Mathematics · May / June 2026 · Paper 21 · Question 24

(0, 7) (4, –25) [6]

B2 for 3x2 – 12x isw second derivative. Condone poor notation for derivative. e.g.

B2 for y = 3x2 – 12x, similarly for M1.

or M1 for intention to find derivative soi by 3x2 + kx or kx2 – 12x or 3x2 – 12x + 7

M1 for setting their d y their d y x = 0 x must not be second derivative. d d or stating d y x = 0 d

M1 for correct method to solve their x(3x – 12) quadratic, e.g. [3]x(x – 4) oe ( ) ( )( ) −− ± − 2 − 12 12 4 3 0 or oe ( ) 2 3

B1 for (4, –25) or for x = 0 and x = 4 soi

A correct sketch with (0, 7) maximum stated (4, –25) minimum stated [3]

B2 for a correct sketch with (0, 7) maximum stated or (4, –25) minimum stated or for a correct sketch with appropriate points labelled as maximum and minimum or for a correct sketch with (0, 7) and (4, –25) marked at the maximum and minimum points For M1, cubic may be positive or negative.

or M1 for reasonable sketch of any cubic Cubic should have only two turning points. Ignore position of any horizontal and / or vertical axes drawn.

or B1 for a sketch not of cubic shape with 0 marks if no sketch drawn. identification of local maximum at (0,7) and a local minimum at (4,-25)