Cambridge A Level Physics 9702 — 2009 Oct/Nov Paper 5 · Variant 1

READ THESE INSTRUCTIONS FIRST 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, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. 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. For Examiner’s Use 1 2 Total This document consists of 8 printed pages. DC (GB/SW) 10905/5 © UCLES 2009 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level PHYSICS 9702/51 Paper 5 Planning, Analysis and Evaluation October/November 2009 1 hour 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. * 7 0 2 0 9 4 3 7 7 9 *

2 9702/51/O/N/09 © UCLES 2009 For Examiner’s Use 1 The volume of air in a bottle affects its resonant frequency. It is suggested that the resonant frequency f is related to the volume V by the equation f 2 = k V where k is a constant. Design a laboratory experiment to determine whether this equation is correct. You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) how to analyse the data, (e) the safety precautions to be taken. [15]

3 9702/51/O/N/09 © UCLES 2009 [Turn over For Examiner’s Use Diagram … … … … … … … … … … … … … …

4 9702/51/O/N/09 © UCLES 2009 For Examiner’s Use … … … … … … … … … … … … … … … … … … … … … … … … … … … …

5 9702/51/O/N/09 © UCLES 2009 [Turn over For Examiner’s Use 2 An experiment is carried out to investigate how the resistance R of a thermistor varies with temperature T. An ohmmeter is used to measure R. The equipment is set up as shown in Fig. 2.1. heat thermometer thermistor ohmmeter Fig. 2.1 Question 2 continues on page 6.

6 9702/51/O/N/09 © UCLES 2009 For Examiner’s Use It is suggested that R and T are related by the equation R = T h g where g and h are constants. (a) A graph is plotted with lg R on the y-axis and lg T on the x-axis. Express the gradient and y-intercept in terms of g and h. gradient = … y-intercept = … [1] (b) Values of T and R are given in Fig. 2.2. T / K R / Ω lg (T / K) lg (R / Ω) 293 990 ± 10 303 860 ± 10 313 760 ± 10 323 680 ± 10 333 610 ± 10 Fig. 2.2 Calculate and record values of lg (T / K) and lg (R / Ω) in Fig. 2.2. Include the absolute errors in lg (R / Ω). [3] (c) (i) Plot a graph of lg (R / Ω) against lg (T / K). Include error bars for lg (R / Ω). [2] (ii) Draw the line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the error in your answer. gradient = …[2]

7 9702/51/O/N/09 © UCLES 2009 [Turn over For Examiner’s Use 2.75 2.46 2.47 lg (T / K) lg (R / Ω) 2.48 2.49 2.50 2.51 2.52 2.53 2.80 2.85 2.90 2.95 3.00

8 9702/51/O/N/09 © UCLES 2009 For Examiner’s Use (iv) Determine the y-intercept of the line of best fit. Include the error in your answer. y-intercept = …[2] (d) Using your answers to (c)(iii) and (c)(iv), determine the values of g and h. Include the error in your values. You need not be concerned with the units of g and h. g = … h = … [3] 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.

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2009 question paper for the guidance of teachers 9702 PHYSICS 9702/51 Paper 51 (Planning, Analysis and Evaluation), maximum raw mark 30 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2009 9702 51 © UCLES 2009 Question 1 Planning (15 marks) Defining the problem (3 marks) P1 Vary V or f [1] P2 Measure f for different V or measure V for different f [1] P3 Keep temperature constant [1] Methods of data collection (5 marks) M1 labelled diagram including source of sound adjacent to the opening e.g. loudspeaker/tuning fork [1] M2 Method of producing sound of different frequencies e.g. several tuning forks or signal generator [1] M3 Method of measuring volume of air – volume of container - volume of water or find total volume of each different container [1] M4 Method of determining resonant frequency e.g. largest sound heard or displayed [1] M5 Perform experiment in quiet room or avoid other noise [1] Method of analysis (2 marks) A1 Plot a graph of f 2 against 1/V or lg f against lg V or or lg f against lg 1/V [1] A2 Relationship is correct if graph is a straight line through the origin or straight line for log-log graph [1] Safety considerations (1 mark) S Switch off power supply when not in use/ ear defenders for loudspeaker method [1] Additional detail (4 marks) D Relevant points might include [4] 1. Detail on measuring volume – use of measuring cylinder/burette 2. Determination of frequency using oscilloscope/read off tuning fork or signal generator 3. Detailed timebase calculation 4. Detail determining resonance e.g. adding/subtracting small amounts of water/changing signal generator to create resonance 5. Discussion of container e.g. end correction/shape of mouth of bottle 6. Gradient = k or lg f = -0.5 lg V + 0.5 lg k or lg f = 0.5 lg 1/V + 0.5 lg k 7. Constant amplitude/intensity of source of sound 8. Method to check fundamental frequency. 15 marks can be scored in total.

Page 3 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2009 9702 51 © UCLES 2009 Question 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 Gradient =h y-intercept = lg g 1 or – lg g Allow log and/or ln (b) T1 T2 2.467 or 2.4669 3.00 or 2.996 2.481 or 2.4814 2.93 or 2.934 2.496 or 2.4955 2.88 or 2.881 2.509 or 2.5092 2.83 or 2.833 2.522 or 2.5224 2.79 or 2.785 T1 for lg T T2 for lg R Allow mixture of dp. U1 ± 0.004 to ± 0.007 Allow more than one significant figure. (c) (i) G1 Five points plotted correctly Must be within half a small square. Use transparency. Ecf allowed from table. U2 Error bars in lg R plotted correctly Check first and last point. Must be accurate within half a small square. Allow ecf from (b) (c) (ii) G2 Line of best fit There must at least four trend plots with a reasonable balance of points about the line. Allow ecf from points plotted incorrectly. Examiner judgement. G3 Worst acceptable straight line. Steepest or shallowest possible line. Line should be clearly labelled or dashed. Should pass from top of top error bar to bottom of bottom error bar or bottom of top error bar to top of bottom error bar. Mark scored only if error bars are plotted. Allow ecf from (b) and (c) (i) (c) (iii) C1 Gradient of best fit line The triangle used should be greater than half the length of the drawn line. Check the read offs. Work to half a small square. Do not penalise POT or sign of gradient. U3 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. (c) (iv) C2 y-intercept Gradient must be used. Check substitution into c = y – mx. Allow ecf from (c) (iii). If gradient negative then y-intercept should be about 11-13. If gradient positive then y-intercept should be about -4 or -5. U4 Uncertainty in y-intercept Method of determining absolute uncertainty Difference in worst y-intercept and y-intercept. Do not allow ecf from false origin read-off. Allow ecf from (c) (iv)

Page 4 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2009 9702 51 © UCLES 2009 (d) C3 g = 1/10y-intercept = 10 – y-intercept y-intercept must be used. g should be about 10-13 Allow ecf from (c) (iv). If FO or positive gradient used then g should be about 10-4. C4 h = candidate’s gradient value Answer must be negative and given to 2 or 3 sf. U5 Method for uncertainty in g and uncertainty in h. Expect to see difference in values for g. Uncertainty in h must be the same as the gradient. [Total: 15] Uncertainties in Question 2 (c) (iii) Gradient [U3] 1. Uncertainty = gradient of line of best fit – gradient of worst acceptable line 2. Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (c) (iv) y-intercept [U4] 1. Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line 2. Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) [U5] 1. Uncertainty = 10 – best y-intercept - 10 – worst y-intercept