Add maths Important

If quadratic equation only have one root how do u completely factorise it for example 4xsq-12x+9

(2x-3)(2x-3)

If only one root means roots are repeated so 4xsq-12x+9= (2x-3)(2x-3)

dy/dx of tanx

sec sq x

What is the formula for scaling a unit vector

vector = unit vector x magnitude

unit vector = vector / magnitude

How to convert degree into radian

Multiply pie/180

for radian to degree is 180/ pie

When circles touching

When circles dun touch

When one circle is in another and is touching

When one circle is in another and not touching

When two circles overlap with two intersection points

r1+ r2 = distance from two centers AB

r1+ r2 < AB

absolute r1-r2= AB

absolute r1-r2> AB

absolute r1-r2 < AB< r1+r2

Center of circle, expanded and simplfied equation of circle, formula for radius

(a,b) (-g,-f)

(x-a) sq + (y-b) sq = rsq / xsq + ysq +2gx + 2fy+ c= 0

sq root gsq + fsq -c

n!

ex (n+2)(n+1)(n)(n-1)(n-2)!

to change smt ex c into base in log base a x

log base c x/ log base c a

log base a (1/x)=

-log base a x

shape of graph e power -x

exponenet <0 it goes downwards

high on left then low on right

graph shape of -logx

coefficient before log <0 then goes downwards

what is mark scheme wording for

not all value of f function domain is valid as output for g function

Range of f function is not subset of domain of g function

how to test if graph is a

function

one to one

A vertical line meets graph more than once (one input multiple output) not function

A horizontal line meets graph more than once( many to one) not one to one

Factorise xsq-3ax+2asq

(x-a)(x-2a)

When see (smt+ smt else) or (smt - smt else)

what do u do

use conjugate by flipping connecting sign

ex (smt+ smt else)(smt- smt else)

If negative in In log e is infront of x what happens

If negative is infont -Inx -e -log what happens

Infront x flips graph horizontally

Negative coefficient infront flips graph vertically

For trigonometry can u divide by a trig function

Yes but u need to make sure the trig function u r dividing by is not equal 0

a

b

a

b

a

b

Whenever you square both sides during solving (especially with square roots), you MUST substitute every solution back into the original equation to check it’s genuinely valid — domain checking alone isn’t enough.

-

when can use Inx 1/x rule

integrating 1/x to Inx make sure (x) the power is 1 not anything else if anything else cant integrate Inx

No matter what is inside Inx u can differentiate to 1/x

b

b

b

b

when does the integration of smt power smt work

when smt is linear x

ex (2x+1) power 2 can act as u

u power 2 then integrate

u power 3 /3 dydx