PAPER 1

Question 1

Finding roots

Answer 1

can also be for two lines crossing each other eg 1 root= 1 intersection between 2 lines !

Question 2

note

Answer 2

do not try cancel out trig values when looking for an answer… it will ruin the solutions !, isntead try make all teh trig identites the same!

Question 3

roots

Answer 3

DONT FORGET TO PUT “+/ - “ NEXT TO IT !

Question 4

exponential model

Answer 4

Ae^kt

Question 5

comment on the reliability

Answer 5

if value from equation is close to the actual value then model is reliable

Question 6

how would you work backwards to verify something ?

Answer 6

https://www.youtube.com/watch?v=WpUrZWTnAFs&t=1038s 43:32

Question 7

With modulus questions

Answer 7

the general trend is to find valeus that make the modulus as close as possible to 0

Question 8

why cant we use the model to predict the time between bounces?

Answer 8

the model assumes that the time between bounces are constant, whereas in reality the time between bounces is not the same

Question 9

explain the relationship between the answers to a) and bi)

Answer 9

state

Question 10

STATE THE GODAMN OBVIOUS

explain the relationship between the answers to a) and bi)

Answer 10

Question 11

DO NOT FORGET TO…

Answer 11

PUT “C” INFRONT OF THE INTERGRAL !

Question 14

-ln(6) + ln(4)

Answer 14

write as ln(4) -ln (6)

ln(-6/4) = ERROR

ln(4/6) = ln(2/3)

Question 15

Answer 15

note: Whenever the question asks you to set it out like THIS.

USE GODAMN LONG DIVISION ON FRACTIONS

and get a remainder

Question 16

NOTE

Answer 16

LOOK BACK AT THE SIGNS UR USING

Question 17

NOTE

Answer 17

when answering intergration questions and final answer is “ln” SOMETHING

DO NOT LEAVE IT IN MODULUS FORM!!!!!!!!!!!!!!!!!!!!!!!

Question 18

note

Answer 18

when findign the area under a graph… ADD THE AREAS SEPERATELY !!!

(and co-ordinates on a trig graph ARE RADIANS )

Question 19

intergration by parts… set u as

Answer 19

Log

Algebra

Trig

Exponential

Question 20

manipulating numbers

Answer 20

look at one of the numbers, and ask, what is it multiplied/ divided by?

I looked at 8 pi and noticed that you multiply by 0.75 to get to 6pi, so i tried multpilying the whole quation by 0.75 and it worked

Question 21

explain why increasing the number of values in trapezium rule leads to higher accuracy

Answer 21

Increasing the number of values decreases the interval. This leads to an approximation more closely following the curve

Question 22

% accuracy

Answer 22

orginal- new/ original

* 100

Question 24

when making everything to e^

Answer 24

make sure to make the WHOLE equation e

EG

e^(5x+3) NOT e^5x + e^3

Question 25

2018 paper starts here

show that eg 3< alpha<4 given that alpha= x (Q4 2018 PAPER)

(deduce that if something = x, then there is meant to be a root )

Answer 25

1. equate function to f(x)=0 AND THEN look for a change in sign

Change of sign and function continuous in interval 3,4 Root (2)

Question 26

iteration forumale and graph

Answer 26

draw a cobweb that closes in on the grapj

Question 27

6 sin^2(theta) + 6cos^2(theta)

Answer 27

=6

NOT 1

Question 28

vertical line dy / dx=

Answer 28

infinity… therefore if dy/dx is a fraction.. then the denominator is 0, making dy/dx inifntiy

Question 30

when subbing something in make sure that it is …

Answer 30

the EXACT VALUE ( not a decimal place )

Question 31

note

Answer 31

try BOTH intergration by parts AND intergration by substitution ( but try itnergration by substitution first !)

normally

Question 32

in intergration by substitution

Answer 32

dont let “u” = square root, let “u” equal whats in the square root

and

dont forget to get “du” to replace “dx”

as well as changing the limits based on “u”

Question 33

two distinct points

Answer 33

use b^2 - 4ac > 0