Physics 9702/52 February/March 2025: question paper and mark scheme
Cambridge AS & A Level Physics (9702), Paper 5 Planning, Analysis and Evaluation, February/March 2025. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Fig. 1.1 shows two identical cylindrical metal conductors P and Q, each of length L and cross‑sectional area A.
L
P
p
q
Q
X
Fig. 1.1
The conductors are placed parallel to each other. The perpendicular distance from the midpoint of
P to point X is p. The perpendicular distance from the midpoint of Q to point X is q.
The two conductors are electrically connected in parallel. This parallel combination is connected in series to a power supply and a resistor. The potential difference V between the ends of P is the
same as the potential difference between the ends of Q.
The magnetic flux density at X due to the currents in the conductors is B.
It is suggested that B is related to p by the relationship
YAV YZAV
B= +
Lp Lq where Y and Z are constants.
Plan a laboratory experiment to test the relationship between B and p.
Draw a diagram showing the arrangement of your equipment.
Explain how the results could be used to determine values for Y and Z.
In your plan you should include:
• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.
Diagram
…… [15]
Mark scheme
1 Defining the problem
Vary p and measure B OR p is the independent variable and B is the dependent variable. 1
Keep V constant or potential difference between the ends of each conductor constant. 1
Methods of data collection
Labelled diagram of workable experiment including: 1
• conductors in parallel connected in series to power supply and resistor
• circuit symbols for (variable) resistor and power supply
• X labelled and one other label from L, P, Q, p and q.
Voltmeter connected in parallel with conductors (to measure V) and conductors in parallel connected to a power supply. 1
Method to measure L and p and q e.g. use a rule / ruler / calipers. 1
Method to measure B, e.g. use a (calibrated) Hall probe and adjust / rotate probe until maximum value. 1
Method of Analysis
1 1
Plots a graph of B against or equivalent.
p
Do not accept logarithms.
1
1 1
B against against B
p p
L × gradient L
Y= Y=
AV AV × gradient
1 1
1 1
B against against B
p p
q × y -intercept Z = −q × y -intercept
Z=
gradient
OR
Lq × y -intercept
Z=
YAV
Additional detail including safety considerations 6
Any six from:
D1 precaution linked to high current / hot conductors, e.g. use gloves / switch off power supply when not measuring
B / between measurements / allow conductors to cool
D2 keep A and L and q constant
πd2
D3 use calipers / micrometer to measure diameter / d of conductor and A =
4
D4 repeat measurements of d in different positions and average d
D5 method to determine the position of X in relation to the conductors, e.g. divide L by two to find the midpoint of P / Q and
use a set square / protractor / plumb line to mark X
OR
divide L by two to find the midpoint of P / Q and use a grid to mark X
D6 measure B (using Hall probe) first in one direction and then in the opposite direction and average B
OR
Measure B with current / p.d. in one direction and then in the opposite direction and average B
D7 additional detail on measuring p and / or q, e.g. measure to the conductor and add on the radius
1 D8 description of method to keep q constant, e.g. tape / adhesive putty to fix conductor Q to the bench OR for vertical
methods fix conductor Q in clamp(s) attached to stand(s) to keep q constant
D9 method to keep P and Q parallel, e.g. measure the separation (between the conductors) at different points
YZAV
D10 relationship valid if a straight line is produced (with a y-intercept = ).
Lq
Do not accept passing through the origin.
D11 method to keep V constant, e.g. adjust / change variable resistor / power supply to keep voltmeter reading constant.
A student investigates the cooling of a liquid in a beaker.
The temperature θR of the laboratory is measured using a thermometer.
Hot water is added to an insulated beaker, as shown in Fig. 2.1.
thermometer stand
beaker
insulation
water bench heat-proof mat
Fig. 2.1
The thermometer measures the temperature of the water. At time t the temperature of the water is θ.
A series of readings of t and θ are taken.
It is suggested that θ and t are related by the equation t θ = θR + (θ 0 – θR) e–( K )
where θ0 is the temperature at t = 0 and K is a constant.
(a) A graph is plotted of ln (θ – θR) on the y‑axis against t on the x‑axis.
Determine expressions for the gradient and y‑intercept.
gradient = ……
y‑intercept = ……
[1]
` (b) Values of t and θ are given in Table 2.1.
Table 2.1
t / min θ / °C (θ – θR) / °C ln ((θ – θR) / °C)
6.0 75.0 ± 0.5
12.0 64.5 ± 0.5
18.0 57.0 ± 0.5
24.0 50.0 ± 0.5
30.0 44.5 ± 0.5
36.0 41.0 ± 0.5
The value of θR is (18.5 ± 0.5) °C.
Calculate and record values of (θ – θR) / °C and ln ((θ – θR) / °C) in Table 2.1.
Include the absolute uncertainties in (θ – θR) and ln ((θ – θR) / °C). [2]
(c) (i) Plot a graph of ln ((θ – θR) / °C) against t / min. Include error bars for ln ((θ – θR) / °C). [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2]
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in
your answer.
gradient = …… [2]
4.1
4.0
ln ((θ – θR) / °C)
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 t / min
(iv) Determine the y‑intercept of the line of best fit. Include the absolute uncertainty in your answer.
y‑intercept = …… [2]
(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of K and θ0. Include appropriate units.
K = ……
θ0 = ……
[2]
(ii) Determine the absolute uncertainty in your value of θ0.
absolute uncertainty = …… [1]
(e) Determine the time t for the temperature to reach 25.0 °C.
t = …… min [1]
[Total: 15]
To avoid the issue of disclosure of answer‑related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.
Mark scheme
2(a) 1 1
gradient = −
K
y-intercept = ln (θ0 − θR )
2(b)
(θ – θR ) / °C ln ((θ – θR ) / °C)
56.5 ± 1.0 4.034 or 4.0342 ± 0.018
46.0 ± 1.0 3.829 or 3.8286 ± 0.022
38.5 ± 1.0 3.651 or 3.6507 ± 0.026
31.5 ± 1.0 3.450 or 3.4500 ± 0.032
26.0 ± 1.0 3.258 or 3.2581 ± 0.038
22.5 ± 1.0 3.114 or 3.1135 ± 0.044
Values of (θ – θR ) / °C and ln (( θ – θR ) / °C) 1
Uncertainties in (θ – θR ) and ln ((θ – θR ) / °C) 1
2(c)(i) Six points from (b) plotted correctly. 1
Must be within half a small square. Diameter of points must be less than half a small square.
Error bars in ln (( θ – θR ) / °C) plotted correctly. 1
All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
2(c)(ii) Straight line of best fit drawn. 1
Do not accept line from top plot to bottom plot.
Line must pass between
(31.5, 3.2) and (33.0, 3.2) and between
(16.0, 3.7) and (17.0, 3.7)
Worst acceptable line drawn. 1
Steepest or shallowest possible line that passes through all the error bars.
All error bars must be plotted.
2(c)(iii) Gradient must be negative. 1
Gradient determined with clear substitution of data into Δy / Δx; distance between data points must be greater than half the
length of the drawn line.
Gradient determined of worst acceptable line with clear substitution of data into Δy / Δx; 1
uncertainty = (gradient of line of best fit – gradient of worst acceptable line)
or
uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
2(c)(iv) y-intercept determined by substitution of correct point with consistent unit of time into y = mx + c 1
y-intercept of worst acceptable line determined by substitution into y = mx + c. 1
uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line, or
uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
Do not accept ecf from false origin method.
2(d)(i) K determined using gradient and 1
K and θ0 given to 3 or 4 sf.
1
K =−
gradient
θ0 determined using y-intercept and 1
K and θ0 given with units with appropriate powers of ten
θ0 = ey -intercept + 18.5
Unit of K: min or minute(s)
unit of θ0: °C
2(d)(ii) Absolute uncertainty determined with clear method shown. 1
( )
Δθ0 = emax y -intercept + 19 − (e y -intercept + 18.5)
OR
(
Δθ0 = (e y -intercept + 18.5) − emin y -intercept + 18 )
OR
Δθ =
(e max y -intercept
) (
+ 19 − emin y -intercept + 18 )
0
2
2(e) t determined to a minimum of 2sf from (c)(iii) and (c)(iv) OR (d)(i) with correct substitution and correct power of ten. 1
ln(25.0 − 18.5) − y -intercept
t=
gradient
OR
t = −K × ( ln(25.0 − 18.5) − y -intercept )
OR
25.0 − 18.5
t = −K × ln
θ0 − 18.5
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On this page, free: the mark scheme for AS & A Level Physics 9702/52, February/March 2025 (9702_m25_ms_52), and the question paper (9702_m25_qp_52), to read or download, with each question's marking points written out underneath.
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Physics 9702/52 for February/March 2025 is out of 30 marks, with 1 hour 15 minutes to answer it.
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