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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level and Advanced Level MATHEMATICS Paper 1 Pure Mathematics 1 (P1) October/November 2005 1 hour 45 minutes
Additional materials: Answer Booklet/Paper Graph paper List of Formulae (MF9)
9709/01
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 on both sides of the paper. 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. 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. The use of an electronic calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers.
This document consists of 4 printed pages.
© UCLES 2005
[Turn over
2 1
Solve the equation 3 sin2 θ − 2 cos θ − 3 = 0, for 0◦ ≤ θ ≤ 180◦ .
[4]
2
In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle AOC = α radians. AC and BD are arcs of circles, centre O and radii 10 cm and 16 cm respectively.
(i) In the case where α = 0.8, find the area of the shaded region. (ii) Find the value of α for which the perimeter of the shaded region is 28.9 cm.
[2] [3]
3
In the diagram, ABED is a trapezium√ with right angles at E and D, and CED is
Additional materials: Answer Booklet/Paper Graph paper List of Formulae (MF9)
9709/01
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 on both sides of the paper. 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. 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. The use of an electronic calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers.
This document consists of 4 printed pages.
© UCLES 2005
[Turn over
2 1
Solve the equation 3 sin2 θ − 2 cos θ − 3 = 0, for 0◦ ≤ θ ≤ 180◦ .
[4]
2
In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle AOC = α radians. AC and BD are arcs of circles, centre O and radii 10 cm and 16 cm respectively.
(i) In the case where α = 0.8, find the area of the shaded region. (ii) Find the value of α for which the perimeter of the shaded region is 28.9 cm.
[2] [3]
3
In the diagram, ABED is a trapezium√ with right angles at E and D, and CED is