AQA A-level MATHEMATICS Paper 3 QP 2021

AQA A-level MATHEMATICS Paper 3 QP 2021




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I declare this is my own work.



A-level
MATHEMATICS
Paper 3


Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the AQA Formulae for A‑level Mathematics booklet.
l You should have a graphical or scientific calculator that meets the Question Mark
requirements of the specification. 1
Instructions 2
l Use black ink or black ball-point pen. Pencil should only be used for drawing. 3
l Fill in the boxes at the top of this page. 4
l Answer all questions. 5
l You must answer each question in the space provided for that question.
If you need extra space for your answer(s), use the lined pages at the end 6
of this book. Write the question number against your answer(s). 7
l Show all necessary working; otherwise marks for method may be lost. 8
l Do all rough work in this book. Cross through any work that you do not want 9
to be marked.
10
Information 11
l The marks for questions are shown in brackets. 12
l The maximum mark for this paper is 100. 13
14
Advice
l Unless stated otherwise, you may quote formulae, without proof, from the 15
booklet. 16
l You do not necessarily need to use all the space provided. 17
18
TOTAL



(JUN217357301)
PB/Jun21/E5 7357/3

, 2
Do not write
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 )  ,1 1,
2 2




(02)
Jun21/7357/3

, 3
Do not write
outside the
2 Simplify fully box


(x þ 3)(6  2 x)
for x 6¼ 3
(x  3)(3 þ x)

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




3 f (x) ¼ 3 x 2

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




Turn over for the next question




Turn over
s




(03)
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, 4
Do not write
outside the
4 (a) Show that the first three terms, in descending powers of x, of the expansion of box



(2 x  3)10

are given by

1024 x 10 þ px 9 þ qx 8

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

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4 (b) Find the constant term in the expansion of
 
3 10
2x 
x
[2 marks]

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(04)
Jun21/7357/3