surname names
Number Number
Paper
■ ■
Advanced Extension Award
Mathematics
An insert for questions 5, 6 and 7 (enclosed)
Instructions
Fill in the boxes at the top of this page with your name, centre
number and candidate number.
Answer the questions in the spaces provided –
there may be more space than you need.
•Information
2π
Answers should be given in as simple a form as possible, e.g. , 2, 3 2 .
3
• The total mark for this paper is 100 of which 7 marks are for style and clarity of
• The style and clarity of presentation marks will be indicated as (+S1) or (+S2).
• The total mark for each question is shown at the end of the question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. In the binomial expansion of
1
1 x
8x
p 8
where p is a positive constant,
• the sum of the coefficient of x and the coefficient of x2 is equal to the
coefficient of x3
• the coefficient of x2 is positive
Determine the value of p.
(7)
,Question 1 continued
(Total for Question 1 is 7 marks)
, 2.
y
2
O x
–2 2
–5
Figure 1
Figure 1 shows the curve defined by the equation
y2 3y 6 sin y 4 x2
The point P(x, y) lies on the curve.
The distance from the origin, O, to P is D.
(a) Write down an equation for D2 in terms of y only.
(1)
(b) Hence determine the minimum value of D giving your answer in simplest form.
(5)
Number Number
Paper
■ ■
Advanced Extension Award
Mathematics
An insert for questions 5, 6 and 7 (enclosed)
Instructions
Fill in the boxes at the top of this page with your name, centre
number and candidate number.
Answer the questions in the spaces provided –
there may be more space than you need.
•Information
2π
Answers should be given in as simple a form as possible, e.g. , 2, 3 2 .
3
• The total mark for this paper is 100 of which 7 marks are for style and clarity of
• The style and clarity of presentation marks will be indicated as (+S1) or (+S2).
• The total mark for each question is shown at the end of the question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. In the binomial expansion of
1
1 x
8x
p 8
where p is a positive constant,
• the sum of the coefficient of x and the coefficient of x2 is equal to the
coefficient of x3
• the coefficient of x2 is positive
Determine the value of p.
(7)
,Question 1 continued
(Total for Question 1 is 7 marks)
, 2.
y
2
O x
–2 2
–5
Figure 1
Figure 1 shows the curve defined by the equation
y2 3y 6 sin y 4 x2
The point P(x, y) lies on the curve.
The distance from the origin, O, to P is D.
(a) Write down an equation for D2 in terms of y only.
(1)
(b) Hence determine the minimum value of D giving your answer in simplest form.
(5)
