Maths Flashcards
Remember for trig questions for min angle, and cos and sun, what should you ALWAYS DO
find the negative values,mbevause adding might give a smaller value
Always fir cos , find cast, -2pi or use even function prorpty
Remember for transformations,
It each transformation into brackets
Therefore don’t make mistakes multiplying something by 2 when shiukdnt
Fucntioms
Are many to Ken or one to on mapping
For an inverse function to be true the function must be one to one so restrict , as inverse of many to one is one to many which is not a fucntiom
The domain and ranges of inverse functions are swapped , but there maybe other thingd too
% find inverse by making y the subject
Inequalities, remember dotted and two inewuakitedfor shaded regions
WHATS A PERIODIC SEQUENCE
One thst keeps repeating st regular intervals, and the period is the number of terms thst repewt
DIFFERENC e between series and seweucney
Sequence is just a det numbers ina Given order
A series is the sum of the sequence
Divergent vs convergent
Diverges means infinity, converged means arrive at a liktm
If b is -1 this will diverge
I’d b is 1 this will converge si it can’t be 1 but it can be -1
Any values outside it will diverge!
Converge between -1 and 1, including 1
Take care for tangent and normal
If they want exact working might be better to sue y- y1 = m (x-x1)
How to solve fraud triangle in semi circle questions with diameter
Never use diameter , use distance from each end of diameter to point in semi circle as yiu can slash find this and do 1/@BH
Path of the particles is what
Motions of particle is what
Oath is dispalcment
Motion is velocity
And Remmeber ti make Cartesian det oath to x and y and parametric t
Bruv don’t be stupid snd remember product rule when there is and x outside bracket s
So when diff twice be wary!
IF VELOCLITY IS NEGATIVE at a time, or whatever how to tell if SPEED IS INCREASING
find the rate if change if velocity so the acceleration
If the accerlwtion is negative, and it already is negative, it’s getting negativer so it’s speed is actually increasing
However if accerlwtion is positbe and it’s negative it’s slowing down
Vice verbs too!
How to show a line is a tangent to a vorfiel
Sub in and discriminatory should be repeated 0 means one solution
How to prove two things are perpendicular again
Make sure brsdients multiply to minus 1!
Show initsl angles
Show that they perpendicular so everything is 90, ,sans a rectangle
Now show two oppsite sides bith hsve the same length so must be sqaure
Why can Unterste bunimial expansionnonly
If the limits of the integral are completely in the renege in which the model is vs,id for
And the limits are not not in the domain!
Accerlwtion better modle now before v goes CONSTSNT?
Because acceleration is “ just ss it goes CONSTSNT, which mesns it rwsches max speed without suddenly changing accerlwtion
How to prove infinitely primes
Ssume there is a if it’s list of primes from p1 to pn
Let P be the number p1 x p2 to n +1
If P is prime, this is not in the list, so contracidts
If p I nit prime, by number theory, it must be able to have a prime factor
But this means the prime factor must be a factor of 1 too,
Which js impossible
Thus the prime number thst csn divide it is not in the lidt
And thus this contradicts the original statement
And there are ifnintiley number of prime
Changing binomial up cna you Stil approximate same baleu
NO CHECK THE NEW RANGE KF VS,IFITY
See transformation, look if it eokesfor zTop and BOTTOM
If CONSTSNT snd trig, what can you don
Jsut keep ti in same form and act like Su using cast
For k CONSTSNT questions and they give you a range how to calculate
Use the maximum and minimum values of range, so you know it will lie here
Do calc
See if it was a sqaure number or something snd msde a difference
Remember if you get equation and answer one looks right consider rest of graph might be diff stick with unstick well done!
Equating effeicmt wackzino
Yeah in this case equate the coeffeicnt that ARE SUPPOSED TO BE THERE
THE REESSON THIS IS 9 BEVSUSE IT SNOT SUPOOSED TO BE THERd
