Moderate -0.5 This is a straightforward application of the first principles definition of differentiation to a simple polynomial. While it requires careful algebraic manipulation and understanding of the limit process, it's a standard textbook exercise with no conceptual surprises—easier than average because the algebra is routine and the question type is well-practiced.
Question 5:
5 | Uses correct formula and notation
for this function; must have
substituted (x +h) correctly | 1.1a | M1 | lim 4(x +h)2 + (x +h) – (4x2 + x)
h→0 h
lim 4x2 + 8xh + 4h2 + x + h – 4x2 – x
h→0 h
lim 8xh + 4h2 + h
h→0 h
lim (8x + 4h + 1)
h→0
= 8x + 1
Multiplies out 4(x +h)2 correctly | 1.1b | B1
Obtains numerator with no x2 or x
terms PI | 1.1b | A1
Completes rigorous argument,
including dividing by h and correctly
using limit | 2.1 | R1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution