Please check the examination details below before entering your candidate information
Candidate surname Other names
Pearson Edexcel Centre Number Candidate Number
International
Advanced Level
Tuesday 15 January 2019
Morning (Time: 2 hours 30 minutes) Paper Reference WMA02/01
Core Mathematics C34
Advanced
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Blue)
Candidates may use any calculator allowed by the regulations of the
Joint Council for Qualifications. 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).
Coloured pencils and highlighter pens must not be used.
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• 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.
• When a calculator is used, the answer should be given to an appropriate
degree of accuracy.
Information
•• The total mark for this paper is 125.
The marks for each question are shown in brackets
– use this as a guide 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
P54948A
©2019 Pearson Education Ltd.
1/1/1/1/
*P54948A0152*
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1. (a) Express 7 sin 2θ − 2 cos 2θ in the form R sin (2θ − α), where R and α are constants,
R > 0 and 0 < α < 90°. Give the exact value of R and give the value of α to
2 decimal places.
DO NOT WRITE IN THIS AREA
(3)
(b) Hence solve, for 0 θ < 90°, the equation
7 sin 2θ − 2 cos 2θ = 4
giving your answers in degrees to one decimal place.
(4)
(c) Express 28 sin θ cos θ + 8 sin2θ in the form a sin 2θ + b cos 2θ + c, where a, b and c
are constants to be found.
(3)
(d) Use your answers to part (a) and part (c) to deduce the exact maximum value of
28 sin θ cos θ + 8 sin2θ
(2)
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2. Given that
3x 2 + 4 x − 7 B C
≡ A+ +
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( x + 1) ( x − 3) x +1 x − 3
(a) find the values of the constants A, B and C.
(4)
(b) Hence, or otherwise, find the series expansion of
3x 2 + 4 x − 7
½x½ < 1
( x + 1) ( x − 3)
in ascending powers of x, up to and including the term in x2
Give each coefficient as a simplified fraction.
(6)
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3. The function f is defined by
f : x 2x2 + 3k x + k2 x ∈ , −4k x 0
DO NOT WRITE IN THIS AREA
where k is a positive constant.
(a) Find, in terms of k, the range of f.
(4)
The function g is defined by
g : x 2k − 3x x∈
Given that gf (−2) = −12
(b) find the possible values of k.
(4)
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DO NOT WRITE IN THIS AREA
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10
*P54948A01052*
Candidate surname Other names
Pearson Edexcel Centre Number Candidate Number
International
Advanced Level
Tuesday 15 January 2019
Morning (Time: 2 hours 30 minutes) Paper Reference WMA02/01
Core Mathematics C34
Advanced
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Blue)
Candidates may use any calculator allowed by the regulations of the
Joint Council for Qualifications. 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).
Coloured pencils and highlighter pens must not be used.
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• 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.
• When a calculator is used, the answer should be given to an appropriate
degree of accuracy.
Information
•• The total mark for this paper is 125.
The marks for each question are shown in brackets
– use this as a guide 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
P54948A
©2019 Pearson Education Ltd.
1/1/1/1/
*P54948A0152*
, Leave
blank
1. (a) Express 7 sin 2θ − 2 cos 2θ in the form R sin (2θ − α), where R and α are constants,
R > 0 and 0 < α < 90°. Give the exact value of R and give the value of α to
2 decimal places.
DO NOT WRITE IN THIS AREA
(3)
(b) Hence solve, for 0 θ < 90°, the equation
7 sin 2θ − 2 cos 2θ = 4
giving your answers in degrees to one decimal place.
(4)
(c) Express 28 sin θ cos θ + 8 sin2θ in the form a sin 2θ + b cos 2θ + c, where a, b and c
are constants to be found.
(3)
(d) Use your answers to part (a) and part (c) to deduce the exact maximum value of
28 sin θ cos θ + 8 sin2θ
(2)
___________________________________________________________________________
DO NOT WRITE IN THIS AREA
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
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DO NOT WRITE IN THIS AREA
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2
*P54948A0252*
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2. Given that
3x 2 + 4 x − 7 B C
≡ A+ +
DO NOT WRITE IN THIS AREA
( x + 1) ( x − 3) x +1 x − 3
(a) find the values of the constants A, B and C.
(4)
(b) Hence, or otherwise, find the series expansion of
3x 2 + 4 x − 7
½x½ < 1
( x + 1) ( x − 3)
in ascending powers of x, up to and including the term in x2
Give each coefficient as a simplified fraction.
(6)
___________________________________________________________________________
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DO NOT WRITE IN THIS AREA
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6
*P54948A0652*
, Leave
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3. The function f is defined by
f : x 2x2 + 3k x + k2 x ∈ , −4k x 0
DO NOT WRITE IN THIS AREA
where k is a positive constant.
(a) Find, in terms of k, the range of f.
(4)
The function g is defined by
g : x 2k − 3x x∈
Given that gf (−2) = −12
(b) find the possible values of k.
(4)
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DO NOT WRITE IN THIS AREA
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