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Title: Edexcel 2024 AS (june) pure paper 1
Description: - Pearson Edexcel 2024 AS (june) - Paper 1, Pure, questions only
Description: - Pearson Edexcel 2024 AS (june) - Paper 1, Pure, questions only
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Please check the examination details below before entering your candidate information
Candidate surname
Centre Number
Other names
Candidate Number
Pearson Edexcel Level 3 GCE
Thursday 16 May 2024
Afternoon (Time: 2 hours)
Paper
reference
Mathematics
8MA0/01
Advanced Subsidiary
PAPER 1: Pure Mathematics
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator
Total Marks
Candidates may use any calculator allowed by the regulations of the
Joint Council for Qualifications
...
Instructions
Use black ink or ball-point pen
...
•
in the boxes at the top of this page with your name,
• Fill
centre number and candidate number
...
the questions in the spaces provided
• Answer
– there may be more space than you need
...
• You
Answers without working may not gain full credit
...
Information
A booklet 'Mathematical Formulae and Statistical Tables' is provided
...
The total mark for this paper is 100
...
Advice
Read each question carefully before you start to answer it
...
•
• Check your answers if you have time at the end
...
F:1/1/1/
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(Total for Question 1 is 4 marks)
*P74087A0344*
3
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2
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Solutions relying entirely on calculator technology are not acceptable
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Given that (x – 4) is a factor of f (x),
(a) use the factor theorem to show that
10a = 32 + b
(2)
Given also that (x – 2) is a factor of f (x),
(b) express f (x) in the form
f (x) = (2x + k) (x – 4) (x – 2)
where k is a constant to be found
...
Relative to a fixed origin O,
• point P has position vector 9i – 8j
• point Q has position vector 3i – 5j
→
(a) Find PQ
→
Given that R is the point such that QR = 9i + 18j
(b) show that angle PQR = 90°
→
→
Given also that S is the point such that PS = 3QR
(c) find the exact area of PQRS
(2)
(2)
(4)
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(Total for Question 3 is 8 marks)
*P74087A0944*
9
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5 correct to 3 significant figures
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(3)
(2)
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Question 4 continued
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(Total for Question 4 is 5 marks)
*P74087A01144*
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5
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(ii) State the equations of any asymptotes to the curve C1
The curve C2 has equation
(3)
y = 3x2 – 4x – 10
(b) Show that C1 and C2 intersect when
3x3 – 4x2 – 13x – 6 = 0
(2)
2
3
Given that the x coordinate of one of the points of intersection is –
(c) use algebra to find the x coordinates of the other points of intersection between
C1 and C2
(4)
(Solutions relying on calculator technology are not acceptable
...
The binomial expansion of
(1 + ax)12
up to and including the term in x2 is
1–
15
x + kx2
2
where a and k are constants
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16
(2)
12
(2)
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(Total for Question 6 is 6 marks)
*P74087A01744*
17
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7
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3)
(6, 2
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On a particular day, the concentration of smoke particles in the air emitted by this
chimney, P parts per million, is measured at various distances, x km, from the chimney
...
The line passes through the point (0, 3
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1)
(a) Find a complete equation for the model in the form
P = ab x
where a and b are constants
...
(b) With reference to the model, interpret the value of ab
(4)
(1)
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(Total for Question 7 is 5 marks)
*P74087A01944*
19
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Solutions relying entirely on calculator technology are not acceptable
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Given that l has equation y = –2x + 7
(a) show, using calculus, that the x coordinate of A is 2
The line l cuts C again at the point B
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Using algebraic integration,
(c) show that the area of R is 108
(3)
(2)
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*P74087A02144*
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*P74087A02244*
Question 8 continued
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(Total for Question 8 is 10 marks)
*P74087A02344*
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Find in terms of p and/or q,
(a) loga 256
(b) loga 100
(c) loga 80 × loga 3
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y
C
Q
P
l
x
O
Figure 4
Figure 4 shows a sketch of the circle C
• the point P (–1, k + 8) is the centre of C
• the point Q (3, k 2 – 2k) lies on C
• k is a positive constant
• the line l is the tangent to C at Q
Given that the gradient of l is –2
(a) show that
k 2 – 3k – 10 = 0
(4)
(b) Hence find an equation for C
(4)
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Question 10 continued
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Question 10 continued
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*P74087A02844*
Question 10 continued
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(Total for Question 10 is 8 marks)
*P74087A02944*
29
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11
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The price per gram of metal A, £ VA , is modelled by the equation
VA = 100 + 20e0
...
The price per gram of metal B, £ VB , is modelled by the equation
VB = pe–0
...
Given that VB = 2VA when t = 0
(a) find the value of p
When t = T, the rate of increase in the price per gram of metal A was equal to the rate
of decrease in the price per gram of metal B
(b) Find the value of T, giving your answer to one decimal place
...
)
(4)
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*P74087A03044*
Question 11 continued
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*P74087A03144*
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Question 11 continued
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*P74087A03244*
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(Total for Question 11 is 6 marks)
*P74087A03344*
33
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The pool is modelled as a quarter of a circle joined to two equal sized rectangles
as shown
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(c) Prove, by further calculus, that this value of x gives a minimum value for P
Access to the pool is by side AB shown in Figure 5
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(4)
(2)
(2)
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*P74087A03444*
Question 12 continued
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*P74087A03544*
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*P74087A03644*
Question 12 continued
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(Total for Question 12 is 13 marks)
*P74087A03744*
37
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13
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Solutions relying entirely on calculator technology are not acceptable
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(4)
(c) Hence find the smallest solution of the equation
sin 4α (7 sin 4α – 4 cos 4α) = 4
in the range 720° < α < 1080°, giving your answer to one decimal place
...
Prove, using algebra, that
n2 + 5n
is even for all n ∈
(4)
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*P74087A04244*
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*P74087A04344*
43
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Question 14 continued
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(Total for Question 14 is 4 marks)
TOTAL FOR PAPER IS 100 MARKS
44
*P74087A04444*
Title: Edexcel 2024 AS (june) pure paper 1
Description: - Pearson Edexcel 2024 AS (june) - Paper 1, Pure, questions only
Description: - Pearson Edexcel 2024 AS (june) - Paper 1, Pure, questions only