ty
#da
opal spire
first q - 8/8 well done
for 2 i) i'll give you 2/3 bc you just need a line to say "squares of real numbers are always positive so therefore (x-4)^2 > 0"
for 2ii) i'll give you 1/2 bc your answer is correct but the reasoning would be better if you just gave one example eg. x = 1 and x = -3 or smth like that (once when it holds, once when it doesnt)
3a is lovely 2/2 :)
3b) you've done the hard work, you've just got to factorise your quadratic so that you've got it in the form of (ax+b)^2 which you do in part c so yk how to do it but yh ill have to drop you a mark for that
3/4
3c is lovely asw :) 3/3
yh alright fine
ill give you 2/2 then ðŸ˜
it's just subbing in x = 15 and showing profits would be negative which is silly
cool
for 4b) they wanted you to set up an inequality so P > 80 and then rearrange the quadratic.
your c) is good though 2/2
you need to show a bit more working for q5. act liek you just happened to guess 2 was a factor and do factor theorem to confirm it, then do long polynomial divison to find a quadratic to find the other two factors with
bc there youve clearly just put it in your calc (which is fine to check and work backwards from btw) youd prob only get like 2 or so
7c it says -f(x-a) whereas youve just done f(x-a) so you'd drop one mark there but the rest of q7 is correct!! 3/4 :)
q8 is lovely 7/7
yh it is
that was really good of you
acc yh you might get 3 marks bc you noticed that
i think it should be the triangle on the bototm
w the x-axis
bc y <= 3x
but youd still get 2 marks or so bc you did the hard part
so id say prob like 75%
overall
which is pretty gooododddd well done!
no problem
lmk if theres anything else i can do
opal spire
yeah write it like the factorised form
like just write (t-2)(t-3)(t-5) to make it look like youve not done it in your calc
when its 7 marks they wont just let you put it in your calc
maybe 3 marks was harsh but you def wouldnt get 7
erm possibly depends on examiner
and also depends on mark scheme
opal spire
you can find what side by using a random coordinate. if you choose a random coordinate like (0, 3) (which is on the right of the line) then that doesnt work bc 3 <= 0 isnt true