AQA AS MATHEMATICS PAPER 2
NEWEST UPDATED 2026-2027 REAL
FINAL EXAM WITH COMPLETE
DETAILED QUESTIONS AND
CORRECT VERIFIED ANSWERS WITH
RATIONALES ALREADY A+ GRADED
1. The curve
y=x
3
−6
x
2
+9
x
+1
y=x
3
−6x
2
+9x+1 has a stationary point at
x
= 1 x=1. The nature of this stationary
point is:
A) Local maximum
B) Local minimum
C) Point of inflection
,D) Not a stationary point
Correct Answer: A – Local maximum
Rationale:
dyd
x
=3
x
2
− 12
x
+9
dx
dy
=3x
2 −12x+9.
At x
=1
x=1,
dy
d
x
=0
dx
dy
,=0. Second derivative
d2yd
x
2
=6
x−
12
dx 2
d 2
y
=6x−12. At x
=
1
x=1,
d2
yd
x
2
=
−
6
<0
dx
2
d 2
, y
=−6<0, so local maximum.
2. The binomial expansion of
(
1
+
2
x
)
5
(1+2x) 5 in ascending
powers of x
x up to and including the
x2
x 2
term is:
A)
1
+ 10
x+
40
x
2
1+10x+40x
2
NEWEST UPDATED 2026-2027 REAL
FINAL EXAM WITH COMPLETE
DETAILED QUESTIONS AND
CORRECT VERIFIED ANSWERS WITH
RATIONALES ALREADY A+ GRADED
1. The curve
y=x
3
−6
x
2
+9
x
+1
y=x
3
−6x
2
+9x+1 has a stationary point at
x
= 1 x=1. The nature of this stationary
point is:
A) Local maximum
B) Local minimum
C) Point of inflection
,D) Not a stationary point
Correct Answer: A – Local maximum
Rationale:
dyd
x
=3
x
2
− 12
x
+9
dx
dy
=3x
2 −12x+9.
At x
=1
x=1,
dy
d
x
=0
dx
dy
,=0. Second derivative
d2yd
x
2
=6
x−
12
dx 2
d 2
y
=6x−12. At x
=
1
x=1,
d2
yd
x
2
=
−
6
<0
dx
2
d 2
, y
=−6<0, so local maximum.
2. The binomial expansion of
(
1
+
2
x
)
5
(1+2x) 5 in ascending
powers of x
x up to and including the
x2
x 2
term is:
A)
1
+ 10
x+
40
x
2
1+10x+40x
2
