Pure 2 Flashcards
∫1/ax+b
dx 1/a ln Iax+bI +c
binomial expansion
give x=1/2 should not be used in the exlantional to find an aproximation to √3
set expression to x and show x=1/2 isnt in the domain of x
trapexium rule
h
what is added to x each time
why does f not have an inverse
one to many function doesnt exist
u=3^x
3^x ln3
first principle sin/cos/tan
use small angle aprox
only for h
20
Σ
n=1
always arithmetic
arithetic equations
d
what you add not times
When co-ordinates are given vectors
With respect to zero
staircase diagram
gets bigger by smaller amounts
x1 = 3
x2 = 3.6
x3 = 3.72
x4 = 3.731
cobweb diagram
gets bigger by
iteration
diverges
moves away from a root, often
increasingly quickly
cobweb
gets bigger then smaller
turnign point
always make first point the opposite of whats in the brackt
sin 2A
2sinAcosA
cos 2A
cos²A - sin²A
2cos²A - sin²A
2cos²A -1
1 - 2sin²A
tan 2A
2 tan / 1-tan²A
differentiate
sin kx dy/dx
kcoskx
differentiate
coskx dy/dx
-ksinkx
e^kx dy/dx
ke^kx
differentiate
lnx dy/dx
1/x
sec x
1/cos x
When asked to form an exponential equation
V= Ae^kt
When asked to check reliability of model
Use a calculator e.g. e to the power of 2.3
When asked to check reliability of model
Use a calculator e.g. e to the power of 2.3
If asked how to change exponential equation for a car thats value decreases slower
Change the k to a less negative jumber
cosec x
1/ sin x
cot x
1/ tan x
cot x
cos x / sin x
cast diagram labeling
start in botom right corner and go antioclockwiese
f(x) = A + where A and B are constants to be found.
f(x) = 8x + 5 2x + 3
x > − 3 2
B 2x + 3
Not partial fractions
Divide them
