Question 1
You are provided with the following:
 A stirrer
 A stand
 a boss and a clamp
 A thermometer
 An ammeter
 A voltmeter
 A beaker
 A source of boiling water
 Two dry cells in a cell holder
 A switch
 Seven connecting wires
 A component labelled X
Proceed as follows:
 Set up the circuit as shown in figure 1.
 Close the switch, read and record the current I through component X and the potential difference V across it. (1 mark)
I= ..........
V= ..........
Open the switch.  Determine the resistance R of component X given that: R=^{V}/_{I }(1 mark)
 Close the switch, read and record the current I through component X and the potential difference V across it. (1 mark)
 Pour hot water into the beaker and set up the apparatus as in figure 2, so that component X and the thermometer bulb are fully immersed.
 Stir the water from time to time, when the temperature falls to 80°, switch on the circuit, read and record the current I and the potential difference V in table 1. Then open the switch.
 Repeat (c) as the temperature falls to the other values shown in table 1. Complete the table.
Table 1 (8 marks)
Temperature of hot water (^{o}C) 80 75 70 65 60 55 T(K) Current I (A) Potentia difference V (V) Resistance R = ^{V}/_{I} Log R (3 decimal places) Log T (3 decimal places) 
 On the axis provided, plot a graph of Log R against log T. (4 marks)
 Determine the slope S of the graph. (3 marks)
 On the axis provided, plot a graph of Log R against log T. (4 marks)
 Given that R and T are related by the equation Log R = Log K + n Log T. Determine the value of
 n (1 mark)
 K (2 marks)
Question 2
You are provided with the following
 A metre rule
 A stand, boss and clamp
 A piece of string
 A 20g mass
 A 50g mass
 A measuring cylinder containing water
 A concave mirror
 A screen
 A candle
 Pieces of sewing threads
 A mirror holder (Lens holder)
Proceed as follows
PART A
 Using a string, suspend the metre rule on the stand so that it balances horizontally at its center of gravity. Record the centimetre mark at which the metre rule balances.
Centimetre mark......................cm (1 mark)  With the metre rule balanced at its centre of gravity, suspend a 20g mass at a distance of 30cm from the centre of gravity. Suspend the 50g mass on the other side of the centre of gravity and adjust its position until the rule is balanced. See figure 3.
Record the distance d of the 50g mass from the centre of gravity.
d=............. cm
d=............. m (1 mark) 
 Record the volume of the water in the measuring cylinder provided.
V=..........................(1 mark)  Immerse the 20g mass fully into the water and adjust the position of the 50g mass so that the rule balances horizontally. Record the volume V, of the water plus 20g mass and the distance d, of the 50 mass from the centre of gravity.
V_{1} = ..................(1 mark)
d_{1} = ................... (1 mark) 
 Determine the volume of the water displaced
 Determine the weight of the water displaced. (density of water = 1 gm^{3}) (3 marks)
 Record the volume of the water in the measuring cylinder provided.

 Use the principle of moments to determine the apparent weight of the 20g mass when fully immersed in water. (g = 10 Nkg^{1}) (2 marks)
 Calculate the weight of the 20 g mass in air (g = 10 Nkg^{1}) (1 mark)
 Determine the apparent loss in weight of the 20g mass (1 mark)
PART B
 Light the candle and place it at distance u = 20 cm in front of the concave mirror. Adjust the position of the screen until a sharp image of the candle flame is obtained. See figure 4.
 Read and record the distance v between the screen and the mirror. (1 mark)
v =.........................(1 mark)  Determine:
 the magnification mof the mirror given that: m =^{v}/_{u} (1 mark)
 the value f_{1} given that: f_{1} = ^{mu}/_{(m+1)} (1 mark)
 Read and record the distance v between the screen and the mirror. (1 mark)
 Repeat part (e) for distance u_{1} = 18cm
 Read and record the distance v belween the the screen and the mirror. (1 mark)
 Determine the magnification m_{1} of the mirror. (1 mark)
 Hence determine f_{2 }(1 mark)
 Determine the average value of f (1 mark)
Confidential
Each candidate will require the following:
Question 1
 A stand, a boss and a clamp
 A thermometer (of range 10°C to 110°C)
 An ammeter (of range 01 A.)
 A voltmeter (of range 0  3 V or 05 V)
 A source of boiling water to be shared)
 A stirrer (may use a glass rod)
 A switch
 Seven connecting wires at least three with crocodile clips at one end
 Two new size D dry cells in a cell holder.
 A thermistor of specification MF72BD11 (or equivalent) of resistance approximately 5 to 10 at room temperature labelled X. (The terminals of the thermistor should be attached to crocodile clips see figure 1)
 One 250 ml beaker.
Question 2
 One metre rule
 One stand, one boss and one clamp .
 One 20g mass (the cylindrical hooked type).
 One 50g mass (or a combination that adds up to 50g)
 One piece of string of length approximately 30 cm.
 Two pieces of strong sewing thread of length approximately 30cm.
 Approximately 17 ml of water in a 25 ml measuring cylinder.
 A concave mirror of focal length 10 + 1 cm
 A white screen at least 18 cm tall.
 A piece of candle approximately 9 + 1 cm
 A mirror holder (a lens holder may be used)
 A match box (to be shared)
Marking Scheme
Question 1
You are provided with the following:
 A stirrer
 A stand
 a boss and a clamp
 A thermometer
 An ammeter
 A voltmeter
 A beaker
 A source of boiling water
 Two dry cells in a cell holder
 A switch
 Seven connecting wires
 A component labelled X
Proceed as follows:
 Set up the circuit as shown in figure 1.
 Close the switch, read and record the current I through component X and the potential difference V across it. (1 mark)
I= ..........0.34 (2 d.p)V= .......... 2.3(1 d.p)
Open the switch.
 Determine the resistance R of component X given that: R=^{V}/_{I }(2 marks)
R = ^{2.3}/_{0.34}
= 0.67Ω
 substitution (1 mark)
 evaluate to 4 s.f or exact (1 mark)
 missing unit (deny ½)
 penalise fully for wrong unit
 Close the switch, read and record the current I through component X and the potential difference V across it. (1 mark)
 Pour hot water into the beaker and set up the apparatus as in figure 2, so that component X and the thermometer bulb are fully immersed.
 Stir the water from time to time, when the temperature falls to 80°, switch on the circuit, read and record the current I and the potential difference V in table 1. Then open the switch.
 Repeat (c) as the temperature falls to the other values shown in table 1. Complete the table.
Table 1 (8 marks)
Temperature of hot water (^{o}C) 80 75 70 65 60 55 T(K) (All 1 mark) 353 348 343 338 333 328 Current I (A) (2d.p 2 marks) 0.76 0.72 0.68 0.64 0.60 0.56 Potentia difference V (V) 1.40 1.50 1.55 1.60 1.70 1.8 Resistance R = ^{V}/_{I} (4 s.f or exact 1 mrk) 1.84 2.08 2.28 2.50 2.83 3.21 Log R (3 decimal places) all (1 mrk) 0.265 0.318 0.358 0.398 0.452 0.507 Log T (3 decimal places) All (1 mark) 2.548 2.542 2.585 2.529 2.522 2.516 
 On the axis provided, plot a graph of Log R against log T. (4 marks)
 Determine the slope S of the graph. (2 marks)
Slope S = – (5.5 – 4.0) × 10^{1}
2.51 – 2.528
= 1.5 × 10^{1}
0.018
= 8.33
 No line no slope
Δy ½ mark
Δx ½ mark
evaluate ^{Δy}/_{Δx }to atleast 4 s.f or exact (1 mk)
 No line no slope
 On the axis provided, plot a graph of Log R against log T. (4 marks)
 Given that R and T are related by the equation Log R = Log K + n Log T. Determine the value of
 n (1 mark)
 n=gradient/slope ½ mark
n= answer above (½ mark) (without the satetement it is implied( ignore units)
 n=gradient/slope ½ mark
 K (2 marks)
 log k = y intercept or log k = C
log K = 0.63
K = antilog of 0.63
K = 4.265
K = 4.3  Correctly obtained log K from the graph (½ mark)
 Antilog obtained at least 4 s.f (½ mark)
 log k = y intercept or log k = C
 n (1 mark)
Question 2
You are provided with the following
 A metre rule
 A stand, boss and clamp
 A piece of string
 A 20g mass
 A 50g mass
 A measuring cylinder containing water
 A concave mirror
 A screen
 A candle
 Pieces of sewing threads
 A mirror holder (Lens holder)
Proceed as follows
PART A
 Using a string, suspend the metre rule on the stand so that it balances horizontally at its center of gravity. Record the centimetre mark at which the metre rule balances.
Centimetre mark ....50.1 cm (1 mark)  With the metre rule balanced at its centre of gravity, suspend a 20g mass at a distance of 30cm from the centre of gravity. Suspend the 50g mass on the other side of the centre of gravity and adjust its position until the rule is balanced. See figure 3.
Record the distance d of the 50g mass from the centre of gravity.
d=............. 11.3 cm (1 dp) (½ mark)
d=.............0.113 m (1 mark) conversion to at least 3 d.p (½ mark) 
 Record the volume of the water in the measuring cylinder provided.
V=..........................17cm^{3} or ml (rule on units apply)(1 mark)  Immerse the 20g mass fully into the water and adjust the position of the 50g mass so that the rule balances horizontally. Record the volume V, of the water plus 20g mass and the distance d, of the 50 mass from the centre of gravity.
V_{1} = ..................19.5cm^{3} or ml (1 mark)
d_{1} = ................... 10 cm (1 mark) 
 Determine the volume of the water displaced
V = V_{1} − V
= 19.5 − 17
= 2.5 cm^{3}
 Exact substitution of V_{1}V cm^{3 }or ml accept answer only
 Determine the weight of the water displaced. (density of water = 1 gm^{3}) (3 marks)
ρV = m
w = mg = 2.5 × 10 × 10^{3}
= 2.5 × 10^{2}
 Conversion of volume to mass i.e ρ×v = m must be shown
 Convert the mass to Newton (1 mk) (Rule on units apply)
 Determine the volume of the water displaced
 Record the volume of the water in the measuring cylinder provided.

 Use the principle of moments to determine the apparent weight of the 20g mass when fully immersed in water. (g = 10 Nkg^{1}) (2 marks)
 Working using principle of moments
W×0.3 = 0.5 × 0.1 (1 mk)
W = 0.166
evaluation (1 mk) (Exact or atleast 4 s.f) Rule on units apply
 Working using principle of moments
 Calculate the weight of the 20 g mass in air (g = 10 Nkg^{1}) (1 mark)
 ^{20}/_{1000}×10 = 0.2N (Rule on units apply)
 Determine the apparent loss in weight of the 20g mass (1 mark)
= 0.2  0.17
= 0.03 N
 Weight of air  weight in water (Unit in Newtons) (Rule on units apply)
OR
Loss in weight = weight of water displaced in Newtons
 Weight of air  weight in water (Unit in Newtons) (Rule on units apply)
 Use the principle of moments to determine the apparent weight of the 20g mass when fully immersed in water. (g = 10 Nkg^{1}) (2 marks)
PART B
 Light the candle and place it at distance u = 20 cm in front of the concave mirror. Adjust the position of the screen until a sharp image of the candle flame is obtained. See figure 4.
 Read and record the distance v between the screen and the mirror. (1 mark)
When U = 15
V = 42 (1 mark)  Determine:
 the magnification mof the mirror given that: m =^{v}/_{u} (1 mark)
M_{1} = ^{42}/_{15}
= 2.8
 substitution (½ mk)
 evaluation (½ mk) (Exact/4 s.f) deny ½ mk if no units
 the value f_{1} given that: f_{1} = ^{mu}/_{(m+1)} (1 mark)
f_{1} = 2.8 × 15
2.8 + 1
= 11.05
 substitution (½ mk)
 evaluation (½ mk) (Exact/4 s.f) wrong/missing units deny ½ mk
 the magnification mof the mirror given that: m =^{v}/_{u} (1 mark)
 Read and record the distance v between the screen and the mirror. (1 mark)
 Repeat part (e) for distance u_{1} = 18cm
 Read and record the distance v belween the the screen and the mirror. (1 mark)
 When U = 18
v = 29 1d.p (rule for units apply)
 When U = 18
 Determine the magnification m_{1} of the mirror. (1 mark)
 M = ^{v}/_{u} = ^{29}/_{18} = 1.6
substitution (½ mark);
evaluate 4 s.f./exact(½)
deny ½ mk if no units
 M = ^{v}/_{u} = ^{29}/_{18} = 1.6
 Hence determine f_{2 }(1 mark)
^{1}/_{f} = ^{1}/_{u} + ^{1}/_{v} or f_{2} = (^{m2+1)}/(m_{1}+1)
f_{2}= 1.6 × 18
1.6 × 1
= 11.08
substitution (½ mark);
evaluate 4 s.f./exact(1 mark)
deny ½ mk if no units
 Read and record the distance v belween the the screen and the mirror. (1 mark)
 Determine the average value of f (1 mark)
Average f = 11.05 + 11.08
2
= 11.1
 f =^{ f1+ f2}/_{2} must be shown
 substitution (½ mark);
evaluate 4 s.f./exact(1 mark)
ignore units
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