New Zealand Scholarship Physics study plan

Map the full scholarship physics syllabus into a personal checklist of topics and subtopics.

Derive from first principles the equations of motion for constant acceleration and solve three multi-step kinematics problems.

Apply Newton's three laws to analyse connected masses, inclines, and friction, showing free-body diagrams for each system.

State and apply the work-energy theorem and conservation of mechanical energy to at least four varied scenarios.

Define impulse and momentum and solve two collision problems (elastic and inelastic) algebraically.

Derive expressions for gravitational potential and field strength inside and outside a uniform sphere.

Apply Newton's law of gravitation to circular orbits, relating orbital speed, period, and radius.

Use Kepler's third law to compare orbits and calculate satellite energies.

Solve problems involving simple harmonic motion: derive the period of a mass-spring system and a simple pendulum.

Analyse energy transformations in SHM and damped oscillations qualitatively.

Derive the wave equation and apply it to transverse and longitudinal waves.

Analyse superposition, standing waves, and resonance in strings and pipes.

Apply the Doppler effect formula to moving source and observer problems.

Explain interference and diffraction qualitatively and quantitatively (double-slit, grating).

Solve problems combining wave phenomena with energy and intensity.

State and apply the laws of thermodynamics to ideal gases and cyclic processes.

Derive the efficiency of a Carnot cycle and compare with real cycles.

Solve problems on heat transfer (conduction, convection, radiation) using appropriate equations.

Apply the first law to isothermal, adiabatic, isobaric, and isochoric processes.

Explain entropy changes qualitatively and calculate entropy changes for simple processes.

Derive the electric field and potential for point charges, dipoles, and continuous charge distributions.

Apply Gauss's law to symmetric charge distributions (sphere, cylinder, plane).

Solve DC circuit problems using Kirchhoff's laws, including internal resistance and power dissipation.

Analyse the motion of charged particles in uniform electric and magnetic fields.

Calculate magnetic fields from currents (straight wire, solenoid) and forces on current-carrying conductors.

Apply Faraday's and Lenz's laws to calculate induced emf and current in changing flux situations.

Derive the energy stored in a capacitor and an inductor.

Analyse AC circuits with resistors, capacitors, and inductors (phasor diagrams, impedance, resonance).

Explain the operation of a transformer and calculate voltage and current ratios.

Solve problems on electromagnetic waves and the speed of light.

Explain the photoelectric effect and derive Einstein's photoelectric equation.

Apply de Broglie's wavelength and the uncertainty principle to simple systems.

Describe the Bohr model and calculate energy levels and spectral lines for hydrogen.

Explain wave-particle duality and the double-slit experiment with single particles.

Solve problems on atomic spectra and photon energy.

Review all topics using the personal checklist from week 1 and identify weak areas.

Complete a timed mock exam under scholarship conditions (3 hours) and self-mark using a rubric.

Re-derive the five most complex formulae from memory and solve a related problem for each.

Explain three difficult concepts aloud (or in writing) as if teaching a peer.

Compile a final one-page 'exam aid' of key constants, formulae, and common pitfalls.