AQA
A-level
MATHEMATICS
Paper 1
June 2023
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 Find the coefficient of x 7 in the expansion of (2x — 3)7
Circle your answer.
[1 mark]
—2187 —128 2 128
dy
3
2 Given that y = 2x find
dx
Circle your answer.
[1 mark]
dy dy dy x4 dy
2 2 3
= =
dxx = dx = 6x
5 dxx
6 dx
2
Jun23/7357/1
, 3
Do not write
outside the
3 The curve with equation y = ln x is transformed by a stretch parallel to the x-axis with box
scale factor 2
Find the equation of the transformed curve.
Circle your answer.
[1 mark]
1
y = ln x y = 2 ln x y = ln y = ln
2 2
x 2x
4 Given that y is a small angle, find an approximation for cos 2y
Circle your answer.
[1 mark]
y2 2 2 2
1— 2 — 2y 1 — 2y 1—y
2
Turn over for the next question
Turn over
s
Jun23/7357/1
, 4
Do not write
outside the
5 box
5 The graph of y = is shown in the diagram below.
ex — 1
y
O 1 4 x
The trapezium rule with 6 ordinates (5 strips) is to be used to find an approximation
for the shaded area.
The values required to obtain this approximation are shown in the table below.
x 1 1.6 2.2 2.8 3.4 4
y 2.90988 1.26485 0.62305 0.32374 0.17263 0.09329
5 (a) Use the trapezium rule with 6 ordinates (5 strips) to find an approximate value for the
shaded area.
Give your answer to four decimal places.
[3 marks]
Jun23/7357/1
A-level
MATHEMATICS
Paper 1
June 2023
, 2
Do not write
outside the
Answer all questions in the spaces provided. box
1 Find the coefficient of x 7 in the expansion of (2x — 3)7
Circle your answer.
[1 mark]
—2187 —128 2 128
dy
3
2 Given that y = 2x find
dx
Circle your answer.
[1 mark]
dy dy dy x4 dy
2 2 3
= =
dxx = dx = 6x
5 dxx
6 dx
2
Jun23/7357/1
, 3
Do not write
outside the
3 The curve with equation y = ln x is transformed by a stretch parallel to the x-axis with box
scale factor 2
Find the equation of the transformed curve.
Circle your answer.
[1 mark]
1
y = ln x y = 2 ln x y = ln y = ln
2 2
x 2x
4 Given that y is a small angle, find an approximation for cos 2y
Circle your answer.
[1 mark]
y2 2 2 2
1— 2 — 2y 1 — 2y 1—y
2
Turn over for the next question
Turn over
s
Jun23/7357/1
, 4
Do not write
outside the
5 box
5 The graph of y = is shown in the diagram below.
ex — 1
y
O 1 4 x
The trapezium rule with 6 ordinates (5 strips) is to be used to find an approximation
for the shaded area.
The values required to obtain this approximation are shown in the table below.
x 1 1.6 2.2 2.8 3.4 4
y 2.90988 1.26485 0.62305 0.32374 0.17263 0.09329
5 (a) Use the trapezium rule with 6 ordinates (5 strips) to find an approximate value for the
shaded area.
Give your answer to four decimal places.
[3 marks]
Jun23/7357/1
