Question 6:
6 | (i) | x = 4
(4, 3) | B1
B1
[2] | or x = 4, y = –3 | condone 4, 3
6 | (ii) | (0, 13) isw
[when y = 0, ] (x 4)2 = 3
8 12
[x ]4 3 or isw
2 | 1
M1
A2
[4] | or [when x = 0], y = 13 isw
0 for just (13, 0) or (k, 13) where k ≠ 0
or x2 8x + 13 [= 0]
need not go on to give coordinate form
A1 for one root correct | annotate this question if partially correct
may be implied by correct value(s) for x
found
allow M1 for y = x2 8x + 13 only if
they go on to find values for x as if y
were 0
6 | (iii) | replacement of x in their eqn by (x 2)
completion to given answer y = x2 12x + 33,
showing at least one correct interim step | M1
A1
[2] | may be simplified; eg [y = ] (x 6)2 3
or allow M1 for (x 6 3)(x 6 + 3)
[=0 or y]
cao; condone using f(x 2) in place of y | condone omission of ‘y =’ for M1, but
must be present in final line for A1
6 | (iv) | x2 12x + 33 = 8 2x or
(x 6)2 3 = 8 2x
x2 10x + 25 = 0
(x 5)2 [= 0]
x = 5 www [so just one point of contact]
point of contact at (5, 2)
alt. method
for curve, y = 2x 12
2x 12 = 2
x = 5, and y shown to be 2 using eqn to
curve
tgt is y + 2 = 2 (x 5)
deriving y = 8 2x | M1
M1
A1
A1
A1
or
M1
M1
A1
A1
A1
[5] | for equating curve and line; correct eqns
only;
or for attempt to subst (8 y)/2 for x in
y = x2 12x + 33
for rearrangement to zero, condoning one
error such as omission of ‘= 0’
or showing b2 = 4ac
may be part of coordinates (5, k)
dependent on previous A1 earned;
allow for y = 2 found
for equating their y to 2 | annotate this question if partially correct
10 0
allow oe if b2 4ac = 0 is not
2
used explicitly
A0 for (x 5)2 = y
allow recovery from (x 5)2 = y
examiners: use one mark scheme or the
other, to the benefit of the candidate if
both methods attempted, but do not use a
mixture of the schemes
condone no further interim step if all
working in this part is correct so far