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AQA MATHEMATICS Paper 1

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AS MATHEMATICS Paper 1 Thursday 16 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae for A‑level Mathematics booklet.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  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 of this book. Write the question number against your answer(s).  Do not write outside the box around each page or on blank pages.  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 80. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. (JUN) 7356/1 box 3 Express √3 + 3√5 √5 – √3 in the form a + √b , where a and b are integers. box Fully justify your answer. [4 marks] Turn over for the next question Turn over U 4 (a) (i) By using a suitable trigonometric identity, show that the equation sin θ tan θ = 4 cos θ box can be written as tan2 θ = 4 [1 mark] 4 (a) (ii) Hence solve the equation sin θ tan θ = 4 cos θ where 0° θ 360° Give your answers to the nearest degree. [3 marks] 4 (b) Deduce all solutions of the equation box sin 3α tan 3α = 4 cos 3α where 0° α 180° Give your answers to the nearest degree. [3 marks] Turn over for the next question Turn over U 5 A student is looking for factors of the polynomial f (x) They suggest that (x – 2) is a factor of f (x) The method they use to check this suggestion is to calculate f (–2) They correctly calculate that f (–2) = 0 They conclude that their suggestion is correct. 5 (a) Make one comment about the student’s method. [1 mark] box 5 (b) Make two comments about the student’s conclusion. [2 marks] 1 2 6 Determine the set of values of x which satisfy the inequality 3x2 + 3x x + 6 Give your answer in exact form using set notation. [4 marks] box Turn over for the next question Turn over U (07)

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I declare this is my own work.



AS
MATHEMATICS
Paper 1

Thursday 16 May 2024 Afternoon Time allowed: 1 hour 30 minutes
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 Questio Mark
n
meets the 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
7
the end of this book. Write the question number against your
answer(s). 8
 Do not write outside the box around each page or on blank pages. 9
 Show all necessary working; otherwise marks for method may be lost. 10
 Do all rough work in this book. Cross through any work that you do 11
not want to be marked. 12
13
Information 14
 The marks for questions are shown in brackets.
15
 The maximum mark for this paper is 80.
16
Advice 17
 Unless stated otherwise, you may quote formulae, without 18
proof, from the booklet. 19
 You do not necessarily need to use all the space provided.
TOTAL




(JUN247356101)
G/LM/Jun24/G4004/
E9 7356/1

, 2
Do not
box
Section A

Answer all questions in the spaces
provided.


1 It is given that tan θ° = k, where k is a

constant. Find tan (θ + 180)°

Circle your answer.
[1 mark]

–k – k1 1
k
k




1
2 Curve C has equation y =
(x –
1)2
State the equations of the asymptotes to curve C

Tick (🗸) one box. [1 mark]


x = 0 and y = 0


x = 0 and y = 1


x = 1 and y = 0


x = 1 and y = 1




(0
2) G/

, 3
Do not
√3 + box
3 Express
3√5 in the form a + √b , where a and b are
integers.
√5 – √3

Fully justify your answer.
[4 marks]




Turn over for the next question




(0
3) G/

, 4
Do not
Turn over U




(0

3) G/

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