ACTUAL 2025 AQA AS FURTHER MATHEMATICS Paper 1 Question Paper & Mark Scheme (Merged) Monday 12 May 2025 [VERIFIED]

ACTUAL 2025 AQA AS FURTHER MATHEMATICS Paper 1 Question Paper & Mark Scheme
(Merged) Monday 12 May 2025 [VERIFIED]

, 2
Do not write
outside the
box
Answer all questions in the spaces provided.



1 Calculate the product

(3 + i)(2 – i)

Circle your answer.
[1 mark]

5–i 5+i 7–i 7+i




2 The complex number 3 + 5i is a root of the quadratic equation

z2 + az + b = 0

where a and b are real constants.

Find the other root of the equation.

Circle your answer.
[1 mark]

3 – 5i 3 + 5i 5 – 3i 5 + 3i




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, 3
Do not write
outside the
box
3 Find the equations of the asymptotes of the curve with equation
(x – 1)(x + 2)
y = (x + 1)(x – 2)

Tick () one box.
[1 mark]


x = 1, x = –2, y = 1


x = 1, x = –2, y = –1


x = –1, x = 2, y = 1


x = –1, x = 2, y = –1




4 Find the first two non‑ zero terms of the Maclaurin series expansion of cos (2x)

Tick () one box.
[1 mark]


1 – x2


1 – 2 x2


2 – x2


2 – 2x2




Turn over U


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, 4
Do not write
outside the
box
5 The quartic equation

3 x 4 + x 2 – 5x – 11 = 0

has roots α, β, γ and δ

5 (a) Write down the value of αβγδ
[1 mark]




5 (b) Write down the value of αβγ + αβδ + αγδ + βγδ
[1 mark]




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