AQA A Level 2022 Paper 2 - IFEM
[Pages:28]Page 1 of 28
AQA A-Level Maths 2022 Paper 2
Do not turn over the page until instructed to do so.
This assessment is out of 100 marks and you will be given 120 minutes.
When you are asked to by your teacher write your full name below
Name: Total Marks:
/ 100
DrBennison
ff
Page 2 of 28
1 The centre and radius of the circle x2 - 6x + y2 + 4y - 1 = 0 are:
Centre : (3, - 2) Radius : 14
Centre : (3, - 2)
Radius : 13
Centre : (-3,2) Radius : 14
Centre : (-3,2)
Radius : 13
[1 mark]
2 Write as a single logarithm 5 log (x) + log (y3z6) - log (xz)
log(yz)
log (x3y3z4)
log (x4y3z5)
log (x5 + y3z6 - xz)
[1 mark]
3 a) Prove that 53 is a prime number.
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[2 marks]
b) Disprove the statement "For n , n3 + 3n - 5 always prime".
[2 marks]
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4 a) Find and classify the stationary points of the polynomial
p(x) = 2x3 + 3x2 - 72x + 18
[5 marks]
b) What would the stationary points of f (x + 2) + 3 be?
[2 marks]
Page 5 of 28
5
Joshua is trying to
nd
the
derivative
of
y
=
1 x
by
rst principles.
He begins by writing:
dy dx
= lim
h0
1 x+h
-
h
1 x
=
lim
h0
h
-h x + h2
a) Identify the mathematical errors Joshua has made.
[2 marks]
if if
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b) Write a complete, rigorous proof for the derivation of the
derivative
of
y
=
1 x
from
rst principles.
if
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6 a) Find the rst three terms, in ascending powers of x, of the
binomial expansion of
1
3 8 + 2x
[3 marks]
b) Hence, nd the expansion of
1
3 8 - 2x2
[2 marks]
if if
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c) Millie uses the rst three terms of the expansion found in (b) to
1 2
nd an approximation to the the integral 0
2 3 8 - 2x2
dx.
Evaluate this approximation.
[3 marks]
if if
................
................
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