Mathematics · May / June 2022 · Paper 42 · Question 12
0580
As printed in the paper
The question as text
A curve has equation y x kx 1 3 2 = - + . When x 2 = , the gradient of the curve is 6.
Read automatically from the paper; the printed page above is exact.
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12(a)[5]
3 x 2 − 2 kx their d y x = 6 d x = 2 substituted in their d y x d Correct working leading to 1.5 oe [8]
−kx
M2 M1 for 3x or 2 2 M1 Dep on at least
M1 for derivative M1 Dep on at least
M1 for derivative A1 A0 if any errors in working leading to 1.5
12(b)[4]
( 0, 1) ( 1, 0.5) [4]
B3 for x = 0 and x = 1 or for (1, 0.5) OR
M1 for their d y x = 0 d
B1 for 2 − x oe or better 3 x 3
12(c)[2]
correct sketch [2]
with max on positive y-axis and min in 1st quadrant
B1 for positive cubic or for graph with one max which is on pos y-axis and one min which is in 1st quadrant
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