Moderate -0.3 This is a straightforward application of the quotient rule with standard derivatives (x³ and sin x). While it requires careful algebraic manipulation to avoid sign errors, it's a routine calculus exercise with no conceptual difficulty or problem-solving required—slightly easier than the average A-level question due to its mechanical nature.
Question 5:
5 | Differentiates x3 and sinx
to obtain 3x2 and cosx
OE | 1.1b | B1 | dy 3x2sinx−x3cosx
=
dx sin2 x
Uses the quotient rule and
obtains numerator
Ax2sinx±Bx3cosx
Condone any denominator
Or
Writes as a product and applies
the product rule to obtain
Ax2cosec(x)±x3cosec(x)cot(x) | 3.1a | M1
3x2sinx−x3cosx
Obtains
sin2 x
ACF
No ISW | 1.1b | A1
Question 5 Total | 3
Q | Marking instructions | AO | Marks | Typical solution