A level Pure Maths - Kyla Robinson
s
Trigonometric Graphs
Radians Exact
Trig Values
Sin 25 3600
1800 Tangent definition
to
1 900 Double formulae
Angle
= = =
Numerical METHODS
~
Sin(0) =
Isinocoso
E 60 =
=
450 I = 300
Los(20) = 1050-SinO
Root Small (20020 I
angle approximations cos(20)
= -
↳achange and function I s a s a Solving equations Reciprocal Trigfunctions 1-2510
COS SinGO cos(20) =
a
12 3
cast
Sin0 ton (201
Cobwebs it
tan
&180 1360
Staircase ta0
=
& x O
-
0
i
y
=
o
LOSO
1- @ 0360-0 1360
"F
1 200 =
-- ! tano o 1 180
Rearranged Double
angle formular
convergeor
aa
addition formulae Integration
I
cofunction
converges
tovre
diesi s
Pythagorean Identities Sio =
-Los2o Coso =
1 + 10520
Starcase
Sin(IB) S
Sin(90 -@)
·
=
SinALOSSISinBlosA . O =
Cos (90-0) COSO =
Sino 1-cos'O
.
Harmonic
Identity
Newton Raphson Method I fails
=
if
Cos (n = 3) =
CusACosS I SinASinB
If Rcosd
Cos = /-Sin "O = a Rsind = b
denominator
tan(A = 3)
-
O
=
Fas
I
=
=
eg + () = 0
Secho = I + tanio
R =b2 + tand =
-a
Coseco = 1 + cot "O
First Principles
DIFFERENTIATION
INTEGRATION
x
f()
f() Rules
-
Trapezium
parameta
Rule Substitution
Jyde "Sirlovessubstantrevaine
Sun rule
th (first last frick)
Quotient
first derivatives + (g() (x) g() h- (x) = + 2 , t
v
+
+ =
Decreasing function f'pc) < 0 product rule
Implicit differentiation Integration by Parts
Potas
tel Extra tips a make things
dy
easier
Stationary Point f (x) = 0 up + ur
f(y)
f(y)x Sov
=
+
&J2 left d /right +
right d(++)
o =
ur-Srir do
Jes put unmat-
Increasing function f
(2)) O function
Integrals Pick
-
Rule
Rio
Chain
Reverse Chain rule
Second Derrature I = Jaxur +
+ C Integrate
f"(x) < 0 :Max Se
do
*
val a Form 2
vex + C
Parametric connected rates of
Change
-"(x) Point inflection
Sk Sk + :(c) [f(x)] dx
=
= 0 of
a= = ( + a
f"(x) 1
Wine [f(x)]v
· +
>
0 be a Rate
Set
y
= In / +(2) Set
y
=
means S coss o Sinx + c
↓
find
by
dos find do
Function >
- derivative ↓ Since 8-cosx + C the
make
A /K =
adjust constant
* dou >
- and d
In Cos -Sinc Ssecis >
- Kanea + C example
example
(G(2x
J 3)
+
3)(x2 30) dx +
=
2(x2 +
+ c
↑ tanx o See's 2Sil
J
=
a ne See talea
Seaton & Sec + <
Si + G) [f(2] des
JLoseciv
↳
(p*]
+ 1
y A
-
=
-
co+ x + c
y (x zx)3
=
InSw
# Cose223
-
Lose Lots & cosecot f -
cosex + C m =
3(x 3) ( =
+ G(2x + 3) ( 3) da+
*
Since - Cosse
Sf(ax b) +
- af(ax +
b) + c
: A = 2
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