Please check the examination details below before entering your candidate information

Candidate surname Other names

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Time 1 hour 30 minutes
Paper
reference WMA12/01
Mathematics
 

International Advanced Subsidiary/Advanced Level

Pure Mathematics P2

You must have: Total Marks

Mathematical Formulae and Statistical Tables (Yellow), calculator

Candidates may use any calculator permitted by Pearson regulations.

Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• Answer the questions in the spaces provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear. Answers
without working may not gain full credit.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 10 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
Try to answer every question.
• Check your answers if you have time at the end. Turn over

*P71377A0132*
P71377A
©2022 Pearson Education Ltd.

Q:1/1/1/1/
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1. Find the first four terms, in ascending powers of x, of the binomial expansion of

10
 3 
 2 + x
8

Give each coefficient as an integer.

(4)
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(Total 4 marks)

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2.
y

O x

Figure 1

Figure 1 shows the graph of

y = 1 − log10 (sin x)      0 < x < π

where x is in radians.

The table below shows some values of x and y for this graph, with values of y given to 3
decimal places.

x 0.5 1 1.5 2 2.5 3

y 1.319 1.001 1.223 1.850

(a) Complete the table above, giving values of y to 3 decimal places.

(2)

(b) Use the trapezium rule with all the y values in the completed table to find, to 2 decimal
places, an estimate for

∫
3

(1 − log
10 )
(sin x) d x
0.5

(3)

(c) Use your answer to part (b) to find an estimate for

∫
3

(3 + log 10 )
(sin x) d x
0.5

(3)
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(Total 8 marks)

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3. (i) Show that the following statement is false:

“ (n + 1)3 − n3 is prime for all n ∈  ”

(2)

(ii) Given that the points A(1, 0) , B(3, −10) and C(7, −6) lie on a circle,
prove that AB is a diameter of this circle.
(5)
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(Total 7 marks)

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4. In this question you must show all stages of your working.

Give your answers in fully simplified surd form.

Given that a and b are positive constants, solve the simultaneous equations

a−b=8
log4 a + log4 b = 3
(6)
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(Total 6 marks)

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5. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Solve, for −180° < θ  180° , the equation

3 tan (θ + 43°) = 2 cos (θ + 43°)

(6)
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(Total 6 marks)

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6. In a geometric sequence u1 , u2 , u3 , …

• the common ratio is r

• u2 + u3 = 6
• u4 = 8

(a) Show that r satisfies

3r 2 − 4r − 4 = 0
(3)

Given that the geometric sequence has a sum to infinity,

(b) find u1
(3)

(c) find S∞
(2)
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(Total 8 marks)

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7. f(x) = Ax 3 + 6x 2 − 4x + B

where A and B are constants.

Given that

• (x + 2) is a factor of f(x)

∫
5

• f ( x) d x = 176
3

find the value of A and the value of B.

(7)
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(Total 7 marks)

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8. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

A curve has equation

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y = 256x4 − 304x − 35 +     x ≠ 0
x2
dy
(a) Find
dx
(3)

(b) Hence find the coordinates of the stationary points of the curve.
(5)
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(Total 8 marks)

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9. A scientist is using carbon‑14 dating to determine the age of some wooden items.

The equation for carbon‑14 dating an item is given by

N = kλt

where

• N grams is the amount of carbon‑14 currently present in the item

• k grams was the initial amount of carbon‑14 present in the item
• t is the number of years since the item was made
• λ is a constant, with 0 < λ < 1

(a) Sketch the graph of N against t for k = 1

(2)

Given that it takes 5700 years for the amount of carbon‑14 to reduce to half its initial value,

(b) show that the value of the constant λ is 0.999878 to 6 decimal places.
(2)

Given that Item A

• is known to have had 15 grams of carbon‑14 present initially

• is thought to be 3250 years old

(c) calculate, to 3 significant figures, how much carbon‑14 the equation predicts is
currently in Item A.
(2)

Item B is known to have initially had 25 grams of carbon‑14 present, but only 18 grams
now remain.

(d) Use algebra to calculate the age of Item B to the nearest 100 years.
(3)
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(Total 9 marks)

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10. The circle C has centre X (3, 5) and radius r

The line l has equation y = 2x + k , where k is a constant.

(a) Show that l and C intersect when

5x 2 + (4k − 26) x + k 2 − 10k + 34 − r 2 = 0

(3)

Given that l is a tangent to C,

(b) show that 5r2 = (k + p)2 , where p is a constant to be found.

(3)

y l

B C
X (3, 5)

O x

Figure 2

The line l

• cuts the y-axis at the point A

• touches the circle C at the point B

as shown in Figure 2.

Given that AB = 2r

(c) find the value of k

(6)
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 *P71377A03132* Turn over
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(Total 12 marks)
TOTAL FOR PAPER IS 75 MARKS
END
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