计算机代数学家资格联合会规定的计算器使用方法说明书
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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.
• I f pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Coloured pencils and highlighter pens must not be used.
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• A nswer all questions and ensure that your answers to parts of questions are
clearly labelled.
• A nswer the questions in the spaces provided
– there may be more space than you need .
• Y ou should show sufficient working to make your methods clear. Answers
without working may not gain full credit.
• W hen a calculator is used, the answer should be given to an appropriate
degree of accuracy.
Information • The total mark for this paper is 75.
• T he 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.
P46718A
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DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1. Use the binomial series to find the expansion of
125253()
,+x x <
in ascending powers of x , up to and including the term in x 3. Give each coefficient as a fraction in its simplest form.
(6)
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(Total 6 marks)
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DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. The curve C has equation
2x 2y + 2x + 4y – cos (ʌ\) = 17
(a) Use implicit differentiation to find d d y x in terms of x and y .(5)
The point P with coordinates 312, ⎛⎝⎜⎞⎠⎟ lies on C . The normal to C at P meets the x -axis at the point A .
(b) Find the x coordinate of A , giving your answer in the form
aπb cπd
++, where a , b , c and d are integers to be determined.(4)
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D O N O T W R I T
E I N T H I S A R E A D O N O T W R I T E I N T H I S A R E A D O N O T W R I T E I N T H I S A R E A ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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Q3
(Total 9 marks)
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. The rate of decay of the mass of a particular substance is modelled by the differential
equation
d d x t =−52
x , t . 0
where x is the mass of the substance measured in grams and t is the time measured in days.
Given that x = 60 when t = 0, (a) solve the differential equation, giving x in terms of t . You should show all steps in
your working and give your answer in its simplest form.
(4)
(b) Find the time taken for the mass of the substance to decay from 60 grams to 20 grams.
Give your answer to the nearest minute.
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