Practice questions
Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not
Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.
Q1Graph & data analysis · Core · Paper 6 style · 7 marksA student hangs loads on a spring and measures its length each time.load F / N: 0, 1.0, 2.0, 3.0, 4.0, 5.0length / cm: 4.0, 5.6, 7.1, 8.7, 10.2, 11.8
- (a) Calculate the extension e of the spring for each load. [1]
- (b) Plot a graph of load F (y-axis) against extension e (x-axis) and draw the best-fit line. [3]
- (c) Determine the gradient of your line. Show clearly on the graph how you obtained the values you used. [2]
- (d) State whether the results show that extension is proportional to load. Give a reason. [1]
Show answer
- (a) 0, 1.6, 3.1, 4.7, 6.2, 7.8 cm
B1 all extensions correct (length − 4.0 cm).
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 0.64 N/cm (accept 0.62–0.66)
B1 large triangle (over half the line) used B1 gradient 0.62–0.66 N/cm, e.g. 5.0 ÷ 7.8 = 0.64.
- (d) Yes: the graph is a straight line passing through the origin.
B1 yes + straight line through origin.
Hot water in a beaker is left to cool. Its temperature θ is recorded every minute.t / min: 0, 1, 2, 3, 4, 5, 6θ / °C: 95, 84, 75, 68, 62, 58, 55
- (a) Describe how the temperature of the water changes during the 6 minutes. [2]
- (b) Calculate the average rate of cooling during the first 2 minutes and during the last 2 minutes. [2]
- (c) Suggest a value for the temperature at t = 7 min. Explain your answer. [2]
Show answer
- (a) The temperature decreases, quickly at first and then more slowly.
B1 temperature decreases B1 rate of decrease gets smaller.
- (b) 10 °C/min and 3.5 °C/min
(95 − 75) ÷ 2 = 10 °C/min B1; (62 − 55) ÷ 2 = 3.5 °C/min B1.
- (c) About 52–53 °C, because the temperature is still falling but each drop is smaller than the previous one (3 °C between 5 and 6 min).
B1 value between 51 and 54 °C B1 reason: decrease continues but smaller than 3 °C.
In this experiment you measure the current I in a resistor for different values of potential difference V. Your readings are:V / V: 1.0, 2.0, 3.0, 4.0, 5.0I / A: 0.21, 0.40, 0.69, 0.81, 1.00
- (a) Identify the anomalous reading and suggest the value of current you would expect. [2]
- (b) Plot a graph of V (y-axis) against I (x-axis), ignoring the anomalous point, and draw the best-fit line. [3]
- (c) Use the gradient of your graph to find the resistance of the resistor. [2]
Show answer
- (a) I = 0.69 A at 3.0 V; expected about 0.60 A
B1 0.69 A (3.0 V) identified B1 about 0.60 A.
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 5.0 Ω (accept 4.8–5.2)
B1 large triangle B1 R = 5.0 ÷ 1.00 = 5.0 Ω.
A student adds different volumes of cold water at 20.0 °C to 100 cm³ of hot water at 70.0 °C, stirs, and records the final temperature.volume of cold water / cm³: 0, 50, 100, 150, 200final temperature / °C: 70.0, 52.5, 44.0, 39.0, 35.5
- (a) Describe the relationship between the volume of cold water added and the final temperature. [1]
- (b) Estimate the final temperature if 125 cm³ of cold water were added. [1]
- (c) Assuming no energy losses, the final temperature when 100 cm³ of cold water is added should be 45.0 °C. Show that this is the expected value. [2]
- (d) Suggest why the measured value is lower than 45.0 °C. [1]
Show answer
- (a) The more cold water is added, the lower the final temperature, but each extra 50 cm³ causes a smaller drop.
B1 temperature decreases as volume increases (by smaller amounts).
- (b) about 41–42 °C
B1 value between 39.0 and 44.0 °C, ≈ 41.5 °C.
- (c) 100 × (70 − T) = 100 × (T − 20), so T = (70 + 20) ÷ 2 = 45.0 °C
M1 energy lost by hot water = energy gained by cold water A1 T = 45.0 °C.
- (d) Energy is lost to the beaker and the surroundings.
B1 energy transferred to the beaker / air / thermometer.
In this experiment you connect different lengths l of a resistance wire into a circuit with an ammeter and a voltmeter. One set of readings is shown.l / cm: 20.0, 40.0, 60.0, 80.0, 100.0V / V: 0.52, 0.81, 0.98, 1.11, 1.18I / A: 0.62, 0.48, 0.39, 0.33, 0.28
- (a) Calculate the resistance R = V/I for each length. Give each value to 2 decimal places. [2]
- (b) Plot a graph of R (y-axis) against l (x-axis) and draw the best-fit line. [3]
- (c) Use your graph to find the resistance of 70.0 cm of the wire. [1]
- (d) Determine the resistance per centimetre of the wire. [1]
Show answer
- (a) 0.84, 1.69, 2.51, 3.36, 4.21 Ω
B1 at least three correct B1 all correct (0.84, 1.69, 2.51, 3.36, 4.21 Ω).
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 2.95 Ω (accept 2.85–3.05)
B1 value read from the line at 70 cm, ≈ 2.95 Ω.
- (d) about 0.042 Ω/cm
B1 gradient ≈ 4.21 ÷ 100 = 0.042 Ω/cm.
A student uses a converging lens to form a sharp image of an illuminated object on a screen. She measures the object distance u and image distance v.u / cm: 20.0, 25.0, 30.0, 40.0v / cm: 59.0, 38.0, 30.5, 23.5
- (a) Calculate f = uv/(u + v) for each pair of readings. Give each value to 3 significant figures. [2]
- (b) Calculate the average value of f. [1]
- (c) A second student finds f = 16.2 cm using a distant window. Take the limit of experimental accuracy as 5%. State whether the two values can be considered equal within this limit. Justify your answer with a calculation. [2]
- (d) Suggest one difficulty in judging the position of the sharpest image and how it can be reduced. [1]
Show answer
- (a) 14.9, 15.1, 15.1, 14.8 cm
B1 at least two correct B1 all four correct.
- (b) 15.0 cm
B1 (14.9 + 15.1 + 15.1 + 14.8) ÷ 4 = 15.0 cm.
- (c) No: the difference (1.2 cm) is 8% of 15.0 cm, which is more than 5%.
B1 percentage difference calculated (1.2 ÷ 15.0 × 100 = 8%) B1 not equal, since 8% > 5%.
- (d) The image looks sharp over a range of positions; move the screen back and forth and use the midpoint of the positions where it just starts to blur (or darken the room).
B1 any sensible technique: find positions either side where image blurs and take midpoint / darken room / use a bright object.
A student pours water into a measuring cylinder on a balance and records the total mass m for different volumes V.V / cm³: 20, 40, 60, 80, 100m / g: 132.0, 152.5, 171.5, 192.0, 212.0
- (a) Plot a graph of total mass m (y-axis) against volume V (x-axis). Start the y-axis at 100 g. Draw the best-fit line. [3]
- (b) Determine the gradient of the line and state what it represents. [2]
- (c) Use your graph to find the mass of the empty measuring cylinder. [1]
- (d) State one precaution when reading the volume of water. [1]
Show answer
- (a) A straight line with a positive intercept.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (b) about 1.0 g/cm³ (accept 0.97–1.03); the density of water
B1 gradient ≈ (212.0 − 132.0) ÷ 80 = 1.0 g/cm³ B1 density of water.
- (c) about 112 g (accept 111–113 g)
B1 intercept at V = 0, ≈ 112 g.
- (d) Read the bottom of the meniscus with the eye level with it.
B1 eye level with bottom of meniscus / cylinder on a flat surface.
A student hangs loads on a rubber band and measures the extension.load / N: 0, 1.0, 2.0, 3.0, 4.0, 5.0extension / cm: 0, 2.0, 4.2, 7.0, 10.6, 15.0
- (a) Calculate extension ÷ load for each load. [2]
- (b) State whether the extension of the rubber band is proportional to the load. Explain your answer using your values from (a). [2]
- (c) Suggest how the student could check whether the band has been permanently stretched. [1]
Show answer
- (a) 2.00, 2.10, 2.33, 2.65, 3.00 cm/N
B1 at least three correct B1 all correct (2.00, 2.10, 2.33, 2.65, 3.00).
- (b) No: extension ÷ load is not constant; it increases from 2.00 to 3.00 cm/N, so the graph would curve upwards rather than be a straight line through the origin.
B1 not proportional B1 ratio not constant (increases) / graph not a straight line through origin.
- (c) Remove all the loads and see whether it returns to its original length.
B1 unload and measure length again.
A student times 20 oscillations of a simple pendulum for different lengths l.l / m: 0.20, 0.40, 0.60, 0.80, 1.00t (20 oscillations) / s: 17.9, 25.4, 31.1, 35.9, 40.1
- (a) Calculate the period T and T² for each length. Record T² to 3 significant figures. [2]
- (b) Plot a graph of T² (y-axis) against l (x-axis) and draw the best-fit line. [3]
- (c) Determine the gradient G of the line. [2]
- (d) Calculate g using g = 4π²/G. Give your answer to 2 significant figures with its unit. [2]
Show answer
- (a) T / s: 0.895, 1.27, 1.56, 1.80, 2.01 (to 3 s.f.); T² / s²: 0.801, 1.61, 2.42, 3.22, 4.02
B1 T = t ÷ 20 all correct B1 T² all correct to 3 s.f.
- (b) A straight line through (or very close to) the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 4.0 s²/m (accept 3.9–4.1)
B1 large triangle B1 G ≈ (4.02 − 0.80) ÷ 0.80 = 4.0 s²/m.
- (d) 9.8 m/s² (accept 9.6–10)
C1 g = 4π² ÷ 4.0 A1 9.8 m/s².
A student traces rays through a glass block and measures the angle of refraction r for different angles of incidence i, to the nearest degree.i / °: 20, 30, 40, 50, 60r / °: 13, 19, 25, 31, 35
- (a) Calculate sin i and sin r for each pair. Give values to 3 decimal places. [2]
- (b) Plot a graph of sin i (y-axis) against sin r (x-axis) and draw the best-fit line. [3]
- (c) Determine the gradient of the line. State what this gradient represents. [2]
- (d) Suggest why the student uses a range of angles of incidence rather than a single angle. [1]
Show answer
- (a) sin i: 0.342, 0.500, 0.643, 0.766, 0.866; sin r: 0.225, 0.326, 0.423, 0.515, 0.574
B1 sin i correct B1 sin r correct.
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 1.50 (accept 1.45–1.55); the refractive index of the glass
B1 gradient ≈ (0.866 − 0.342) ÷ (0.574 − 0.225) = 1.50 B1 refractive index.
- (d) A graph from several readings averages out random errors in measuring the angles, giving a more reliable value.
B1 reduces effect of random error / checks the relationship holds / more reliable.
A metre rule is balanced at its centre on a pivot. A fixed load hangs on one side. A student places different masses m on the other side and moves each until the rule balances, recording the distance d of the mass from the pivot.m / g: 50, 100, 150, 200, 250d / cm: 30.2, 14.9, 10.1, 7.4, 6.0
- (a) Calculate 1/m for each mass, in g⁻¹. [1]
- (b) Plot a graph of d (y-axis) against 1/m (x-axis) and draw the best-fit line. [3]
- (c) Determine the gradient of the line. [2]
- (d) Use the principle of moments to explain why the graph of d against 1/m is a straight line through the origin. [2]
Show answer
- (a) 0.020, 0.010, 0.0067, 0.0050, 0.0040
B1 all correct.
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 1500 g cm (accept 1450–1550)
B1 large triangle B1 ≈ (30.2 − 6.0) ÷ (0.020 − 0.0040) = 1500 g cm.
- (d) The moment of the fixed load on the other side is constant, so m × d = constant for balance; therefore d = constant × (1/m), which is a straight line through the origin with gradient equal to the constant.
B1 clockwise moment = anticlockwise moment, the other moment is constant B1 so md = constant, d ∝ 1/m.
A ball is released from rest at the top of a long ramp. A student measures the time t for the ball to roll different distances s.s / m: 0.20, 0.40, 0.60, 0.80, 1.00t / s: 0.90, 1.26, 1.55, 1.80, 2.00
- (a) Calculate t² for each distance. Give values to 2 significant figures where appropriate. [1]
- (b) Plot a graph of s (y-axis) against t² (x-axis) and draw the best-fit line. [3]
- (c) Determine the gradient of the line. [2]
- (d) The relationship is s = ½at². Use your gradient to find the acceleration a of the ball. [1]
- (e) Suggest why it is difficult to obtain accurate values of t for the shorter distances, and one improvement. [2]
Show answer
- (a) 0.81, 1.6, 2.4, 3.2, 4.0 s²
B1 all correct.
- (b) A straight line through the origin.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (c) about 0.25 m/s² (accept 0.24–0.26)
B1 large triangle B1 (1.00 − 0.20) ÷ (4.00 − 0.81) = 0.25.
- (d) about 0.50 m/s²
B1 a = 2 × gradient ≈ 0.50 m/s².
- (e) The times are short, so human reaction time is a large fraction of each time; repeat each timing and average (or use light gates).
B1 reaction time large compared with short times B1 repeat and average / use light gates / data logger.
In this experiment you heat 0.50 kg of water in an insulated beaker with a 50 W immersion heater, recording the temperature θ every 2 minutes.t / s: 0, 120, 240, 360, 480, 600θ / °C: 21.0, 23.6, 26.4, 29.1, 31.7, 34.4
- (a) Plot a graph of θ (y-axis) against t (x-axis) and draw the best-fit line. [3]
- (b) Determine the gradient G of the line, in °C/s. [2]
- (c) Calculate the specific heat capacity of water using c = P/(mG). Give your answer to 2 significant figures. [2]
- (d) Suggest one reason why this value differs from 4200 J/(kg °C) and one improvement. [2]
Show answer
- (a) A straight line with positive gradient and intercept at 21 °C.
B1 axes labelled with quantity and unit, sensible scale (points fill more than half the grid) B1 all points plotted to within half a small square B1 single thin best-fit line
- (b) about 0.022 °C/s (accept 0.021–0.023)
B1 large triangle B1 G ≈ (34.4 − 21.0) ÷ 600 = 0.0223 °C/s.
- (c) 4500 J/(kg °C) (about 4.5 × 10³)
C1 c = 50 ÷ (0.50 × 0.0223) A1 ≈ 4500 J/(kg °C).
- (d) The heater's power may not all go into the water / the stated power may be inaccurate; the water may not be evenly heated. Improvement: insulate and cover the beaker and stir before each reading.
B1 reason (e.g. power rating not accurate / uneven temperature / thermometer reading) B1 matching improvement (stir; insulate; lid; use joulemeter).
You wind 25 turns of copper wire closely around a pencil. With a millimetre ruler, you find that the 25 turns cover a length of 2.0 cm.
- (a) Calculate the diameter of the wire in mm. [2]
- (b) Explain why measuring 25 turns gives a more accurate result than measuring the width of one turn with the ruler. [1]
- (c) State one precaution when winding the wire. [1]
Show answer
- (a) 0.80 mm
C1 d = 20 mm ÷ 25 A1 = 0.80 mm.
- (b) One turn is too small to measure accurately with a mm ruler; measuring many turns makes the uncertainty in each turn much smaller.
B1 reduces (percentage) uncertainty / one turn smaller than ruler precision.
- (c) Wind the turns tightly with no gaps and no overlaps.
B1 turns touching, no gaps or overlaps.
A student records the time for a ball to roll down a ramp for different lengths in a table:Heading row: length | timeRow 1: 20 | 2.1Row 2: 40 | 2.15Row 3: 60 cm | 2
- (a) Identify two mistakes in the way the student has recorded these results. [2]
- (b) Rewrite the column headings correctly. [1]
- (c) The stopwatch reads to 0.01 s. Suggest to how many decimal places the student should record the times, and why. [1]
Show answer
- (a) The time column heading has no unit; the times are recorded to different numbers of decimal places (2.1, 2.15, 2); a unit is written next to a value in the table body ("60 cm").
1 mark each for any two of: missing unit in heading; inconsistent decimal places; unit in body of table; length heading uses no '/ unit' form.
- (b) length / cm and time / s
B1 both headings with quantity / unit.
- (c) 1 decimal place (or 2 d.p. consistently): human reaction time (about 0.1–0.2 s) makes the second decimal place meaningless.
B1 0.1 s / 1 d.p. justified by reaction time (accept 2 d.p. consistently if justified as the instrument precision).
You time 20 complete oscillations of a pendulum twice. The readings are 31.6 s and 31.8 s.
- (a) Calculate the average time for 20 oscillations and the period T of the pendulum. [2]
- (b) Explain why you time 20 oscillations rather than one. [1]
- (c) Suggest where a fixed reference mark (fiducial marker) should be placed, and why. [2]
Show answer
- (a) 31.7 s; T = 1.585 s ≈ 1.59 s
B1 average 31.7 s B1 T = 31.7 ÷ 20 = 1.585 s (accept 1.58 or 1.59 s).
- (b) Reaction time errors become small compared with the total time, so T is more accurate.
B1 reduces the effect of reaction time / percentage uncertainty.
- (c) At the centre (lowest point) of the swing, because the bob moves fastest there, so the moment it passes can be judged most precisely.
B1 at the centre / lowest point of the swing B1 bob moves fastest there – easier to judge when it passes.
A student measures the temperature of water in a beaker heated on a Bunsen burner.
- (a) The thermometer is marked in 1 °C intervals. A student records the temperature as 24.37 °C. Comment on this reading. [1]
- (b) State two things the student should do to make sure each temperature reading of the water is accurate. [2]
- (c) Suggest why the bulb of the thermometer should not touch the bottom of the beaker when water is being heated from below. [1]
Show answer
- (a) It is too precise: the thermometer can only be read to about 0.5 °C, so it should be recorded as 24.5 °C (or 24 °C).
B1 not possible to read to 0.01 °C – record to nearest 0.5 °C (or 1 °C).
- (b) Stir the water before reading; read the scale with the eye level with the top of the liquid thread (avoid parallax); wait until the reading is steady; keep the bulb fully in the water but not touching the beaker.
1 mark each for any two of: stir; eye level / avoid parallax; wait for reading to stop changing; bulb fully immersed, not touching beaker.
- (c) The base of the beaker is hotter than the water, so the reading would be too high.
B1 base hotter than the water – reading too high.
You find the density of a small stone collected from the bank of the River Swat. The mass of the stone is 49.6 g. You put water in a measuring cylinder to the 50.0 cm³ mark; after the stone is lowered in, the level is at 68.5 cm³.
- (a) Calculate the volume of the stone. [1]
- (b) Calculate the density of the stone. Give your answer to 3 significant figures. [2]
- (c) State two precautions you should take to obtain an accurate volume. [2]
Show answer
- (a) 18.5 cm³
68.5 − 50.0 = 18.5 cm³ B1.
- (b) 2.68 g/cm³
C1 ρ = 49.6 ÷ 18.5 A1 = 2.68 g/cm³.
- (c) Lower the stone gently (tilted cylinder / on a thread) so no water splashes out; read the bottom of the meniscus with the eye level; make sure no air bubbles cling to the stone; make sure the stone is fully covered.
1 mark each for any two of: no splashing; eye level with bottom of meniscus; no air bubbles; stone fully submerged; cylinder on a level surface.
You measure the resistance of a resistor using a battery, a switch, an ammeter and a voltmeter.
- (a) Describe how the ammeter and voltmeter must be connected in the circuit. [2]
- (b) Before the switch is closed, the ammeter reads 0.02 A. With the switch closed it reads 0.36 A. State the correct current. [1]
- (c) The voltmeter reads 2.7 V. Calculate the resistance, giving your answer to 2 significant figures. [1]
- (d) Suggest why the switch should be opened between readings. [1]
Show answer
- (a) Ammeter in series with the resistor; voltmeter in parallel with (across) the resistor.
B1 ammeter in series B1 voltmeter in parallel across the resistor.
- (b) 0.34 A
B1 zero error: 0.36 − 0.02 = 0.34 A.
- (c) 7.9 Ω
B1 R = 2.7 ÷ 0.34 = 7.9 Ω.
- (d) To stop the resistor heating up, which would change its resistance.
B1 prevents heating / temperature rise changing resistance (and saves the battery).
A student measures the thickness of a stack of 200 sheets of exam paper with a ruler at three different places. The readings are 2.18 cm, 2.22 cm and 2.20 cm.
- (a) Calculate the average thickness of the stack in cm. [1]
- (b) Calculate the thickness of one sheet in mm. Give your answer to 2 significant figures. [2]
- (c) Explain why the stack was measured in three places. [1]
- (d) The student used a ruler whose end was slightly worn, so it was measured from the 1.0 cm mark. Explain why this is a sensible technique. [1]
- (e) Suggest why calipers would give a better result than a ruler. [1]
Show answer
- (a) 2.20 cm
(2.18 + 2.22 + 2.20) ÷ 3 = 2.20 cm B1.
- (b) 0.11 mm
C1 22.0 mm ÷ 200 A1 = 0.11 mm.
- (c) The stack may not be the same thickness everywhere (pages not pressed flat), so averaging gives a more representative value.
B1 thickness varies / averaging reduces random error.
- (d) It avoids a zero error caused by the worn end; the reading is taken as the difference between two marks.
B1 avoids zero error from worn end.
- (e) Calipers read to 0.1 mm (or better), so the percentage uncertainty in the stack thickness is smaller; they also squeeze the stack evenly.
B1 higher precision / smaller uncertainty.
A student traces a ray through a rectangular glass block using optical pins. She draws round the block, marks the normal, and uses two pins on each side of the block.
- (a) State two techniques that make the positions of the pins and the drawn rays as accurate as possible. [2]
- (b) The angle of incidence is 40° and the measured angle of refraction is 25°. Calculate the refractive index of the block, to 3 significant figures. [2]
- (c) Suggest one source of inaccuracy in measuring the angle of refraction and how it could be reduced. [2]
Show answer
- (a) Place the pins well apart (at least 5 cm); look at the bases of the pins when lining them up; draw thin pencil lines; mark pin positions with small crosses.
1 mark each for any two of: pins far apart; view bases of pins; thin sharp pencil lines; pins vertical.
- (b) 1.52
C1 n = sin 40° ÷ sin 25° A1 = 1.52.
- (c) The normal may not be drawn exactly at 90° to the surface; use a protractor or set square to draw it carefully (or: the block outline may move – draw round it and check its position).
B1 source (normal not at 90° / block moved / thick lines / protractor reading) B1 matching improvement.
You measure the outside diameter of a test tube in two ways.Method 1: two set squares are placed against the tube on a ruler. Readings at the edges: 4.3 cm and 5.9 cm. Two more diameters, measured at other points along the tube, are 1.7 cm and 1.6 cm.Method 2: a thin string is wound 5 times around the tube; the unwound length is 25.6 cm.
- (a) Calculate the diameter from the first set-square reading and the average diameter from the three readings. [2]
- (b) Use the string measurement to calculate the diameter of the test tube. Give your answer to 3 significant figures. [2]
- (c) State whether the two methods agree within the limits of experimental accuracy. Justify your answer. [1]
- (d) Explain how the set squares should be used to avoid parallax error. [1]
Show answer
- (a) 1.6 cm; average 1.63 cm
B1 5.9 − 4.3 = 1.6 cm B1 (1.6 + 1.7 + 1.6) ÷ 3 = 1.63 cm.
- (b) 1.63 cm
C1 circumference = 25.6 ÷ 5 = 5.12 cm; d = 5.12 ÷ π A1 = 1.63 cm.
- (c) Yes: 1.63 cm and 1.63 cm differ by much less than 5% (less than 0.1 cm).
B1 yes, with difference compared to a stated limit (e.g. within 5% / 0.1 cm).
- (d) Place the set squares with their vertical edges touching the sides of the tube and resting on the ruler, so the reading is taken straight where the edge meets the scale, viewed from directly above.
B1 set square edges perpendicular to ruler, touching tube; read with eye directly above the edge.
- (a) Plan an experiment to investigate how the resistance of a metal wire depends on its length. You are provided with: a length of thin constantan wire on a metre rule, a battery, an ammeter, a voltmeter, connecting leads with crocodile clips and a switch.In your plan, you should:• describe the circuit (in words) and how you would carry out the investigation• state the key variables to keep constant• draw a table with column headings to show how you would display your readings• explain how you would use your readings to reach a conclusion. [7]
Show answer
- (a) Connect the battery, switch, ammeter and the wire in series, with the voltmeter across the wire between the crocodile clips. Vary length (e.g. 20, 40, 60, 80, 100 cm), record V and I, calculate R = V/I; keep wire material/diameter and temperature constant (switch off between readings); table l / cm | V / V | I / A | R / Ω; plot R against l – straight line through origin shows R ∝ l.
1 mark each, up to 7: correct circuit in words (ammeter in series, voltmeter across the measured length) (B1); measure length between clips with metre rule (B1); record V and I and calculate R = V/I (B1); at least five lengths over a wide range (B1); control: same wire (material, thickness) and constant temperature / switch off between readings / low current (B1); table with l / cm, V / V, I / A, R / Ω (B1); plot R against l; straight line through origin ⇒ proportional (B1).
Two methods are used to find the spring constant of the same spring. From a load–extension graph, k = 25.0 N/m. From timing vertical oscillations of a mass on the spring (5 oscillations timed once), k = 23.5 N/m.
- (a) Calculate the percentage difference between the two values, using the graph value as the reference. [1]
- (b) A student says the two values are equal within the limits of experimental accuracy. State whether you agree, using a 10% limit. [1]
- (c) Suggest two improvements to the method that would make the oscillation value more reliable. [2]
- (d) Suggest one reason why the load–extension method might give an inaccurate value. [1]
Show answer
- (a) 6%
B1 (25.0 − 23.5) ÷ 25.0 × 100 = 6%.
- (b) Agree: 6% is within 10%.
B1 agree, 6% < 10%.
- (c) Time more oscillations (e.g. 20) and repeat each timing then average; use a fiducial marker at the centre of oscillation; use smaller amplitude oscillations so the spring stays vertical.
1 mark each for any two sensible improvements: more oscillations; repeat and average; fiducial marker; small vertical oscillations.
- (d) Parallax when reading the ruler beside the spring (eye not level with the pointer), or the ruler not vertical.
B1 parallax / ruler not vertical / spring overstretched beyond limit of proportionality.
- (a) Plan an experiment to investigate how the thickness of insulation around a beaker affects the rate of cooling of hot water. You are provided with: beakers, a supply of hot water, cotton wool, a thermometer, a stopwatch, a measuring cylinder. You may also use other apparatus usually found in a school laboratory.In your plan, you should:• explain briefly how you would carry out the investigation• state the key variables to keep constant• draw a table, or tables, with column headings, to show how you would display your readings• explain how you would use your readings to reach a conclusion. [7]
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- (a) Wrap beakers in different thicknesses of cotton wool (e.g. 0, 1, 2, 3, 4 cm), add the same volume of hot water at the same starting temperature, record the temperature drop over a fixed time (e.g. 10 min); keep volume, start temperature, beaker size, room temperature, lid same; table: thickness / cm | initial θ / °C | final θ / °C | drop / °C; plot temperature drop against thickness.
1 mark each, up to 7: measure thickness with a ruler / use number of layers (B1); same volume of water measured with measuring cylinder (B1 method detail); measure θ at start and after a fixed time, e.g. 10 min (B1); repeat for at least 5 thicknesses (B1); two control variables, e.g. starting temperature, volume of water, size of beaker, room temperature, lid/no lid (B1); table with thickness / cm and temperatures / °C with units (B1); conclusion: plot temperature fall (or rate) against thickness and see whether fall decreases as thickness increases (B1).
- (a) Plan an experiment to investigate how the angle of a ramp affects the average speed of a toy car rolling down it. You are provided with: a long wooden ramp, a toy car, a stack of books, a protractor, a metre rule and a stopwatch.In your plan, you should:• explain briefly how you would carry out the investigation• state the key variables to keep constant• draw a table with column headings• explain how you would use your readings to reach a conclusion. [7]
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- (a) Set the ramp at angles (e.g. 5°, 10°, 15°, 20°, 25°) measured with a protractor; release the car from rest from the same start line; time it over a fixed measured distance (e.g. 1.00 m), repeat 3 times and average; average speed = distance ÷ time; keep car, distance, release method, ramp surface same; table angle / ° | t₁ / s | t₂ / s | t₃ / s | average t / s | speed / m/s; plot speed against angle.
1 mark each, up to 7: measure angle with protractor (or height with rule) (B1); release from rest from same mark – do not push (B1); time over a fixed measured distance (B1); repeat timings and average (B1); at least five angles over a suitable range (B1); control variable, e.g. same car / distance / surface (B1); table with units and conclusion by plotting average speed against angle and describing the trend (B1).
A student times 10 oscillations of a pendulum with a 50 g bob and then with a 100 g bob, keeping the string length the same. Times: 50 g bob 15.8 s; 100 g bob 16.1 s.
- (a) Calculate the period for each bob. [1]
- (b) A student suggests that the period does not depend on the mass of the bob. State whether these results support this, if the experiment is accurate to within 5%. Justify your answer with a calculation. [2]
- (c) Suggest two improvements that would make this conclusion more reliable. [2]
- (d) Explain why the length must be measured to the centre of each bob. [1]
Show answer
- (a) 1.58 s and 1.61 s
B1 15.8 ÷ 10 = 1.58 s; 16.1 ÷ 10 = 1.61 s.
- (b) Yes: the difference is 1.9% of 1.58 s, which is less than 5%.
B1 percentage difference ≈ 1.9% (or 0.03 s) B1 within 5% so supports the suggestion.
- (c) Use more masses (at least five) over a wide range; repeat each timing and average; time 20 oscillations; keep the length (to the centre of the bob) and amplitude exactly the same.
1 mark each for any two of: more masses; repeat and average; more oscillations; keep length measured to centre of bob the same; small, equal amplitude.
- (d) Bobs of different sizes would otherwise give different effective lengths, which changes the period.
B1 effective length changes with bob size.
- (a) Plan an experiment to investigate whether the colour of a surface affects the rate at which it absorbs infrared radiation. You are provided with: identical metal cans (some painted matt black, matt white, shiny silver), an infrared lamp, thermometers, a stopwatch, a measuring cylinder and water at room temperature.In your plan, you should:• explain briefly how you would carry out the investigation• state the key variables to keep constant• draw a table with column headings to show how you would display your readings• explain how you would use your readings to reach a conclusion. [7]
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- (a) Put the same volume of water at the same starting temperature in each can, place each the same distance from the infrared lamp (or arrange them at equal distances around it), record temperature every minute for 10 minutes; keep volume, distance, start temperature, lamp power, can size same; table: time / min | θ black / °C | θ white / °C | θ silver / °C; compare temperature rise (or plot θ against t for each) – greatest rise means best absorber.
1 mark each, up to 7: same volume of water measured in a measuring cylinder (B1); cans the same distance from the lamp (B1); record temperature at regular intervals or after fixed time (B1); stir before reading / lids with thermometer through hole (B1 technique); two control variables, e.g. initial temperature, lamp power, can size, room conditions (B1); table with time / min and temperatures / °C for each colour (B1); conclusion: compare temperature rises / plot graphs; the largest rise in the same time shows the best absorber (B1).
- (a) Plan an experiment to investigate how the number of turns of wire on an electromagnet affects its strength. You are provided with: a soft-iron nail, a reel of insulated copper wire, a battery, a variable resistor, an ammeter, a switch and a box of small steel paper clips.In your plan, you should:• explain briefly how you would carry out the investigation, including how you would measure the strength• state the key variables to keep constant• draw a table with column headings• explain how you would use your readings to reach a conclusion. [7]
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- (a) Wind 10, 20, 30, 40, 50 turns on the nail; connect in series with battery, switch, ammeter and variable resistor; adjust the variable resistor so the current is the same each time; dip the nail end into the clips and count how many are lifted; repeat three times and average; switch off between readings; keep current, nail, clip size the same; table number of turns | clips lifted (1, 2, 3, average); plot average number of clips against number of turns.
1 mark each, up to 7: circuit in series with ammeter and variable resistor (B1); strength measured by number of paper clips lifted (B1); adjust variable resistor to keep current constant (key control) (B1); second control, e.g. same nail / same size clips / same part of nail dipped (B1); at least five different numbers of turns, repeated and averaged (B1); table: turns | clips lifted with average (B1); conclusion: plot clips against turns and describe the trend (B1). Safety/precaution: switch off between readings so the wire does not overheat.
- (a) Plan an experiment to investigate how the height from which a tennis ball is dropped affects the height of its first bounce. You are provided with: a tennis ball, two metre rules, a clamp stand and a smartphone that can record slow-motion video.In your plan, you should:• explain briefly how you would carry out the investigation, including how you would measure the bounce height accurately• state the key variables to keep constant• draw a table with column headings• explain how you would use your readings to reach a conclusion. [7]
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- (a) Clamp two metre rules vertically; drop the ball from rest (not thrown) from heights 40–200 cm measured to the bottom of the ball; film the bounce in slow motion against the rule and read the top of the bounce; repeat 3 times and average; keep the same ball, same floor surface, same release method, same measuring point on the ball; table drop height / cm | bounce height 1, 2, 3 / cm | average / cm; plot bounce height against drop height and describe the relationship (e.g. proportional if straight line through origin).
1 mark each, up to 7: release from rest from measured height (bottom of ball, eye level / set square) (B1); bounce height measured using slow-motion video against the rule (B1); repeat and average (B1); at least five heights over a wide range (B1); two control variables: same ball, same surface, same temperature/pressure of ball, same reference point (B1); table with heights / cm and average (B1); conclusion: plot bounce height against drop height and state the trend / check for a straight line through the origin (B1).
