Question 8:
--- 8(a) ---
8(a) | States the correct derivative | AO1.1b | B1 | 2xln2
(b) | Selects an appropriate method
for integrating, which could lead
to a correct exact solution
(this could be indicated by an
attempt at a substitution or
attempting to write the
integrand in the form
f'(x)f(x)n) | AO3.1a | M1 | Let u2x
du
Then 2xln2
dx
1 du
And 2x
ln2 dx
1 1 du
I = (3u)2 dx
ln2 dx
1 1
= (3u)2 du
ln2
2 3
= (3u)2 c
3ln2
2
 2 3 
Sub limits: (3u)2 
3ln2 
1
2 1  
× 5 58
3 ln2
ALT (direct inspection)
2x 32x dx
1
 2xln2 32x dx
ln2
1 1
 2xln2(32x)2 dx
ln2
1 2 3
  (32x)2
ln2 3
1
 1 2 3
  (32x)2
ln2 3 
0
2 1
 (5 58)
3 ln2
Correctly writes integrand in a
form which can be integrated
(condone missing or incorrect
limits) | AO1.1b | A1
Integrates ‘their’ expression
(allow one error) | AO1.1a | M1
Substitutes correct limits
corresponding to ‘their’ method | AO1.1a | M1
Obtains correct value in an
exact form | AO1.1b | A1
Mark awarded if they have a
completely correct solution,
which is clear, easy to follow
and contains no slips
Substitution should be clearly
stated in exact form and change
of variable or solution by direct
inspection should be achieved
correctly with correct use of
symbols and connecting
language | AO2.1 | R1
Total | 7
Q | Marking Instructions | AO | Marks | Typical Solution