Mathematics · May / June 2021 · Paper 42 · Question 9

2 [2]

M1 for x(x2 – 4x + 4) or x (x – 2)2 or (x2 – 2x) (x – 2) or x3 – 2ax2 + a2x

Correct sketch with curve passing through O and touching (2, 0) [4]

B1 for any positive cubic

B1 for sketch through or touching O

B1 for sketch with min or max touching x-axis once only but not at (0, 0) B1FT their (a)(i) for sketch with min or max touching x-axis at (their 2, 0) and their 2 is labelled or clearly indicated

y = 20x – 64 final answer nfww [7]

B6 for equivalent correct equation OR

B2 for 3x2 – 8x + 4 isw

or B1 for 3x2 or –8x seen M2dep for [grad =] 20 soi nfww or M1dep for substituting 4 into their derivative isw

B1 for (4, 16) soi M1dep for 16 = their 20 × 4 + c oe