AQA A-level MATHEMATICS Paper 2 June 2023

AQA

A-level
MATHEMATICS
Paper 2

June 2023

, 2
Do not write
outside the
Section A box


Answer all questions in the spaces provided.




1 The graph of y = ax2 + bx + c has roots x = 2 and x 5 , as shown in the
diagram below. =

y




O 2 5 x




State the set of values of x which satisfy

ax 2 + bx + c > 0
Tick () one box.
[1 mark]
{x : x < 2} ¨ {x : x > 5}


{x : 0 < x < 2} ˙{ x : x >
5}


{x : 2 < x < 5}


{x : 2 > x > 5}




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Jun23/7357/2

, 3
Do not write
outside the
2 It is given that box


ð6 ð6
f (x) d x= 20 and f (x) d x = —
0 10
3
ð 3
Find the value of f (x) d
0 x
Circle your answer.
[1 mark]
—30 —10 10 30




3 A circle has equation

(x — 5)2 + ( y — 13)2 =
16
Find the radius of the circle.

Circle your answer.
[1 mark]

4 12 16 256




Turn over for the next question




Turn over


Jun23/7357/2

, 4
Do not write
outside the
4 A curve has equation box


x2 ,ffiffi
ffi

y= +4
dy x 8
4 (a) Find an expression for
dx
[3 marks]




4 (b) The point P with coordinates (4, 10) lies on the curve.

Find an equation of the tangent to the curve at the point P
[2 marks]




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Jun23/7357/2