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Alevel pure mathematics summary sheet

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Course
Pure mathematics (H240)

Institution
OCR

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...

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Uploaded on October 22, 2024
Number of pages 1
Written in 2024/2025
Type Summary

ocr
pure mathematics
differentiation methods
integration methods
trigonometric methods
vector methods
full alevel pure mathematics summary
study guide

Study Level
A/AS Level
Examinator
OCR
Subject
Mathematics
Unit
Pure mathematics (H240)

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functions The discriminant Circle Theorems
⑮
Angles Angle
o

One to 2 real Segment Centre
b2 (a) > 0 roots
in
at twice
one function
-> o ,
is

Inverse functions are
equal . ⑫ the
ongle
at Circumference
One to to
Switch many not a function root
domain and
doman
Range r
Finding Range
b2 -

49c =
0 repeated
finding
domain
R

Range
domain of (linear cubic) IR Range of near function is

output
quadratic =

real
is

Input
·
, ,

b24ac 40 no
<(x- 2)21
Quadratic

JAK a
= = roots
e

we
y =

X
The
The perpendicular opposite angles
3
rational function set to in
O
to find doman
bisector
·
a
of

reflect 3
=
in
y chord Cyclic quadrilatual total
of a
chord 1800
, splits the
·

composite function
Into

S
two
equal pieces .

100
Set as
-y ,
then make a replace
fg(x) -
>
do g in terms of
Partial Fractions
&(2
Subject
as
y that terms B
· in of
g O

=+
o
Angle between
targent and chord

+
~
(x a) (x + R) Angle in Semicircle [
is equal to
angle subtended by

Graphs
S is 900
the same Chord in alternate
segment.

n 9

Circle equation
Transformations
Vector
(x a) -

+
(y b) - = r Reciprocal Graph
f(x) +
a(a) f(x
a))-) Area of Segment
Geometric

!
+
centre
(a b) radius ~
Formulae (Radians)
= =
,

EQUATIONS
Stretch [ra(0 -S in0)
f(x) Stretchaxis
·

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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