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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/11
Paper 1 Pure Mathematics 1 (P1) October/November 2010
1 hour 45 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 75.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
has centre Q and radius 2 cm. Points R and S lie on C1
and C2
respectively, and RS is
a tangent to both circles.
(i) Show that RS = 8 cm. [2]
(ii) Find angle RPQ in radians correct to 4 significant figures. [2]
(iii) Find the area of the shaded region. [4]
10 The equation of a curve is y = 3 + 4x − x2.
(i) Show that the equation of the normal to the curve at the point (3, 6) is 2y = x + 9. [4]
(ii) Given that the normal meets the coordinate axes at points A and B, find the coordinates of the
mid-point of AB. [2]
(iii) Find the coordinates of the point at which the normal meets the curve again. [4]
11 The equation of a curve is y = 9
2 − x.
(i) Find an expression fordy
dxand determine, with a reason, whether the curve has any stationary
points. [3]
(ii) Find the volume obtained when the region bounded by the curve, the coordinate axes and the
line x = 1 is rotated through 360◦ about the x-axis. [4]
(iii) Find the set of values of k for which the line y = x + k intersects the curve at two distinct points.
[4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/12/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/13
Paper 1 Pure Mathematics 1 (P1) October/November 2010
1 hour 45 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 75.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 5 printed pages and 3 blank pages.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/13/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Subsidiary Level
MATHEMATICS 9709/21
Paper 2 Pure Mathematics 2 (P2) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
2 Use logarithms to solve the equation 5x = 22x+1, giving your answer correct to 3 significant figures.
[4]
3 Show that ã 1
0
(ex + 1)2 dx = 12e2 + 2e − 3
2. [5]
4 The parametric equations of a curve are
x = 1 + ln(t − 2), y = t + 9
t, for t > 2.
(i) Show thatdy
dx= (t2 − 9)(t − 2)
t2. [3]
(ii) Find the coordinates of the only point on the curve at which the gradient is equal to 0. [3]
5 Solve the equation 8 + cot θ = 2 cosec2θ, giving all solutions in the interval 0◦ ≤ θ ≤ 360◦. [6]
6 The curve with equation y = 6
x2intersects the line y = x + 1 at the point P.
(i) Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6. [2]
(ii) Show that the x-coordinate of P satisfies the equation
x = √( 6
x + 1). [2]
(iii) Use the iterative formula
xn+1
= √( 6
xn+ 1
),
with initial value x1= 1.5, to determine the x-coordinate of P correct to 2 decimal places. Give
the result of each iteration to 4 decimal places. [3]
7 The polynomial 3x3 + 2x2 + ax + b, where a and b are constants, is denoted by p(x). It is given that(x − 1) is a factor of p(x), and that when p(x) is divided by (x − 2) the remainder is 10.
(i) Find the values of a and b. [5]
(ii) When a and b have these values, solve the equation p(x) = 0. [4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/21/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Subsidiary Level
MATHEMATICS 9709/22
Paper 2 Pure Mathematics 2 (P2) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
2 Use logarithms to solve the equation 5x = 22x+1, giving your answer correct to 3 significant figures.
[4]
3 Show that ã 1
0
(ex + 1)2 dx = 12e2 + 2e − 3
2. [5]
4 The parametric equations of a curve are
x = 1 + ln(t − 2), y = t + 9
t, for t > 2.
(i) Show thatdy
dx= (t2 − 9)(t − 2)
t2. [3]
(ii) Find the coordinates of the only point on the curve at which the gradient is equal to 0. [3]
5 Solve the equation 8 + cot θ = 2 cosec2θ, giving all solutions in the interval 0◦ ≤ θ ≤ 360◦. [6]
6 The curve with equation y = 6
x2intersects the line y = x + 1 at the point P.
(i) Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6. [2]
(ii) Show that the x-coordinate of P satisfies the equation
x = √( 6
x + 1). [2]
(iii) Use the iterative formula
xn+1
= √( 6
xn+ 1
),
with initial value x1= 1.5, to determine the x-coordinate of P correct to 2 decimal places. Give
the result of each iteration to 4 decimal places. [3]
7 The polynomial 3x3 + 2x2 + ax + b, where a and b are constants, is denoted by p(x). It is given that(x − 1) is a factor of p(x), and that when p(x) is divided by (x − 2) the remainder is 10.
(i) Find the values of a and b. [5]
(ii) When a and b have these values, solve the equation p(x) = 0. [4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/22/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Subsidiary Level
MATHEMATICS 9709/23
Paper 2 Pure Mathematics 2 (P2) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/23/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Level
MATHEMATICS 9709/31
Paper 3 Pure Mathematics 3 (P3) October/November 2010
1 hour 45 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 75.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
The diagram shows the curve y = x3 ln x and its minimum point M.
(i) Find the exact coordinates of M. [5]
(ii) Find the exact area of the shaded region bounded by the curve, the x-axis and the line x = 2. [5]
10 A certain substance is formed in a chemical reaction. The mass of substance formed t seconds after
the start of the reaction is x grams. At any time the rate of formation of the substance is proportional
to (20 − x). When t = 0, x = 0 anddx
dt= 1.
(i) Show that x and t satisfy the differential equation
dx
dt= 0.05(20 − x). [2]
(ii) Find, in any form, the solution of this differential equation. [5]
(iii) Find x when t = 10, giving your answer correct to 1 decimal place. [2]
(iv) State what happens to the value of x as t becomes very large. [1]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
The diagram shows the curve y = x3 ln x and its minimum point M.
(i) Find the exact coordinates of M. [5]
(ii) Find the exact area of the shaded region bounded by the curve, the x-axis and the line x = 2. [5]
10 A certain substance is formed in a chemical reaction. The mass of substance formed t seconds after
the start of the reaction is x grams. At any time the rate of formation of the substance is proportional
to (20 − x). When t = 0, x = 0 anddx
dt= 1.
(i) Show that x and t satisfy the differential equation
dx
dt= 0.05(20 − x). [2]
(ii) Find, in any form, the solution of this differential equation. [5]
(iii) Find x when t = 10, giving your answer correct to 1 decimal place. [2]
(iv) State what happens to the value of x as t becomes very large. [1]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/33/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/41
Paper 4 Mechanics 1 (M1) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
Where a numerical value for the acceleration due to gravity is needed, use 10 m s−2.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
Particles P and Q, of masses 0.2 kg and 0.5 kg respectively, are connected by a light inextensible
string. The string passes over a smooth pulley at the edge of a rough horizontal table. P hangs freely
and Q is in contact with the table. A force of magnitude 3.2 N acts on Q, upwards and away from the
pulley, at an angle of 30◦ to the horizontal (see diagram).
(i) The system is in limiting equilibrium with P about to move upwards. Find the coefficient of
friction between Q and the table. [6]
The force of magnitude 3.2 N is now removed and P starts to move downwards.
(ii) Find the acceleration of the particles and the tension in the string. [4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/42/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/43
Paper 4 Mechanics 1 (M1) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
Where a numerical value for the acceleration due to gravity is needed, use 10 m s−2.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
7 A car of mass 1250 kg travels along a horizontal straight road. The power of the car’s engine is
constant and equal to 24 kW and the resistance to the car’s motion is constant and equal to R N. The
car passes through the point A on the road with speed 20 m s−1 and acceleration 0.32 m s−2.
(i) Find the value of R. [3]
The car continues with increasing speed, passing through the point B on the road with speed 29.9 m s−1.
The car subsequently passes through the point C.
(ii) Find the acceleration of the car at B, giving the answer in m s−2 correct to 3 decimal places. [2]
(iii) Show that, while the car’s speed is increasing, it cannot reach 30 m s−1. [2]
(iv) Explain why the speed of the car is approximately constant between B and C. [1]
(v) State a value of the approximately constant speed, and the maximum possible error in this value
at any point between B and C. [1]
The work done by the car’s engine during the motion from B to C is 1200 kJ.
(vi) By assuming the speed of the car is constant from B to C, find, in either order,
(a) the approximate time taken for the car to travel from B to C,
(b) an approximation for the distance BC.
[4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
A particle P is projected from a point O with initial speed 10 m s−1 at an angle of 45◦ above the
horizontal. P subsequently passes through the point A which is at an angle of elevation of 30◦ from
O (see diagram). At time t s after projection the horizontal and vertically upward displacements of P
from O are x m and y m respectively.
(i) Write down expressions for x and y in terms of t, and hence obtain the equation of the trajectory
of P. [3]
(ii) Calculate the value of x when P is at A. [3]
(iii) Find the angle the trajectory makes with the horizontal when P is at A. [4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
A particle P is projected from a point O with initial speed 10 m s−1 at an angle of 45◦ above the
horizontal. P subsequently passes through the point A which is at an angle of elevation of 30◦ from
O (see diagram). At time t s after projection the horizontal and vertically upward displacements of P
from O are x m and y m respectively.
(i) Write down expressions for x and y in terms of t, and hence obtain the equation of the trajectory
of P. [3]
(ii) Calculate the value of x when P is at A. [3]
(iii) Find the angle the trajectory makes with the horizontal when P is at A. [4]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
A particle P of mass 0.2 kg is projected with velocity 2 m s−1 upwards along a line of greatest slope on
a plane inclined at 30◦ to the horizontal (see diagram). Air resistance of magnitude 0.5v N opposes the
motion of P, where v m s−1 is the velocity of P at time t s after projection. The coefficient of friction
between P and the plane is1
2√
3. The particle P reaches a position of instantaneous rest when t = T .
(i) Show that, while P is moving up the plane,dv
dt= −2.5(3 + v). [3]
(ii) Calculate T . [4]
(iii) Calculate the speed of P when t = 2T . [5]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/61/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/62
Paper 6 Probability & Statistics 1 (S1) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/62/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education
Advanced Subsidiary Level and Advanced Level
MATHEMATICS 9709/63
Paper 6 Probability & Statistics 1 (S1) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
A small aeroplane has 14 seats for passengers. The seats are arranged in 4 rows of 3 seats and a back
row of 2 seats (see diagram). 12 passengers board the aeroplane.
(i) How many possible seating arrangements are there for the 12 passengers? Give your answer
correct to 3 significant figures. [2]
These 12 passengers consist of 2 married couples (Mr and Mrs Lin and Mr and Mrs Brown), 5 students
and 3 business people.
(ii) The 3 business people sit in the front row. The 5 students each sit at a window seat. Mr and Mrs
Lin sit in the same row on the same side of the aisle. Mr and Mrs Brown sit in another row on
the same side of the aisle. How many possible seating arrangements are there? [4]
(iii) If, instead, the 12 passengers are seated randomly, find the probability that Mrs Lin sits directly
behind a student and Mrs Brown sits in the front row. [4]
7 The times spent by people visiting a certain dentist are independent and normally distributed with a
mean of 8.2 minutes. 79% of people who visit this dentist have visits lasting less than 10 minutes.
(i) Find the standard deviation of the times spent by people visiting this dentist. [3]
(ii) Find the probability that the time spent visiting this dentist by a randomly chosen person deviates
from the mean by more than 1 minute. [3]
(iii) Find the probability that, of 6 randomly chosen people, more than 2 have visits lasting longer
than 10 minutes. [3]
(iv) Find the probability that, of 35 randomly chosen people, fewer than 16 have visits lasting less
than 8.2 minutes. [5]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/71/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Level
MATHEMATICS 9709/72
Paper 7 Probability & Statistics 2 (S2) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
9709/72/O/N/10
www.maxpapers.com
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
General Certificate of Education Advanced Level
MATHEMATICS 9709/73
Paper 7 Probability & Statistics 2 (S2) October/November 2010
1 hour 15 minutes
Additional Materials: Answer Booklet/Paper
Graph Paper
List of Formulae (MF9)
READ THESE INSTRUCTIONS FIRST
If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying larger
numbers of marks later in the paper.
This document consists of 3 printed pages and 1 blank page.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.