Forgottone Knowldege Flashcards
What does the discriminate b2 -4ac tell you
If 0 = one real
If above 2 real
If below then none
Damn if it says ALTEAST ONE then it means either one OR TWO thus it’s a greater than = to sign!
Can loose easy marks like this
Remember dividing by - sign for inequalities?
Flip the sign
Two lines are parallel vs perpendicularly about grsdienrs
Same vs -1
Remember circled thst when a chord bisected it always goes through the
Radius
Thus 3 points ti find equation find the equation if the line of the visecotrs if bith and equate will give you the coordinated and then it should be easy
Things about the sun and case graphs
Sin has rotational symmetry about origin so that sin 10 = x is same as sin-10 =-x
Cos has symmetry abkut origin so that cos 90 = cos-90
Sin also has some too lol
Tan also has rotational symmetry, sin and tan
So why can’t sometimes you divide by say cos theta or sin theta
But when can you?
Because in case they might be 0, ofc yiu csn’t divide by 0 as that’s not possible
Say you want to divide by cos0 check what happens if it is 0
If cos theta is 0, the. See if sin theta has to be 0. If it is, then yiu can divide because this means cos theta can’t be 0 as sin theta can’t be 0 too for the same values of
Thus you can divide! And make tan and continue
For trig try to factorise first and be wary of dividing by cos0 (0) not actually multiplying
Remember square rooting in trig thingd gives you plus - so way more solutions
Remember even if you factorise and have anither solution, always check first if thst can even be 0. If it can then go ahead if not then ignore!
Remember for the ambiguous case and see if the other is a solution too
What happens if other is a solution
This is importsnt , write bith of them down!
What is cosine rule bruv
A2= b2 + c2 -2bc CosA
Area of a triangle
1/2ab sin c, works for ANY TRIANGLE
If it’s cos 2x, then it repeats every 180 now (remember all x values oppsite), so have to say + 180 etc
Remember if they give sin theta then yiu can use solid values in the identities, get values for cos theta and tan without even knowing what theta is
If they gave you a graoh especially in jnequakities it’s for a reason, make sure to use it to answer final psrt of question stuck on
Polynomials
How to add and subtract
Just do that normally
Rules for graphs of polynomials (roots and turning points )
At most it has n amount of roots if it is degree n
And n-1 turning points if it’s degree n
(Rest if the roots are complex )
Quartier shapes
These are W and m or just close together
Sketching a graoh what do you need
Amd if one root is x what will y be always!
All intersections with axis INCLUDING Y
If one root is x y will have to be 0 too!
Factor theorem
What will this usually be?
If f (2) = 0, then x-2 a factor
Etc
A factor of thr k constant
When factorising make sure ti show discriminate is less than 0 or something ti show it can’t be factorised anymore, use cal first to check then do
Remmeber there is normally a constant a at the start of every polynomial, so if the y intercept isn’t matching thstswhy
Also what should you just do Esch time
Put in Calculator it’s easier
