AQA
A-level
FURTHER MATHEMATICS
Paper 2
June 2023
, 2
Do not write
Answer all questions in the spaces provided. outside the
box
1 Given that y = sin x + sinh x , d2y +
find d x2
y
Circle your answer.
[1 mark]
2 sin x —2 sin x 2 sinh x —2 sinh
x
2 Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
lim (x2 e—x ) lim (x5 ln x) lim
ex lim (x3 ex)
x →∞ x→0 x →∞ x5 x→ 0
Jun23/7367/2
, 3
Do not write
1 1 1 outside the
box
3 The determinant A = 2 0 2
3 2 1
Which one of the determinants below has a value which is not equal to the value of A?
Tick () one box.
[1 mark]
3 1 3
2 0 2
3 2 1
1 2 3
1 0 2
1 2 1
2 2 2
1 0 1
3 2 1
1 1 1
3 2 1
2 0 2
4 It is given that f (x) = cosh—1 (x —
3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x ≥ 4g fx : x ≥ 3g fx : x ≥ 1g fx : x ≥
0g
Turn over
Jun23/7367/2
A-level
FURTHER MATHEMATICS
Paper 2
June 2023
, 2
Do not write
Answer all questions in the spaces provided. outside the
box
1 Given that y = sin x + sinh x , d2y +
find d x2
y
Circle your answer.
[1 mark]
2 sin x —2 sin x 2 sinh x —2 sinh
x
2 Which one of the expressions below is not equal to zero?
Circle your answer.
[1 mark]
lim (x2 e—x ) lim (x5 ln x) lim
ex lim (x3 ex)
x →∞ x→0 x →∞ x5 x→ 0
Jun23/7367/2
, 3
Do not write
1 1 1 outside the
box
3 The determinant A = 2 0 2
3 2 1
Which one of the determinants below has a value which is not equal to the value of A?
Tick () one box.
[1 mark]
3 1 3
2 0 2
3 2 1
1 2 3
1 0 2
1 2 1
2 2 2
1 0 1
3 2 1
1 1 1
3 2 1
2 0 2
4 It is given that f (x) = cosh—1 (x —
3)
Which of the sets listed below is the greatest possible domain of the function f ?
Circle your answer.
[1 mark]
fx : x ≥ 4g fx : x ≥ 3g fx : x ≥ 1g fx : x ≥
0g
Turn over
Jun23/7367/2
