AQA A Level 2022 Paper 2 - IFEM

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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

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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]

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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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