100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
AS Level/ A-Level Further Pure 1 – A* Further Mathematics Pearson Edexcel Summary Notes (8FM0) (9FM0) $7.81   Add to cart
Quickly navigate to
Preview
  2.  
  3. PEARSON (PEARSON)
  4.  
  5. Further Mathematics
  6.  
  7. Further Pure 1

Summary

AS Level/ A-Level Further Pure 1 – A* Further Mathematics Pearson Edexcel Summary Notes (8FM0) (9FM0)
 22 views  0 purchase
  • Course
  • Further Pure 1
  • Institution
  • PEARSON (PEARSON)

AS Level/ A-Level Further Pure 1 Further Mathematics Pearson Edexcel Summary Notes (8FM0) (9FM0) All key points and example questions (including step-by-step workings) are included! Notes were designed based on the Edexcel syllabus in preparation for the 2023 Summer Exam. Chapter 1: Vectors ...

[Show more]

Preview 2 out of 7  pages

Document information

  • March 11, 2024
  • 7
  • 2022/2023
  • Summary

Subjects

  • further math
  • fmath
  • further mathematics
  • math
  • mathematics
  • 8fm0
  • 9fm0
  • as level
  • a level
  • gce a level
  • edexcel
  • detailed
  • core pure
  • further pure
  • summer exam
  • pearson
  • summary
  • notes
  • a

Written for

  • A/AS Level
  • PEARSON (PEARSON)
  • Further Mathematics
  • Further Pure 1
All documents for this subject (1)

Seller

avatar-seller
celinesim9988

Content preview

FURTHER PURE 1


Chapter 1 : Vectors
Vector Product /Cross product) :
Refer back to CPI notes
1

a x
1 =
/9/16/ sino 1 b R
A X



equation of lines :
x

&
-
L
1
"




49
↓
Direction of I determined
by (1 4)
A
↓ is the 1 0
x =
N
-




-
b =
1 -




A

right-handed screw rule. OR 2 Xb =
2 Where AXb =
C o
.




7
i 1 x
1 =
1
4 bxq 0 Direction cosines
-




1 x =
1 x
1 = :
-




-

-


L xj =
-




1
let A = 9 1 +
A21 + As 1 ↓ 6
-
if 1 = x1 +
y +
21
1
,
x
1 = O (C
Ya
=

b b, l (0SX m cosB n cos0
b c1
=

bs1
= = = = =
= + + a I ·
a




a
2
+y
(4


d
+




=
AX1 l + M + D = = =

>Us A 43 A -
:
=
= -



= + I
..
+ M2 +
D = 1
=
(AcDs-AsDc)[ -19 Ds-AsDa)[ ,
+
(9 ,
b. -Acbi) L

l equation of normal (

Areas & volumes


a a asi
. (b x
2) =
4 .
(2x1)
. XC
-




B triple scalar product :
1 =
1




B C 4 .

(1xb) =
0
>

D
D D
A
>
A D 1
C C
C T
7
Parallelogram
A B C A ↓
> >

= Ac AB
-




Area 1 x Area = x
AD parallele piped A B
pyramid B Tetrahedron


FB (FC ( 5 AB (1 x FD) 5 13 ↑D)
>

(1
-




V = . x AD V = .

V = .
x




Point of intersection betweenI T
and :




>
intersects in a line : a vector that is perpendicular to both n ,
and n = lies in both planes
T1 e. g. A ,: .

(= = 2
find point of intersection,


/-
Ha
(1) 5
|e+ 1 211 2y (1) 2 x
3y
Ni =
5
=
1 z +
12 : =
-


= - -
.
,




.
Tz O 4) ...
2x
2y 3 by =
0
- -
. . .
=




nin n ,
x nc =
( = )x(-) (i) =

0 -




0 : -




2y
-

( -




6y) = -

5


5
4y
=
-




Shortest distance between 2 skew lines :
= - ,
x =



: -
xi
r,
= a + xb F = -


A
*

MA
A
P2 2 +

&
=

normal to 1 and 1 = b x


d

d =
(2 q) -
.
((x1)
X

C b x d




Chapter 2 : Conic Sections
PARABOLA

Y loci proof :
y= 496




↑ i
X I X
Pl at2 2at)
If 2 JaJ
,
=
&
1 .

PX = x + A 2 .



y 49)
y
=




AB2 # =
-




-
PA = +
PB PA = ( -


291 +
9 + 494 I =
25a(

( 94
A
s
= (x -


a) +
y2 = + 2ax +
OR 2
2y
= 49
O




m
= x' -

2ax + a +
y PA =
(c) +
a)
=
+ =

2
PA
A
.
=
PX ·

2 y = 2at ; =
20
y 49/
() = -

A then PX = PA' So (1) +
a) " = (11 a) -

+
y
,
I =
at2 ; =
2at
Focus : (a 0 ) , ( + 29x + a = x -


2ax + q +
y2
Directrix : () = -

A
y
" = 49s) Cartesian form - = =
&
: = 4 96 E) DX PA Parabola general point () at 2at Parametric form
y y
= : = =

, RECIPROCAL Rectangular Hyperbola loci proof :




Y At
Y
general point :
<= Ct , y
= = parametric ↓ Plat" sat) , x =
2 y
=
at
t
4(π)
:




y
=
c Cartesian + =
4 .. x =

2
Plct E
M/A y
,

x

py = C Reciprocal ,
at x =

29

=
> y 2ax
> /

dy
O O
=
c


or
=
-jik --
1
+
= 496
y




Chapter 3 : Conic Sections

Ellipse = P ,
PF =
(x-de) +
y2 and PD = (4 - 1)
(2
&

Y e
a
+
p
= 1
PlacOSO ,
bsinO e =

(laesiy
form /
(standard form (
(parametric
One 1 for ellipses
,
c =
p p(a -




2x xY + =
( -


2aex + a
y
+




Y if foci ( 0)
a > b = 92 -29ex 2 ( 292x a y
+
= -
+ +

,
,




fe




↑
↓ ] <11-04




↑
b directrices ( = I a'll-e =
(11-24) +
ya
= 9


b

D' P(x y) ,
D
a


b " = a 2(1 2) -
" qxB +

y
=
1


· 1


bu




NOT
O
if b >a foci /0 Ibe) PF =
ePD PF' = DPD'
(C
,
,

A
! O
I
A
F F
-




1 -

42 , 0) (ae 0 ,
b
directrices y
=
I PD =
* -



/ DD =
G + C


A



a2= b2(1 22 -

PD +
PD =
2(8 -



x +
8 x) +




-
b PD +
PD' =
29




x =
- x =

ellipse : Ocel


1
(parametric form) of parabola e
Hyperbold eccentricity distance PF
:
e
=

= = ratio To PD

- Y =


Placosht ,
bsinht OR P(asect ,
btant /
hyperbola : I




I standard form / asymptotes

y = x
P
=

> 1 ,
for hyperbolas = ,
PF =
(x-de) +
y2 and PD (x-4)=




I See
*
foci (lae) e
y




(190 ,
0 e =




directrices : 1 =
I Ge e(l - +
) =
x-2aex + a +
y


b
=
a'(ec 1 -

e's'-2aex + a =
( -

29ex + a +
y



(C asymptotes :
y
= I B ( 2 1) - -




y =
a (e' -


1) = a'e' -

1




+page 1.
=



bu




Factorisation of Cubics : P= q =
(p 9) (p + +
pq
+
q'




Finding locus of midpoint :
Proving SQ =
eSP :




Point P lies on ellipse
-
Y = 1
, N is the foot of the perpendicular from P to the line ( =
8. Normal to
hyperbola -Yi = / at Plasect , btant) is allsint +
by =
(a' b)
+ .
Tant The normal meets (1-axis at Q.




M is the midpoint of PN .
Find locus of M .
Prove SQ = eSP ,
where S is the focus and e is the
eccentricity
.


Y x =
8 P(610S0 3 sinO) and N18 3 sinO Y x =
e b " = a (e- 1 e =

S




h
, ,


X




9. . .
3 M 8
/61030
+


Px 3sin0)
-




H
LN X
M :
,
Q :

y
=
0 ,
all sint =
(a
=
+
b) Tant SP =
ePN




- O ·
x
M)3COSO + 4 , 3sinO) x =
"e SP +e (a sect -


Q E of
-




3
-




let X 31098 + 4 Y 3 SinO SP =
de sect a
-




= =
, ,




coso =**, sino = so = -de
SP =
a lesect-1)


a "+ 9 'e' 1
Y
4)"
(X-
-




COSO sinO
+ = 1 =
-


af
1 SQ
=
eSP/
+ = : =
a cost




(X -

4) + Y =

9/
=
a -ae




SQ =
Ge/esect-1)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller celinesim9988. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $7.81. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

75323 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$7.81
  • (0)
  Add to cart