essential need- to learn shit

Question 1

PROOF of the sum of arithmetic series

Answer 1

Question 2

PROOF of the sum of geometric series

Answer 2

Question 3

standard solutions for itnergraiton (memorise )

Answer 3

Question 4

ALWAYS ADD

Answer 4

+ C in intergration !!!!!!!!!!!!!!!!1

Question 5

note, if a question wants something in a certain formm..

Answer 5

make sure to actually execute the individual powers

eg 3^5/2 and keep them that way

Question 6

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

Answer 6

Question 7

trigonometric ratios

Answer 7

sin(theta ) = cos(90-theta)

cos(theta)= sin(theta- 90)

Question 8

parametric intergration formula

Answer 8

Question 9

when you get a square root, what do you do ?

Answer 9

ADD - AND + INFRONT OF IT!

Question 10

npte, if diferrentation or nything looks dodgy

Answer 10

go back to the question, do it from scratch and THOROUGHLY ANAYLSE IT

Question 11

differentiate a^x

Answer 11

Question 13

HUGE NOT ABOUT TRIG

Answer 13

tanx= sinx/cosx not (sin/cos)x

Question 14

what cancels (3/2)^t

Answer 14

(2/3)^t

Question 15

(a-b)^2=

Answer 15

(b-a)^2

Question 16

what to do when something is in the form

“cos(theta) - sin (Theta)” ?

Answer 16

use the Rsin(theta + alpha) equation thingy

Question 17

AREA OF CIRCLE

Answer 17

PI(R)^2

NOT “1/2 (PI)R^2”

Question 18

DONT FORGET TO PUT “+C” !!!!!!!!!!!

Answer 18

IN INTERGRATION

Question 19

Quadratic formula

Answer 19

-b + /- sqrt(b^2- 4ac)

/

2a

Question 20

intergration by parts priority

Answer 20

LATE

Question 21

when to use U substitution

Answer 21

if one bit of the equation has a SIMILAR DERIVATIVE as the other

https://www.youtube.com/watch?v=6PX5hNY8kvQ&t=168s

Question 22

note: look over this paper ..

Answer 22

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

Question 23

DONT FORGET THE GODAMN C

Answer 23

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

Question 24

make everything the same variable to make life EASIER

Answer 24

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

Question 25

what do do when you want to intergrate a trig function squared

Answer 25

convert it to the double angle formula form (eg 1/2cos2x - 1/2)

Question 26

IMPORTANT intergral rule !

Answer 26

(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

Question 27

when to use intergration by u substituiton