essential need- to learn shit Flashcards
PROOF of the sum of arithmetic series
PROOF of the sum of geometric series
standard solutions for itnergraiton (memorise )
ALWAYS ADD
+ C in intergration !!!!!!!!!!!!!!!!1
note, if a question wants something in a certain formm..
make sure to actually execute the individual powers
eg 3^5/2 and keep them that way
N choose R equation
+
note: in binomial expansion ; if the power is smaller than 1 or non integer (negative) , then use the manual method
if the power is larger than 1 or not negative then use normal method
trigonometric ratios
sin(theta ) = cos(90-theta)
cos(theta)= sin(theta- 90)
parametric intergration formula
when you get a square root, what do you do ?
ADD - AND + INFRONT OF IT!
npte, if diferrentation or nything looks dodgy
go back to the question, do it from scratch and THOROUGHLY ANAYLSE IT
differentiate a^x
HUGE NOT ABOUT TRIG
tanx= sinx/cosx not (sin/cos)x
what cancels (3/2)^t
(2/3)^t
(a-b)^2=
(b-a)^2
what to do when something is in the form
“cos(theta) - sin (Theta)” ?
use the Rsin(theta + alpha) equation thingy
AREA OF CIRCLE
PI(R)^2
NOT “1/2 (PI)R^2”
DONT FORGET TO PUT “+C” !!!!!!!!!!!
IN INTERGRATION
Quadratic formula
-b + /- sqrt(b^2- 4ac)
/
2a
intergration by parts priority
LATE
when to use U substitution
if one bit of the equation has a SIMILAR DERIVATIVE as the other
https://www.youtube.com/watch?v=6PX5hNY8kvQ&t=168s
note: look over this paper ..
https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FEdexcel%2FPaper-1%2FSpecimen%2520MA%2520-%2520Paper%25201%2520Edexcel%2520Maths%2520A-level.pdf
DONT FORGET THE GODAMN C
DONT FORGE THE GODDAMN C
DONT FORGET IT
JUST DONT
SERIOUSLY
DONT FORGET C
LITERALLYJ UST ADD +C AT THE END
ITS FREE MARKS
IF YOU FORGET IT YOUR OFICIALLY A CLOWN
make everything the same variable to make life EASIER
https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fwww.madasmaths.com%2Farchive%2Fiygb_practice_papers%2Fmp2_practice_papers%2Fmp2_y_solutions.pdf
Last question
what do do when you want to intergrate a trig function squared
convert it to the double angle formula form (eg 1/2cos2x - 1/2)
IMPORTANT intergral rule !
(intergral sign) (n+1)(f ‘ (x)) [f(x)]^n = [f(x)]^n+1 + C
use it when there are two derviative ( adjacent powers next to each ither )
e^x^6 * (6x^5) two derivative next to each other so intergral is e^x^6
when to use intergration by u substituiton
