9702 Physics — summer bridging work

Year 12 → Year 13 · Vijay International School, Praslin · Cambridge International AS & A Level

Year 12 consolidation Year 13 preview Maths skills Practical and data Thermal physics Quantum and nuclear Fields

This booklet contains 30 tasks spread across all major 9702 topic areas. Work through at least one tab from each module before September. Tick each task when complete — your progress is saved in the browser. Bring all written work to your first physics lesson.

Tasks are marked with their style: Problem set Past paper style Reading Investigative

Mechanics, materials and waves

1. Projectile motion — worked example then you try Problem set

A ball is launched horizontally from a cliff at 15 m s⁻¹ and lands 45 m from the base.

Worked example — find the height of the cliff

① Horizontal: x = u_x t → 45 = 15t → t = 3.0 s

② Vertical (u_y = 0): h = ½gt² → h = ½ × 9.81 × 9.0

③ h = 44 m

Q1a

A stone is thrown horizontally at 8.0 m s⁻¹ from a bridge 20 m above a river. Find the horizontal distance it travels before hitting the water.

[3]

Q1b

Find the magnitude and direction of the stone's velocity at the moment of impact.

[3]

Q1c

Sketch the trajectory. On the same sketch, draw what you'd expect if air resistance were significant.

[2]

Task complete

2. Past paper — circular motion and SHM Past paper style

Q2a

Define simple harmonic motion.

[2]

Q2b

A mass of 0.25 kg on a spring (k = 16 N m⁻¹) oscillates with amplitude 4.0 cm. Calculate (i) the period and (ii) the maximum speed.

[4]

Q2c

Sketch graphs of displacement, velocity, and acceleration against time for two complete oscillations, starting from maximum positive displacement. Show correct phase relationships.

[4]

Hints

Period: T = 2π√(m/k)

Max speed: v_max = Aω where ω = 2π/T

Velocity leads displacement by 90°; acceleration is antiphase with displacement.

Task complete

3. Superposition and standing waves — investigative Investigative

Search for "Audacity software" (free) or use any online tone generator. Play two tones at 440 Hz and 444 Hz simultaneously.

Record what you hear and explain it using the principle of superposition.
Calculate the beat frequency and check it against what you hear.
Extend: what would you observe at 440 Hz and 880 Hz? Explain your prediction using standing wave theory.

This directly links to 9702 section 5 (superposition) and is the kind of real-world application that appears in Paper 4 extended questions.

Task complete

Electricity

4. Kirchhoff's laws — worked example then you try Problem set

Worked example — two-loop circuit

EMF₁ = 12 V, EMF₂ = 6 V, R₁ = 4 Ω, R₂ = 2 Ω, R₃ = 6 Ω. Find all branch currents.

① KCL at node A: I₁ = I₂ + I₃

② KVL loop 1: 12 = 4I₁ + 2I₂

③ KVL loop 2: 6 = 2I₂ − 6I₃ → solve simultaneously

Result: I₁ = 1.8 A, I₂ = 2.4 A, I₃ = −0.6 A (negative → assumed direction wrong)

Q4a

A battery of EMF 9.0 V and internal resistance 1.2 Ω drives a current through two resistors in series: 3.8 Ω and 5.0 Ω. Find the terminal p.d. and the power dissipated internally.

[4]

Q4b

Three identical resistors, each 12 Ω, are connected in a triangle (delta). Find the effective resistance between any two vertices.

[3]

Task complete

5. Potential divider — past paper style Past paper style

Q5a

Explain why a voltmeter must have a high resistance to give an accurate reading of terminal p.d.

[2]

Q5b

A 6.0 V supply drives a potential divider with R₁ = 4.0 kΩ and a thermistor R₂. At 20 °C, R₂ = 8.0 kΩ. Find the output voltage V_out across R₂. Show that V_out falls as temperature increases.

[5]

Q5c

Sketch V_out vs temperature. Explain how you could redesign the circuit so V_out increases with temperature.

[3]

Task complete

6. Reading — charge carriers in semiconductors Reading

Read about n-type and p-type semiconductors (your A-level textbook or Isaac Physics).

Write a short explanation (150–200 words) of why a semiconductor's resistance decreases with temperature, while a metal's increases.
Connect this to the I–V characteristic of a thermistor you would have seen in Year 12.
Stretch: how does doping change carrier density, and why does this matter for diodes?

Task complete

Mathematical skills for A-level Physics

7. Logarithms — essential for Year 13 Problem set

Worked example — radioactive decay and ln

N = N₀ e^(−λt). Taking natural log: ln N = ln N₀ − λt

So a graph of ln N vs t is a straight line, gradient = −λ, y-intercept = ln N₀.

This is how we linearise exponential data in practicals.

Q7a

A capacitor discharges through a resistor: V = V₀ e^(−t/RC). Show how to plot a straight-line graph from this equation and state what the gradient represents.

[3]

Q7b

Solve for t: 8 = 24 e^(−t/40). Give your answer to 3 significant figures.

[2]

Q7c

Using the data below, plot ln(count rate) vs time and use the gradient to find the decay constant λ and hence the half-life of the source.

t / min: 0, 5, 10, 15, 20, 25
C / min⁻¹: 960, 640, 427, 285, 190, 127

[5]

Q7c answer

ln values: 6.87, 6.46, 6.06, 5.65, 5.25, 4.84

Gradient ≈ −0.0823 min⁻¹ = −λ

t½ = ln2 / λ = 0.693 / 0.0823 ≈ 8.4 min

Task complete

8. Uncertainty and significant figures Problem set

Q8a

A student measures a wire diameter five times: 0.42, 0.41, 0.43, 0.42, 0.44 mm. Calculate the mean, the range, and express the result with its absolute uncertainty.

[3]

Q8b

The student calculates the cross-sectional area using A = π(d/2)². If the percentage uncertainty in d is 2.4%, what is the percentage uncertainty in A?

[2]

Q8c

Explain why plotting a graph is usually a better way to determine a physical constant from experimental data than using a single measurement.

[3]

Task complete

9. Gradient and area under graphs — investigative Investigative

Open a spreadsheet (Google Sheets or Excel). Enter the following displacement–time data for a car:

t / s: 0, 2, 4, 6, 8, 10
x / m: 0, 4, 14, 28, 44, 60

Plot x vs t. Does it look linear? Why not?
Calculate approximate velocities at each point using the chord method.
Plot v vs t. Estimate the acceleration from the gradient.
Stretch: fit a trendline and display its equation. What does the coefficient of t² tell you?

Task complete

Year 13 topic preview

10. Gravitational fields — first look Reading

In Year 13 you'll move from "g = 9.81 m s⁻²" to a full field model. Before term starts, look up gravitational field strength g and gravitational potential φ.

Write down (with units) what g and φ represent physically — not just the equations.
Explain why g is always positive but φ is always negative for a planet.
Use g = GM/r² to estimate g at the surface of the Moon (look up M and r).

The relationship g = −dφ/dr will be new — you don't need to use it yet, but notice that g is the negative gradient of the φ vs r graph. We'll build this up in September.

Task complete

11. Capacitors — conceptual introduction Reading

Read the first section on capacitors in your textbook or at Isaac Physics.

Q11a

What is stored in a capacitor — charge, energy, or both? Explain carefully.

[2]

Q11b

A 470 μF capacitor is charged to 12 V. Calculate (i) the charge stored and (ii) the energy stored.

[3]

Q11c

Sketch how voltage varies with time as a capacitor charges through a resistor. Mark the time constant τ = RC on your sketch.

[3]

Formulae to use

Charge: Q = CV

Energy: E = ½CV²

Charging: V = V₀(1 − e^(−t/RC))

Task complete

12. Nuclear physics — reading and reflection Reading

Read about binding energy and mass defect before Year 13 begins.

Explain, in your own words, why fission and fusion can both release energy. Use a sketch of the binding energy per nucleon curve to support your answer.
Look up the mass of a proton, neutron, and helium-4 nucleus. Calculate the mass defect of He-4 and hence its binding energy.
Reflection: why is nuclear energy described as "energy from mass"? Is this consistent with conservation of energy?

Useful data: m_p = 1.00728 u, m_n = 1.00867 u, m(He-4) = 4.00260 u, 1 u = 931.5 MeV c⁻²

Task complete

Practical skills and data analysis

13. Home experiment — timing a pendulum Investigative

You need: a piece of string (0.5–1 m), a small mass (key, nut), a ruler, and a phone timer.

Measure T for at least 6 different lengths. Time 10 swings each time to reduce random error.
Plot T² vs L. Explain why this gives a straight line, and find g from the gradient.
Estimate uncertainties in L and T, and hence in g. Comment on your value.
Identify one systematic and one random source of error in your method.

Theory reminder

T = 2π√(L/g) → T² = (4π²/g) × L

Gradient of T² vs L graph = 4π²/g

Task complete

14. Analysing real data — speed of sound Past paper style

A student uses a signal generator and microphones to measure the speed of sound.

Distance d / cm: 20, 40, 60, 80, 100
Time delay t / ms: 0.59, 1.18, 1.76, 2.35, 2.94

Q14a

Plot d vs t. Draw the best-fit line and calculate the speed of sound from the gradient.

[4]

Q14b

The student's value differs from 340 m s⁻¹. Suggest two experimental reasons and state whether each would cause an overestimate or underestimate.

[4]

Q14c

Describe how you would improve the experiment to get a more reliable value. Include at least one change that reduces random error and one that reduces systematic error.

[4]

Task complete

15. Reflection — preparing for Paper 3 Reading

Read the 9702 syllabus section on practical assessment (available on the Cambridge website).

List the five main skills assessed in Paper 3 (Advanced Practical Skills).
Write one sentence for each explaining what you think the examiners are actually looking for.
Which skill do you feel least confident about? Write a specific action you'll take in Year 13 to improve it.

Task complete

Thermal physics

16. Ideal gas law — worked example then you try Problem set

Worked example

A gas occupies 2.0 × 10⁻³ m³ at 300 K and 1.0 × 10⁵ Pa. Find the number of moles.

pV = nRT → n = pV/RT = (1.0×10⁵ × 2.0×10⁻³) / (8.31 × 300) = 0.080 mol

Q16a

A sealed container holds 0.050 mol of ideal gas at 27 °C and 1.5 × 10⁵ Pa. Find the volume of the container.

[3]

Q16b

The container is heated to 127 °C at constant volume. Calculate the new pressure, and explain in terms of molecular motion why it increases.

[4]

Q16c

Show that the root-mean-square speed of nitrogen molecules (M = 0.028 kg mol⁻¹) at 300 K is approximately 516 m s⁻¹. State one assumption of the kinetic model you used.

[4]

Hint

Use c_rms = √(3RT/M)

Task complete

17. Specific heat capacity — home experiment Investigative

You need: a kettle (or saucepan), a thermometer, a known mass of water, and a timer.

Measure how long it takes to heat 0.5 kg of water from room temperature to 60 °C.
Use the kettle's rated power (printed on the base, usually 2000–3000 W) to calculate the energy supplied.
Calculate the specific heat capacity of water from your data. Compare with 4200 J kg⁻¹ K⁻¹.
Your value will likely be too high. Explain why, and suggest two ways to improve the experiment.

Key equation

Q = mcΔθ and Q = Pt → c = Pt / mΔθ

Task complete

18. Internal energy and the first law — past paper style Past paper style

Q18a

State what is meant by the internal energy of a gas.

[2]

Q18b

1.5 × 10⁻³ m³ of gas at 2.0 × 10⁵ Pa expands at constant pressure to 4.0 × 10⁻³ m³. During this process, 300 J of thermal energy is added to the gas. Calculate (i) the work done by the gas and (ii) the change in internal energy.

[5]

Q18c

For an ideal gas at constant temperature (isothermal expansion), state what happens to the internal energy and explain your answer using molecular theory.

[3]

Hints

Work done by gas: W = pΔV

First law: ΔU = Q − W

For an ideal gas, internal energy depends only on temperature.

Task complete

Quantum physics and nuclear

19. Photoelectric effect — worked example then you try Problem set

Worked example

Light of wavelength 250 nm hits a metal with work function 3.0 eV.

Energy of photon: E = hc/λ = (6.63×10⁻³⁴ × 3×10⁸) / (250×10⁻⁹) = 4.97 eV

Max KE: KE_max = hf − φ = 4.97 − 3.0 = 1.97 eV

Q19a

Light of frequency 8.2 × 10¹⁴ Hz hits a surface with work function 2.8 eV. Calculate the maximum kinetic energy of emitted photoelectrons in joules.

[3]

Q19b

Explain why increasing the intensity of light below the threshold frequency produces no photoelectrons, however long you wait.

[3]

Q19c

In a stopping potential experiment, the stopping voltage is 1.4 V for light of wavelength 350 nm. Use these values to calculate the Planck constant, and comment on any assumptions you make.

[5]

Task complete

20. Energy levels and spectra — reading and reflection Reading

Look up a diagram of the hydrogen energy levels (the Bohr model). You'll find one in your textbook or at HyperPhysics.

Explain why emission spectra consist of discrete lines rather than a continuous spread of colours.
The Lyman series (transitions to n = 1) produces UV, while the Balmer series (to n = 2) produces visible light. Explain why, using the energy level diagram.
Calculate the wavelength of the photon emitted when an electron in hydrogen falls from n = 3 to n = 2. Use E₃ = −1.51 eV and E₂ = −3.40 eV.
Stretch: why does the emission spectrum of helium look different from hydrogen's, even though helium also emits visible light?

Task complete

21. Radioactive decay — data analysis Past paper style

Q21a

Define the decay constant λ and state its SI unit.

[2]

Q21b

A sample initially contains 5.0 × 10¹⁸ atoms of a radioisotope with half-life 6.0 hours. Calculate (i) the decay constant, (ii) the initial activity, (iii) the number of atoms remaining after 24 hours.

[6]

Q21c

Explain why it is not possible to say when a specific nucleus will decay, yet the decay of a large sample follows a precise exponential law.

[3]

Q21b answer

(i) λ = ln2 / t½ = 0.693 / (6 × 3600) = 3.21 × 10⁻⁵ s⁻¹

(ii) A₀ = λN₀ = 3.21×10⁻⁵ × 5.0×10¹⁸ = 1.61×10¹⁴ Bq

(iii) 24 hours = 4 half-lives → N = 5.0×10¹⁸ / 2⁴ = 3.1×10¹⁷

Task complete

22. Wave-particle duality — investigative reading Investigative

Research the double-slit experiment with electrons (Jönsson, 1961) and with single electrons (Tonomura, 1989).

Describe what is observed and why it is surprising.
Calculate the de Broglie wavelength of an electron accelerated through 50 V. Compare this to the wavelength of visible light.
Explain what this tells us about the nature of electrons.
Reflection: in what sense can a single electron "interfere with itself"? What does this imply about the meaning of the wavefunction?

This is one of the deepest results in physics — you are not expected to resolve the philosophical puzzle, just to engage with it carefully.

Task complete

Electric and magnetic fields

23. Electric fields — worked example then you try Problem set

Worked example — field between parallel plates

Two plates separated by 4.0 mm have a p.d. of 200 V between them.

Field strength: E = V/d = 200 / 4.0×10⁻³ = 5.0×10⁴ V m⁻¹

Force on charge q = 3.2×10⁻¹⁹ C: F = qE = 1.6×10⁻¹⁴ N

Q23a

Two point charges, +4.0 μC and −4.0 μC, are separated by 0.12 m in vacuum. Calculate the force between them and state its direction.

[3]

Q23b

An electron (m = 9.11×10⁻³¹ kg, q = 1.6×10⁻¹⁹ C) enters a uniform electric field of 3.0×10³ V m⁻¹ perpendicular to the field lines at 2.0×10⁶ m s⁻¹. Treating it like a projectile, find its deflection after travelling 50 mm horizontally.

[5]

Q23c

Sketch the electric field pattern (i) around a single positive point charge and (ii) between two oppositely charged parallel plates. Mark any regions of uniform field.

[4]

Task complete

24. Magnetic fields and the motor effect — past paper style Past paper style

Q24a

State Fleming's left-hand rule and explain what each finger represents.

[2]

Q24b

A wire of length 0.15 m carrying a current of 4.0 A lies perpendicular to a magnetic field of flux density 0.30 T. Calculate the force on the wire.

[2]

Q24c

A proton (m = 1.67×10⁻²⁷ kg, q = 1.6×10⁻¹⁹ C) moves at 3.0×10⁶ m s⁻¹ perpendicular to a magnetic field of 0.25 T. Show that it follows a circular path and find the radius of the orbit.

[4]

Hint

Magnetic force provides centripetal force: Bqv = mv²/r

Rearrange: r = mv / Bq

Task complete

25. Comparing gravitational and electric fields — reading Reading

Write out Coulomb's law and Newton's law of gravitation side by side. Identify every similarity and every difference.
Explain why gravitational fields can only be attractive, while electric fields can be either.
Both fields follow an inverse-square law. What does this mean physically, and what does it imply about field strength at very large distances?
Stretch: look up the ratio of the electrostatic force to the gravitational force between two protons. What does this tell you about the relative importance of the two forces inside an atomic nucleus?

Task complete

Motion, momentum, and energy

26. Momentum and collisions — worked example then you try Problem set

Worked example — perfectly inelastic collision

Mass 3.0 kg at 4.0 m s⁻¹ hits stationary mass 2.0 kg. They stick together.

Conservation of momentum: 3.0 × 4.0 = 5.0 × v → v = 2.4 m s⁻¹

KE before: 24 J · KE after: 14.4 J · KE lost: 9.6 J → inelastic

Q26a

A ball of mass 0.20 kg moving at 6.0 m s⁻¹ collides head-on with a ball of mass 0.30 kg moving at 2.0 m s⁻¹ in the opposite direction. After the collision the 0.20 kg ball moves at 2.0 m s⁻¹ in its original direction. Find the velocity of the 0.30 kg ball after the collision.

[3]

Q26b

Show whether the collision in Q26a is elastic or inelastic.

[3]

Q26c

Explain, using the concept of impulse, why crumple zones in cars improve passenger safety.

[3]

Task complete

27. Energy conservation — investigative Investigative

Drop a ball from a measured height h and record how high h' it bounces using slow-motion video on your phone.

Measure h and h' for at least 5 different drop heights. Tabulate your results.
Calculate the coefficient of restitution e = √(h'/h) for each trial and find the mean.
Plot h' vs h. What does the gradient represent?
Where does the "lost" energy go? Describe what you observe experimentally that supports your answer.

Task complete

28. Motion graphs — interpreting and sketching Past paper style

Q28a

A car accelerates uniformly from rest for 8.0 s, reaching 20 m s⁻¹. It then travels at constant speed for 10 s, before braking uniformly to rest in 5.0 s. Sketch the v–t graph and calculate the total distance travelled.

[5]

Q28b

On the same time axis, sketch the corresponding a–t graph. Mark numerical values on both axes.

[3]

Q28c

A ball is thrown vertically upward with initial speed 15 m s⁻¹. Taking upward as positive, sketch the v–t and s–t graphs for the motion from launch to when it returns to the launch point. Mark key values.

[4]

Task complete

Stretch and extension tasks

29. Fermi estimation — order-of-magnitude thinking Investigative

For each question below, make a reasoned estimate, showing your assumptions clearly. Aim for an answer within a factor of 10 of the real value.

Q29a

How many air molecules are in this classroom right now? State any dimensions you assume.

Q29b

Estimate the power output of the Sun, using only the fact that 1 kW m⁻² of solar radiation reaches the Earth's surface and the Earth–Sun distance (~1.5 × 10¹¹ m).

Q29c

How many heartbeats does a human have in a lifetime?

Q29d

Estimate the kinetic energy of a large cruise ship at cruising speed. Compare this to the energy stored in its fuel tank.

Fermi questions appear in Paper 4 and in university physics interviews. The method — identify the key quantities, estimate each, combine — is more important than the numerical answer.

Task complete

30. Extended reading — choose your own Reading

Choose one of the following and write a one-page summary (~300–400 words) aimed at a fellow Year 12 student who has not read it.

The Elegant Universe — Ch. 1 or 2 (Brian Greene) — on the quest for a unified theory
Six Easy Pieces — any one chapter (Richard Feynman) — on the nature of physics
A recent article from physicsworld.com or quantamagazine.org of your choice
The 9702 syllabus section on any Year 13 topic you're most curious about

Your summary should include: what the key idea is, one thing that surprised you, and one question it raised that you don't yet know the answer to.

Bring your summary to the first lesson. We'll spend 10 minutes sharing the best ones.

Task complete

9702 AS & A Level Physics · Vijay International School, Praslin, Seychelles
30 tasks across 10 topic areas · Progress is saved in this browser
Bring all written work to your first physics lesson in September