References only, not question text. Open Official paper ↗ where Cambridge publishes the paper,
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school. “Paper 42” means Paper 4, variant 2.
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.
Q1Errors & uncertainties · Core · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) B They have a systematic error, so they may be precise but are not accurate.
A zero error shifts every reading by the same amount: a systematic error. Readings can still be close together (precise) but are all wrong by 0.03 mm (not accurate). Averaging (C, D) reduces random error only, not a systematic one.
Q2Errors & uncertainties · Core · Paper 2 style · 5 marks
A student in Multan measures a cylindrical pencil. Its length L is 14.6 ± 0.1 cm (metre rule) and its diameter d is 7.12 ± 0.01 mm (micrometer).
(a)Calculate the percentage uncertainty in the length.[1]
(b)Calculate the percentage uncertainty in the diameter.[1]
(c)The volume of the pencil is V = πd²L/4. Calculate V in cm³ and its absolute uncertainty.[3]
Q3Errors & uncertainties · Core · Paper 2 style · 6 marks
(a)Explain the difference between a systematic error and a random error.[2]
(b)For each of the following, state whether it causes a systematic or a random error and suggest how it can be reduced.(i) An electronic balance reads 0.4 g with nothing on its pan.(ii) A student's reaction time varies when starting and stopping a stopwatch to time a falling ball.[4]
Show answer
(a) Systematic: readings all differ from the true value by the same amount or in the same direction. Random: readings scatter unpredictably either side of the true value.
B1: systematic error – same size/same sign for every reading (e.g. zero error); B1: random error – scatter of readings about the mean, different each time
(b) (i) systematic – take the zero reading and subtract it from every reading (or tare the balance). (ii) random – repeat and average, or use light gates connected to a timer.
B1 systematic; B1 correct for zero error/tare; B1 random; B1 repeat and average or use light gates/video with timer
Q4Errors & uncertainties · Core · Paper 1 style · 1 mark
(a)Five readings of the diameter of a wire are 2.43 mm, 2.45 mm, 2.41 mm, 2.46 mm and 2.44 mm. Which value and uncertainty best represent these readings?[1]
Show answer
(a) B 2.44 ± 0.03 mm
Mean = 12.19/5 = 2.438 ≈ 2.44 mm; uncertainty = half the range = (2.46 − 2.41)/2 = 0.025 ≈ 0.03 mm. C uses the full range; D quotes too many s.f.
Q5Errors & uncertainties · Standard · Paper 2 style · 6 marks
In a laboratory in Lahore, the length L of a simple pendulum is 0.865 ± 0.002 m. The time for 20 oscillations is 37.4 ± 0.2 s.
(a)Calculate the period T of the pendulum.[1]
(b)The acceleration of free fall is given by g = 4π²L/T². Calculate g.[2]
(c)Determine the absolute uncertainty in g and write g with its uncertainty to an appropriate number of significant figures.[3]
(d) Measure the time with light gates and an electronic timer (or use a longer distance).
B1 – timing uncertainty dominates
Q12SI units & homogeneity · Core · Paper 1 style · 1 mark
(a)Which of the following is an SI base unit?[1]
Show answer
(a) C kelvin
The kelvin is one of the base units (with kg, m, s, A, mol). The coulomb is a derived unit (A s), a common distractor.
Q13SI units & homogeneity · Core · Paper 2 style · 4 marks
(a)Distinguish between a base quantity and a derived quantity.[1]
(b)Show that the unit of pressure, the pascal, is kg m⁻¹ s⁻² in SI base units.[2]
(c)Express the joule in SI base units.[1]
Show answer
(a) A base quantity is one of the chosen fundamental quantities (e.g. mass, length, time); a derived quantity is defined in terms of base quantities.
B1
(b) kg m⁻¹ s⁻²
p = F/A; N = kg m s⁻² (C1); kg m s⁻² ÷ m² = kg m⁻¹ s⁻² (A1)
(c) kg m² s⁻²
J = N m = kg m s⁻² × m (B1)
Q14SI units & homogeneity · Core · Paper 1 style · 1 mark
(a)Which pair of quantities have the same SI base units?[1]
Show answer
(a) B momentum and impulse
Momentum kg m s⁻¹; impulse N s = kg m s⁻² × s = kg m s⁻¹. Charge (A s) and current (A) differ by a factor of s.
Q15SI units & homogeneity · Standard · Paper 2 style · 5 marks
(a)State what is meant by an equation being homogeneous.[1]
(b)Show that the equation v² = u² + 2as is homogeneous.[2]
(c)The pressure p at depth h in a liquid of density ρ is p = ρgh. Show that this equation is homogeneous.[2]
Show answer
(a) Each term in the equation has the same base units.
B1
(b) All terms have units m² s⁻².
v², u²: (m s⁻¹)² = m² s⁻² (M1); 2as: m s⁻² × m = m² s⁻² (A1)
(c) Both sides kg m⁻¹ s⁻².
ρgh: kg m⁻³ × m s⁻² × m (M1) = kg m⁻¹ s⁻² = unit of p (A1)
Q16SI units & homogeneity · Standard · Paper 2 style · 4 marks
(a)Define the volt.[1]
(b)Show that the volt is kg m² s⁻³ A⁻¹ in SI base units.[2]
(c)Hence determine the SI base units of resistance.[1]
Show answer
(a) One joule of energy transferred per coulomb of charge (1 V = 1 J C⁻¹).
B1
(b) kg m² s⁻³ A⁻¹
V = J/C = kg m² s⁻² ÷ (A s) (C1) = kg m² s⁻³ A⁻¹ (A1)
(c) kg m² s⁻³ A⁻²
Ω = V/A (B1)
Q17SI units & homogeneity · Standard · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) B kg m⁻¹ s⁻¹
C = F/(rv) = kg m s⁻² ÷ (m × m s⁻¹) = kg m⁻¹ s⁻¹. A forgets to divide by r.
Q18SI units & homogeneity · Standard · Paper 2 style · 4 marks
Water flows steadily through a narrow pipe in a hospital drip. The volume flow rate Q is given by Q = πr⁴Δp/(8ηL), where r is the radius of the pipe, L its length, Δp the pressure difference between its ends and η a property of the liquid called viscosity.
(a)State the SI base units of volume flow rate Q and of pressure difference Δp.[2]
(b)Determine the SI base units of η.[2]
Show answer
(a) Q: m³ s⁻¹; Δp: kg m⁻¹ s⁻²
B1 each
(b) kg m⁻¹ s⁻¹
η = πr⁴Δp/(8QL) (C1); m⁴ × kg m⁻¹ s⁻² ÷ (m³ s⁻¹ × m) = kg m⁻¹ s⁻¹ (A1)
Q19SI units & homogeneity · Challenge · Paper 2 style · 6 marks
The speed v of a transverse wave on a stretched sitar string depends on the tension T in the string and its mass per unit length μ. A student suggests v = k T^x μ^y, where k is a dimensionless constant.
(a)Write down the SI base units of T and of μ.[2]
(b)Use base units to find the values of x and y.[3]
(c)Explain why this method cannot give the value of k.[1]
Show answer
(a) T: kg m s⁻²; μ: kg m⁻¹
B1 each
(b) x = ½, y = −½
kg: x + y = 0; m: x − y = 1; s: −2x = −1 (M1 for setting up, M1 solving); x = ½, y = −½ (A1)
(c) k is a pure number with no units, so it does not appear in the unit equation.
B1
Q20SI units & homogeneity · Challenge · Paper 2 style · 5 marks
(a)A student writes s = ut + at² for uniformly accelerated motion. Show that this equation is homogeneous.[2]
(b)Explain why the equation can be homogeneous but still incorrect.[1]
(c)The gravitational force between two masses is F = Gm₁m₂/r². Determine the SI base units of G.[2]
Show answer
(a) Each term has unit m.
ut: m s⁻¹ × s = m (M1); at²: m s⁻² × s² = m (A1)
(b) Homogeneity cannot check dimensionless constants; the correct equation has ½at².
B1
(c) m³ kg⁻¹ s⁻²
G = Fr²/(m₁m₂) (C1) = kg m s⁻² × m² ÷ kg² = m³ kg⁻¹ s⁻² (A1)
Q21Scalars & vectors · Core · Paper 2 style · 3 marks
(a)Distinguish between a scalar quantity and a vector quantity.[1]
(b)From the list below, state all the vector quantities.kinetic energy, momentum, temperature, weight, speed, acceleration, power[2]
Show answer
(a) A scalar has magnitude only; a vector has magnitude and direction.
B1
(b) momentum, weight, acceleration
B2 all three and no scalars; B1 two correct
Q22Scalars & vectors · Core · Paper 2 style · 3 marks
A traveller at Karachi airport pulls a wheeled suitcase with a force of 50.0 N along the handle. The handle makes an angle of 35° with the horizontal floor.
(a)Calculate the horizontal component of the force.[1]
(b)Calculate the vertical component of the force.[1]
(c)The suitcase moves at constant velocity. State the size of the frictional force on it.[1]
Show answer
(a) 41.0 N
50.0 cos 35° = 41.0 N (B1)
(b) 28.7 N
50.0 sin 35° = 28.7 N (B1)
(c) 41.0 N
Equal and opposite to the horizontal component (B1)
Q23Scalars & vectors · Standard · Paper 2 style · 4 marks
Two horizontal forces act on a crate on a smooth floor: 12.0 N towards the east and 5.0 N towards the north.
(a)Calculate the magnitude of the resultant force on the crate.[2]
(b)Calculate the angle between the resultant force and the east direction.[2]
Show answer
(a) 13.0 N
R = √(12.0² + 5.0²) (C1) = 13.0 N (A1)
(b) 22.6° north of east
tan θ = 5.0/12.0 (C1); θ = 22.6° (A1)
Q24Scalars & vectors · Standard · Paper 2 style · 4 marks
A light aircraft leaves Islamabad heading due north with a speed of 240 km h⁻¹ relative to the air. A steady wind blows from west to east at 60 km h⁻¹.
(a)Calculate the magnitude of the velocity of the aircraft relative to the ground.[2]
(b)Determine the direction of this velocity as an angle from north.[2]
Show answer
(a) 247 km h⁻¹
v = √(240² + 60²) (C1) = 247 km h⁻¹ (A1)
(b) 14.0° east of north
tan θ = 60/240 (C1); θ = 14.0° east of north (A1)
Q25Scalars & vectors · Challenge · Paper 2 style · 4 marks
A ferry crosses a river 180 m wide. The water flows parallel to the banks at 1.5 m s⁻¹. The speed of the ferry relative to the water is 3.0 m s⁻¹. The ferry must travel straight across, perpendicular to the banks.
(a)Calculate the angle between the direction in which the ferry must be steered and the straight-across direction (perpendicular to the banks) so that the ferry moves straight across. State whether the ferry is steered upstream or downstream.[2]
(b)Calculate the time taken to cross the river.[2]
Show answer
(a) 30° upstream of the straight-across direction (60° to the bank)
The upstream component of the ferry's velocity must cancel the current: sin θ = 1.5/3.0 (C1); θ = 30°, steered upstream (A1)
(b) 69 s
speed across = 3.0 cos 30° = 2.60 m s⁻¹ (C1); t = 180/2.60 = 69 s (A1)
Q26Scalars & vectors · Challenge · Paper 2 style · 5 marks
A street lamp of weight 30.0 N hangs at rest from two cables tied at the same point. One cable makes an angle of 40° with the horizontal and the other makes an angle of 60° with the horizontal, on the opposite side.
(a)State the condition for the point where the cables meet to be in equilibrium.[1]
(b)By resolving forces horizontally and vertically, determine the tension in each cable.[4]
Show answer
(a) The resultant force on it is zero (the horizontal components balance and the vertical components balance).
B1 resultant (vector sum of) force zero
(b) Cable at 40°: 15.2 N; cable at 60°: 23.3 N
Horizontal: T₁ cos 40° = T₂ cos 60° (C1); vertical: T₁ sin 40° + T₂ sin 60° = 30.0 (C1); solving T₂ = 23.3 N (A1); T₁ = 15.2 N (A1)
Q27Estimates & prefixes · Core · Paper 1 style · 1 mark
(a)What is the best estimate of the kinetic energy of a family car travelling on a motorway?[1]
Show answer
(a) C 10⁶ J
m ≈ 1500 kg, v ≈ 30 m s⁻¹: E = ½ × 1500 × 30² ≈ 7 × 10⁵ J ≈ 10⁶ J. 10⁴ J would correspond to a speed of only about 4 m s⁻¹.
Q28Estimates & prefixes · Core · Paper 2 style · 4 marks
(a)Write each quantity in SI units using powers of ten:(i) 450 nm (ii) 2.5 GHz (iii) 3.3 kΩ (iv) 470 µF[2]
(b)Write 0.000 038 A and 72 000 000 W using a suitable prefix.[2]
Show answer
(a) (i) 4.50 × 10⁻⁷ m (ii) 2.5 × 10⁹ Hz (iii) 3.3 × 10³ Ω (iv) 4.70 × 10⁻⁴ F
B2 all four; B1 two or three
(b) 38 µA; 72 MW
B1 each
Q29Estimates & prefixes · Standard · Paper 2 style · 3 marks
(a)Estimate the gain in gravitational potential energy of a student who runs up one flight of stairs between two floors of a school building. State the values you assume.[2]
(b)The student takes about 4 s. Estimate the useful power output.[1]
