null
US
Entrar
Registre-se gratuitamente
Registre-se
Detectamos que o JavaScript não está habilitado no teu navegador. Habilite o Javascript para o funcionamento correto do nosso site. Por favor, leia os
Termos e Condições
para mais informações.
Próximo
Copiar e Editar
Você deve estar logado para concluir esta ação!
Inscreva-se gratuitamente
2694559
FP1
Descrição
Mind map of the entire FP1 module including equations and diagrams
Sem etiquetas
fp1
maths
further maths
revision
a levels
alevel
maths
a-level
Mapa Mental por
rb.russell1
, atualizado more than 1 year ago
Mais
Menos
Criado por
rb.russell1
mais de 9 anos atrás
34
1
0
Resumo de Recurso
FP1
Complex Numbers
i= √(-1)
i^2= -1
i^odd= ± i
i^even= ± 1
Dividing
"realise" the denominator
if you have x/(a+bi)
times by (a-bi)/(a-bi)
sames as x1
complex conjugate
if z = a+ib
z*=a-ib
zz*= real no.
difference of 2 squares
make bottom a real no.
modulus and argument
argand diagram
vectors
magnitude
modulus, r or |z|
length
pythag
direction
argument, Arg(z)
angle between vector and x-axis
tanθ= y/x
modulus-argument form
if z=x+iy
by trig
x=rcosθ
y=rsinθ
z=r(cosθ+i sinθ)
in equations
equating real and imaginary
if a+ib=c+id
a=c and b=c
find √(15+8i)
let √(15+8i)= a+ib
15+8i=(a+ib)^2
etc.
quadratic roots
if z is a root
so is z*
Co-ordinate Systems
Parabola
equation
cartesian
y^2=4ax
parametric
x=at^2
y=2at
Rectangular Hyperbola
equations
cartesian
xy=c^2
Parametric
x=ct
y=c/t
tangents and normals
m(t)=dy/dx
m(n)=-1/m(t)
m(n)x m(t)=-1
y-y1=m(x-x1)
Proof by Induction
method
prove true for n=1
assume true for n=k
show true for n=k+1
state true for all n≥1 where nϵ Ζ+
types
series
swap k for n
NOT r
divisibility
consider f(k+1)-mf(k)
show difference is divisible by a
therefore f(k+1) is also divisible by a
remember rules of indicies
a^n x a^m= a^n+m
(a^n)^m= a^nm
Matrices
Sub step 2 into step 3
M^k+1
same as M(M^k)
recurrence relationships
show true for
n=1 AND n=2
for step 3
use recurrence formula for U k+1
sub U k in
write your target!
Series
General formulae
r
r^2
r^3
1
sum between 2 limits
sum up to top limit
minus sum up to bottom limit -1
to show a summation formula = ....
take out common factors
Numerical Methods
show root in interval [a,b]
find f(a) and f(b)
change in sign
root between a and b
Interval bisection
next estimate
midpoint
(a+b)/2
between a and b
where f(a) -ve and f(b) +ve
linear interpolation
if root lies in [a,b]
use similar triangles
or formula
not in data book
Newton Raphson
find f'(x)
write out f(a) and f'(a)
in formula book
doesn't work @ turning point
f'(x)=0
Matrices
multiplying
only multiply if
no. of columns of 1st matrix
same as no. of rows of 2nd
product dimensions
same no. rows as 1st matrix
Same no. of columns as 2nd
not comutative
AB≠BA
dimensions
(nxm)
n= rows
m=columns
simultaneous equations
Transformations
vectors
position vector
from origin
can be written (x,y)
translation vector
from given point
linear
linear expressions
point (0,0) unchanged
reflections
y-axis
x-axis
y=x
y=-x
enlargement
scale factor a
rotation
180°
90°
clockwise
anticlockwise
45°
clockwise
anticlockwise
inverse matrix
transforms back to original
Inverse
A^-1
AA^-1=I
I= identity matrix
determinant
ad-bc
singular if =0
transform shape
straight line
0 area
Anexos de mídia
6e7d2861-b774-4da4-a705-cbdb77df43c1.gif (image/gif)
020bf3b6-54f5-4136-a768-05c8bef2c680 (image/jpg)
7494433b-2ec7-4e81-bcff-af6f0f3485ff (image/png)
047c59d7-5bd9-4139-bbed-28fe6d197abf (image/jpg)
c6798e89-cfd4-4d5c-b864-292cc3137d39.gif (image/gif)
374f45b7-d8f3-47aa-886f-7ef90b8e8713 (image/png)
b63262e5-0b2a-4e3f-b6e2-a9cbaa7e09fd (image/png)
437488c5-26a7-4406-ad83-6b42ea3ab2f6 (image/png)
1c38c5a5-59c8-4cb7-b41d-b06c6d7c4be2 (image/png)
860da697-d95b-433c-86e2-02761e6db6dc.gif (image/gif)
82e08cd5-2ba5-4cf1-8756-63a2becd3ecc (image/png)
b41db547-29ee-4913-806b-e801f5b4f123 (image/png)
e2322e37-4cda-4aa4-8258-d151bca7aa58 (image/jpg)
80c0907a-408f-4577-81d6-03bddc6bdd72 (image/png)
48d6b195-248c-466a-ab26-d47f9ac3edc0 (image/png)
d0c15411-4f96-451e-b841-1df12219fe15 (image/png)
f97dce4b-a63b-4b03-80ad-7d501b800f79 (image/png)
5df3b411-f364-4f72-979a-d6988738e734 (image/png)
0d46439b-8e62-4bab-950b-daa3ecd13003 (image/png)
769af54c-3f02-47c9-8d54-e774b2284d7c (image/png)
548fe3df-590b-4d9c-994e-9e02524dde09 (image/png)
bb68239e-0566-43d6-aca8-44da8183578d (image/png)
a3521ba3-9042-41f6-a470-003ea898dcbe (image/png)
f66db66d-9856-4a4c-ae8e-41268e8dc1d4 (image/png)
a33ee672-585c-43b3-a9d5-52a664683a30 (image/png)
dd9ea091-0a05-4829-a356-7a8acf20f38d (image/png)
c975d5ef-91a4-4208-a870-c93ecc9a5435 (image/png)
c97f0b4a-3cf5-4e23-95c7-cebc0434c704 (image/png)
58801988-4b18-4db5-990b-8c6b6aa28a91 (image/png)
606d3423-9247-425b-9dab-71a667a3f3a6 (image/png)
f0b3f8e8-a5a2-4113-bb85-295b7a9007c1 (image/png)
45bda8a2-9ddd-4026-99dc-3c5a6dd41809 (image/png)
0ff0c37f-4579-4116-bb91-87e24ed8980b (image/png)
e82e47a5-e3a4-4d5a-99f7-5d8fbe93afac (image/png)
Quer criar seus próprios
Mapas Mentais
gratuitos
com a GoConqr?
Saiba mais
.
Semelhante
CUMULATIVE FREQUENCY DIAGRAMS
Elliot O'Leary
Fractions and percentages
Bob Read
GCSE Maths Symbols, Equations & Formulae
Andrea Leyden
FREQUENCY TABLES: MODE, MEDIAN AND MEAN
Elliot O'Leary
HISTOGRAMS
Elliot O'Leary
GCSE Maths: Geometry & Measures
Andrea Leyden
GCSE Maths: Understanding Pythagoras' Theorem
Micheal Heffernan
Using GoConqr to study Maths
Sarah Egan
New GCSE Maths
Sarah Egan
Maths GCSE - What to revise!
livvy_hurrell
GCSE Maths Symbols, Equations & Formulae
livvy_hurrell
Explore a Biblioteca