o.e. (NB must be positive) A1 Attempts to take out or or M1 x –x. Substitutes for in o.e. or awrt 6160 A1 x (4 marks) Differentiates o.e. M1 f ʹ(x) Substitutes into f States , so in part b is a maximum value. A1 V ʹʹ(x) (2 marks) Total: 11 marks A sketch of a rectangular prism with a base of by and a height of is acceptable NOTES: (a): x x h for the first method mark. (c): Other complete methods for demonstrating that is a maximum are acceptable. V For example a sketch of the graph of against or calculation of values of or V x V on either side.
o.e. (NB must be positive) A1 Substitutes for x in o.e. or awrt 6160 A1 (4 marks) Differentiates f ʹ(x) o.e. M1 Substitutes into f ʹʹ(x) States , so V in part b is a maximum value. A1 (2 marks) Total: 11 marks NOTES: (a): A sketch of a rectangular prism with a base of x by x and a height of h is acceptable for the first method mark. (c): Other complete methods for demonstrating that V is a maximum are acceptable. For example a sketch of the graph of V against x or calculation of values of V or on either side. Attempts to take out x or –x. or M1
19725_02_as_pure_mathematics_practice_paper_a_mark_scheme.docx