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AQA A LEVEL FURTHER MATHEMATICS 7367/2D PAPER 3 DISCRETE VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
The simple-connected graph G is shown below. 
The graph G has n faces. 
State the value of n 
Circle your answer. 
[1 mark] 
2 3 4 5 
2 Jonathan and Hoshi play a zero-sum game. 
The game is represented by the following pay-off matrix for Jonathan. 
Hoshi 
Strategy H1 H2 H3 
Jonathan 
J1 ÿ2 3 2 
J2 3 2 0 
J3 4 ÿ1 3 
J4 3 1 0 
The game does not have a stable solution. 
Which strategy should Jonathan never play? 
Circle your answer. 
[1 mark] 
J1 J2 J3 J4 
Jun23/7367/3D 
Do not write 
outside the...
- Exam (elaborations)
- • 38 pages •
The simple-connected graph G is shown below. 
The graph G has n faces. 
State the value of n 
Circle your answer. 
[1 mark] 
2 3 4 5 
2 Jonathan and Hoshi play a zero-sum game. 
The game is represented by the following pay-off matrix for Jonathan. 
Hoshi 
Strategy H1 H2 H3 
Jonathan 
J1 ÿ2 3 2 
J2 3 2 0 
J3 4 ÿ1 3 
J4 3 1 0 
The game does not have a stable solution. 
Which strategy should Jonathan never play? 
Circle your answer. 
[1 mark] 
J1 J2 J3 J4 
Jun23/7367/3D 
Do not write 
outside the...
AQA A LEVEL MATHEMATICS 7367/2 PAPER 2 VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
Given that y ¼ sin x þ sinh x , find d2y 
dx2 þ y 
Circle your answer. 
[1 mark] 
2 sin x ÿ2 sin x 2 sinh x ÿ2 sinh x 
2 Which one of the expressions below is not equal to zero? 
Circle your answer. 
[1 mark] 
lim 
x ! 1 
(x2eÿx) lim 
x ! 0 
(x5 ln x) lim 
x ! 1 
ex 
 x5 xlim ! 0(x3ex)
- Exam (elaborations)
- • 52 pages •
Given that y ¼ sin x þ sinh x , find d2y 
dx2 þ y 
Circle your answer. 
[1 mark] 
2 sin x ÿ2 sin x 2 sinh x ÿ2 sinh x 
2 Which one of the expressions below is not equal to zero? 
Circle your answer. 
[1 mark] 
lim 
x ! 1 
(x2eÿx) lim 
x ! 0 
(x5 ln x) lim 
x ! 1 
ex 
 x5 xlim ! 0(x3ex)
AQA A LEVEL FURTHER MATHEMATICS 7367/1 PAPER 1 VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
Find the number of solutions of the equation tanh x ¼ cosh x 
Circle your answer. 
[1 mark] 
0 1 2 3 
2 The diagram below shows a locus on an Argand diagram. 
2 Re 
Im 
–3 
O 
Which of the equations below represents the locus shown above? 
Circle your answer. 
[1 mark] 
jz ÿ 2 þ 3ij ¼ 2 jz þ 2 ÿ 3ij ¼ 2 jz ÿ 2 þ 3ij ¼ 4 jz þ 2 ÿ 3ij ¼ 4
- Exam (elaborations)
- • 52 pages •
Find the number of solutions of the equation tanh x ¼ cosh x 
Circle your answer. 
[1 mark] 
0 1 2 3 
2 The diagram below shows a locus on an Argand diagram. 
2 Re 
Im 
–3 
O 
Which of the equations below represents the locus shown above? 
Circle your answer. 
[1 mark] 
jz ÿ 2 þ 3ij ¼ 2 jz þ 2 ÿ 3ij ¼ 2 jz ÿ 2 þ 3ij ¼ 4 jz þ 2 ÿ 3ij ¼ 4
AQA AS FURTHER MATHEMATICS 73666/2M PAPER 2 MECHANICS VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
A particle moves along the x‑axis under the action of a force, F newtons, where 
F = 3x2 + 5 
Find the work done by the force as the particle moves from x = 0 metres 
to x = 2 metres. 
Circle your answer. 
[1 mark] 
12 J 17 J 18 J 34 J 
2 Two particles are moving directly towards each other when they collide. 
Given that the collision is perfectly elastic, state the value of the coefficient 
of restitution. 
Circle your answer. 
[1 mark] 
e = –1 e = 0 e = 1 
2 e = 1 
3 A stone of mass 0.2 kg...
- Exam (elaborations)
- • 29 pages •
A particle moves along the x‑axis under the action of a force, F newtons, where 
F = 3x2 + 5 
Find the work done by the force as the particle moves from x = 0 metres 
to x = 2 metres. 
Circle your answer. 
[1 mark] 
12 J 17 J 18 J 34 J 
2 Two particles are moving directly towards each other when they collide. 
Given that the collision is perfectly elastic, state the value of the coefficient 
of restitution. 
Circle your answer. 
[1 mark] 
e = –1 e = 0 e = 1 
2 e = 1 
3 A stone of mass 0.2 kg...
AQA AS FURTHER MATHEMATICS 7366/2S PAPER 2 STATISTICS VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
The continuous random variable X has variance 9 
The discrete random variable Y has standard deviation 2 and is independent of X 
Find Var(X + Y ) 
Circle your answer. 
[1 mark] 
5 11 13 85 
2 The random variable T has a discrete uniform distribution and takes the 
values 1, 2, 3, 4 and 5 
Find the variance of T 
Circle your answer. 
[1 mark] 
15 
43 
2 13 
6 
Turn over for the next question
- Exam (elaborations)
- • 31 pages •
The continuous random variable X has variance 9 
The discrete random variable Y has standard deviation 2 and is independent of X 
Find Var(X + Y ) 
Circle your answer. 
[1 mark] 
5 11 13 85 
2 The random variable T has a discrete uniform distribution and takes the 
values 1, 2, 3, 4 and 5 
Find the variance of T 
Circle your answer. 
[1 mark] 
15 
43 
2 13 
6 
Turn over for the next question
AQA AS FURTHER MATHEMATICS 7366/2M PAPER 2 MECHANICS VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
A particle moves along the x‑axis under the action of a force, F newtons, where 
F = 3x2 + 5 
Find the work done by the force as the particle moves from x = 0 metres 
to x = 2 metres. 
Circle your answer. 
[1 mark] 
12 J 17 J 18 J 34 J 
2 Two particles are moving directly towards each other when they collide. 
Given that the collision is perfectly elastic, state the value of the coefficient 
of restitution. 
Circle your answer. 
[1 mark] 
e = –1 e = 0 e = 1 
2 e = 1 
3 A stone of mass 0.2 kg...
- Exam (elaborations)
- • 29 pages •
A particle moves along the x‑axis under the action of a force, F newtons, where 
F = 3x2 + 5 
Find the work done by the force as the particle moves from x = 0 metres 
to x = 2 metres. 
Circle your answer. 
[1 mark] 
12 J 17 J 18 J 34 J 
2 Two particles are moving directly towards each other when they collide. 
Given that the collision is perfectly elastic, state the value of the coefficient 
of restitution. 
Circle your answer. 
[1 mark] 
e = –1 e = 0 e = 1 
2 e = 1 
3 A stone of mass 0.2 kg...
AQA AS FURTHER MATHEMATICS 7366/2D PAPER 2 DISCRETE VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
The graph G has 8 vertices and 13 edges as shown in the diagram below. 
P 
Q S T V 
R 
U W 
Graph H is a simple‑connected subgraph of graph G 
Which of the following diagrams could represent graph H ? 
Tick () one box. 
[1 mark] 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V
- Exam (elaborations)
- • 34 pages •
The graph G has 8 vertices and 13 edges as shown in the diagram below. 
P 
Q S T V 
R 
U W 
Graph H is a simple‑connected subgraph of graph G 
Which of the following diagrams could represent graph H ? 
Tick () one box. 
[1 mark] 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V 
P Q 
U T 
R S 
W V
AQA AS FURTHER MATHEMATICS 7366/1 PAPER 1 VERSION 1.0 FINAL QUESTIONS WITH A MERGED MARKING SCHEME|JUNE 2023
Which expression below is equivalent to tanh x ? 
Circle your answer. 
[1 mark] 
sinh x cosh x sinh x 
cosh x 
cosh x 
sinh x 
sinh x + cosh x 
2 The two vectors a and b are such that a.b = 0 
State the angle between the vectors a and b 
Circle your answer. 
[1 mark] 
0° 45° 90° 180
- Exam (elaborations)
- • 50 pages •
Which expression below is equivalent to tanh x ? 
Circle your answer. 
[1 mark] 
sinh x cosh x sinh x 
cosh x 
cosh x 
sinh x 
sinh x + cosh x 
2 The two vectors a and b are such that a.b = 0 
State the angle between the vectors a and b 
Circle your answer. 
[1 mark] 
0° 45° 90° 180
AQA GERMAN 7662/2 PAPER 2 WRITING VERSION 1.0 FINAL VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
Heinrich Böll: Die verlorene Ehre der Katharina Blum 
Either 
0 1 . 1 Die einen nennen Katharina eine Nonne, die anderen eine Mörderbraut. Wofür 
halten Sie Katharina? Erklären Sie warum. 
[40 marks] 
or 
0 1 . 2 „Man kann sich in dieser Gesellschaft auf niemanden verlassen.“ Inwiefern stimmt 
diese Aussage für dieses Werk? 
[40 marks] 
0 2 Bertolt Brecht: Mutter Courage und ihre Kinder 
Either 
0 2 . 1 Inwiefern spielt das Thema Treue eine wichtige Rolle in diesem Theaterstück? 
[40 m...
- Exam (elaborations)
- • 34 pages •
Heinrich Böll: Die verlorene Ehre der Katharina Blum 
Either 
0 1 . 1 Die einen nennen Katharina eine Nonne, die anderen eine Mörderbraut. Wofür 
halten Sie Katharina? Erklären Sie warum. 
[40 marks] 
or 
0 1 . 2 „Man kann sich in dieser Gesellschaft auf niemanden verlassen.“ Inwiefern stimmt 
diese Aussage für dieses Werk? 
[40 marks] 
0 2 Bertolt Brecht: Mutter Courage und ihre Kinder 
Either 
0 2 . 1 Inwiefern spielt das Thema Treue eine wichtige Rolle in diesem Theaterstück? 
[40 m...
AQA GEOGRAPHY PAPER 1 7036/1,PAPER 2 7036/2
AQA GEOGRAPHY PAPER 1 7036/1,PAPER 2 7036/2 VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
- Package deal
- • 2 items •
- AQA AS GEOGRAPHY 7036/1 PAPER 1 PHYSICAL GEOGRAPHY AND PEOPLE AND THE ENVIRONMENT VERSION 1.0 FINAL QUESTION WITH MERGED MARKING SCHEME |JUNE 2023 • Exam (elaborations)
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AQA GEOGRAPHY PAPER 1 7036/1,PAPER 2 7036/2 VERSION 1.0 FINAL QUESTIONS WITH MERGED ANSWERS |JUNE 2023
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