AQA A LEVEL MATHS PAPER 3 QUESTION PAPER JUNE 2021

AQA A LEVEL MATHS PAPER 3
QUESTION PAPER JUNE 2021

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A-level
MATHEMATICS
Paper 3


Time allowed: 2 hours
Materials For Examiner’s Use
 You must have the AQA Formulae for A‑ level Mathematics booklet.
 You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
Instructions 2
 Use black ink or black ball‑ point pen. Pencil should only be used for drawing. 3
 Fill in the boxes at the top of this page. 4
 Answer all questions. 5
 You must answer each question in the space provided for that question.
6
If you need extra space for your answer(s), use the lined pages at the end
7
8

, of this book. Write the question number against your answer(s).
 Show all necessary working; otherwise marks for method may be lost.
 Do all rough work in this book. Cross through any work that you do not want
to be marked.

Information
 The marks for questions are shown in brackets.
 The maximum mark for this paper is 100.

Advice
 Unless stated otherwise, you may quote formulae, without proof, from the
booklet.
 You do not necessarily need to use all the space provided.




(JUN2173573D PB/Jun21/E5 7357/3

, 2
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outside the
Section A box




Answer all questions in the spaces provided.




1 The graph of y ¼ arccos x is shown.

y
P




x

State the coordinates of the end point P.

Circle your answer.
[1 mark]

p p
(—p, 1) (—1, p) —2 , 1 —1, 2




(02)
Jun21/7357/3

, 3
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outside the
2 Simplify fully box


(x þ 3)(6 — 2x)
for x ¼ 3
(x — 3)(3 þ x)

Circle your answer.
[1 mark]
(6 — 2x) (2x — 6)
—2 2
(x — 3) (x — 3)




3 f (x) ¼ 3 x 2

Obtain lim f (x þ h) — f (x)
h!0 h
Circle your answer.
[1 mark]
2
3h 3(x þ h)2 — 3x2
x3 6x
h h




Turn over for the next question




Turn over
s




(03)
Jun21/7357/3

, 4
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outside the
4 (a) Show that the first three terms, in descending powers of x, of the expansion of box



(2x — 3)10

are given by

1024x10 þ px9 þ qx8

where p and q are integers to be found.
[3 marks]




4 (b) Find the constant term in the expansion of

10
3
2x —
x
[2 marks]




(04)
Jun21/7357/3

, 5
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outside the
5 A gardener is creating flowerbeds in the shape of sectors of circles. box


The gardener uses an edging strip around the perimeter of each of the flowerbeds.

The cost of the edging strip is £1.80 per metre and can be purchased for any length.

One of the flowerbeds has a radius of 5 metres and an angle at the centre of
0.7 radians as shown in the diagram below.



5m



0.7




5 (a) (i) Find the area of this flowerbed.
[2 marks]




Question 5 continues on the next page




Turn over
s




(05)
Jun21/7357/3

, 6
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outside the
5 (a) (ii) Find the cost of the edging strip required for this flowerbed. box

[3 marks]




5 (b) A flowerbed is to be made with an area of 20 m2

5 (b) (i) Show that the cost, £C, of the edging strip required for this flowerbed is given by

18 20
C¼ þr
5 r

where r is the radius measured in metres.
[3 marks]




(06)
Jun21/7357/3

, 7
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outside the
box




5 (b) (ii) Hence, show that the minimum cost of the edging strip for this flowerbed occurs
when r ≈ 4:5

Fully justify your answer.
[5 marks]




Turn over

(07)
Jun21/7357/3

, 8
Do not write
outside the
6 Given that x > 0 and x 6¼ 25 , fully simplify box


1 3
10 2 x 2 x2
5x
þ — —
pffiffiffi
5— x
Fully justify your answer.
[4 marks]




(0 )
Jun21/7357/3