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NZ Scholarship Physics formula sheet (93103)

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Formula sheet

The card below opens today's Level 3 Physics paper with the Scholarship sheet in the drawer. The contents follow in our own layout, grouped by topic. NZQA prints them as one unlabelled block of three columns. This is the 2025 page, the latest NZQA has published, and NZQA's 2026 specification says formulae, constants and data will be provided again.

Formula sheet

NCEA Level 3 Physics

Open formula sheet

Linear motion, circular motion and momentum

v_f=v_i+atFinal velocity
d=v_it+\frac{1}{2}at^2Distance, from the initial velocity
d=\frac{v_i+v_f}{2}tDistance, from the average velocity
v_f^2=v_i^2+2adFinal velocity, without time
F_{net}=maNewton's second law
p=mvMomentum
\Delta p=F\Delta tImpulse
F_g=\frac{GMm}{r^2}Gravitational force
F_c=\frac{mv^2}{r}Centripetal force
W=FdWork done
E_{\text{K(LIN)}}=\frac{1}{2}mv^2Linear kinetic energy
\Delta E_p=mg\Delta hChange in gravitational potential energy
x_{\text{COM}}=\frac{m_1x_1+m_2x_2}{m_1+m_2}Centre of mass of two masses

Rotation

\omega=2\pi fAngular velocity and frequency
d=r\thetaArc length
v=r\omegaSpeed on a circle
a=r\alphaTangential acceleration
\omega=\frac{\Delta\theta}{\Delta t}Angular velocity
\alpha=\frac{\Delta\omega}{\Delta t}Angular acceleration
L=I\omegaAngular momentum
L=mvrAngular momentum of a point mass
\tau=I\alphaTorque and angular acceleration
\tau=FrTorque from a force
E_{\text{K(ROT)}}=\frac{1}{2}I\omega^2Rotational kinetic energy
\omega_f=\omega_i+\alpha tFinal angular velocity
\omega_f^2=\omega_i^2+2\alpha\thetaFinal angular velocity, without time
\theta=\frac{\omega_i+\omega_f}{2}tAngle turned, from the average angular velocity
\theta=\omega_it+\frac{1}{2}\alpha t^2Angle turned, from the initial angular velocity

Oscillations

T=2\pi\sqrt{\frac{l}{g}}Period of a pendulum
T=2\pi\sqrt{\frac{m}{k}}Period of a mass on a spring
E_p=\frac{1}{2}ky^2Elastic potential energy
F=-kyHooke's law
a=-\omega^2yAcceleration and displacement
y=A\sin\omega tDisplacement, starting from the centre
v=A\omega\cos\omega tVelocity, starting from the centre
a=-A\omega^2\sin\omega tAcceleration, starting from the centre
y=A\cos\omega tDisplacement, starting from the maximum
v=-A\omega\sin\omega tVelocity, starting from the maximum
a=-A\omega^2\cos\omega tAcceleration, starting from the maximum

Electricity and magnetism

\Delta E=VqEnergy change of a charge
P=VIPower
V=IROhm's law
Q=CVCharge on a capacitor
C_T=C_1+C_2Capacitors in parallel
\frac{1}{C_T}=\frac{1}{C_1}+\frac{1}{C_2}Capacitors in series
E=\frac{1}{2}QVEnergy stored in a capacitor
C=\frac{\varepsilon_0\varepsilon_rA}{d}Parallel plate capacitor
\tau=RCTime constant of an RC circuit
\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}Resistors in parallel
R_T=R_1+R_2Resistors in series
F=BILMagnetic force on a current in a wire
V=BvLInduced voltage in a moving conductor
F=BqvForce on a moving charge in a magnetic field
F=EqForce on a charge in an electric field
E=\frac{V}{d}Uniform electric field
\phi=BAMagnetic flux
\varepsilon=-\frac{\Delta\phi}{\Delta t}Induced emf from changing flux
\varepsilon=-L\frac{\Delta I}{\Delta t}Induced emf in an inductor
\frac{N_p}{N_s}=\frac{V_p}{V_s}Transformer
E=\frac{1}{2}LI^2Energy stored in an inductor
\tau=\frac{L}{R}Time constant of an LR circuit

Alternating current

I=I_{\text{MAX}}\sin\omega tAlternating current
V=V_{\text{MAX}}\sin\omega tAlternating voltage
I_{\text{MAX}}=\sqrt{2}I_{\text{rms}}Peak and rms current
V_{\text{MAX}}=\sqrt{2}V_{\text{rms}}Peak and rms voltage
X_C=\frac{1}{\omega C}Capacitive reactance
X_L=\omega LInductive reactance
V=IZImpedance
f_0=\frac{1}{2\pi\sqrt{LC}}Resonant frequency

Waves and modern physics

v=f\lambdaWave speed
f=\frac{1}{T}Frequency and period
n\lambda=\frac{dx}{L}Two-slit pattern
n\lambda=d\sin\thetaDiffraction grating
f'=f\frac{V_W}{V_W\pm V_S}Doppler effect
E=hfPhoton energy
hf=\phi+E_KPhotoelectric effect
E=\Delta mc^2Mass-energy equivalence
\frac{1}{\lambda}=R\left(\frac{1}{S^2}-\frac{1}{L^2}\right)Hydrogen spectral lines
E_n=-\frac{hcR}{n^2}Hydrogen energy levels

What is not on the sheet

  • Constants. The page has none. In 2025 Question Three, for example, the charge of an electron, Planck's constant and the speed of light were printed with the question. Read each question for what it supplies.
  • The de Broglie wavelength. NZQA's specification requires wave and particle duality, but the page does not print λ = h/p. NZQA says all necessary formulae will be provided, so a question that needs it should give it.
  • What the symbols mean. The page does not define S and L in the hydrogen spectral formula or say what φ is in the photoelectric line. You must know them.
  • Binding energy and nuclear reactions in detail. The spec requires binding energy and mass deficit, and the sheet gives only E = Δmc².
  • Reasoning and extended discussion. NZQA says some questions involve extended discussion where you judge what is needed, and questions about practical work may involve error, reliability and validity.

NZQA's 2026 specification says there are four questions, that you need an approved calculator, a ruler and a protractor, and that content is limited to a selection of the Level 3 Physics standards, with modern physics content for P3.5: the Bohr model, the photoelectric effect, wave and particle duality, the strong interaction and binding energy.

How to use the sheet in the exam

  1. Read the question for the data it supplies, then list the quantities.
  2. Find the line and check what each symbol means before you substitute.
  3. Keep unrounded values and give the answer with a unit and sensible significant figures.
  4. Write the reasoning: Scholarship marks the justification as much as the number.

Oscillations: a pendulum

A pendulum has a length of 0.80 m, and g is 9.81 m s⁻². Use the pendulum line:

T=2\pi\sqrt{\frac{l}{g}}=2\pi\sqrt{\frac{0.80}{9.81}}=1.79\ \text{s}

Modern physics: the photoelectric effect

Light of wavelength 400 nm strikes a metal with a work function of 3.0 × 10⁻¹⁹ J. Planck's constant is given in the question as 6.63 × 10⁻³⁴ J s, and the speed of light is 3.00 × 10⁸ m s⁻¹. The wave speed line gives the frequency, and the photoelectric line gives the maximum kinetic energy:

f=\frac{v}{\lambda}=\frac{3.00\times10^8}{4.00\times10^{-7}}=7.5\times10^{14}\ \text{Hz}
E_K=hf-\phi=6.63\times10^{-34}\times7.5\times10^{14}-3.0\times10^{-19}=4.97\times10^{-19}-3.0\times10^{-19}=1.97\times10^{-19}\ \text{J}

The photon carries 4.97 × 10⁻¹⁹ J, and 3.0 × 10⁻¹⁹ J of it frees the electron, leaving 1.97 × 10⁻¹⁹ J. Practise photon energy in our Light and Energy course, then press Mark to check your answer there:

Work out a photon energy from its frequency or wavelength, in units of 10^-19 J.

Press Mark to have your answer marked in the Light & Energy course.

The Scholarship sheet and the others

The Level 3 Physics booklet is a subset of this: it lacks linear motion, the force laws for charges and currents, and the modern physics lines. The Level 3 booklet also prints five constants, which the Scholarship page does not. The Scholarship Calculus booklet is a separate document. For how the Scholarship exam works, see the NCEA Level 3 Physics guide.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper with the sheet open beside you, mark it, and the worked answers show which line each question wanted. We do not publish official or past paper answers. Every question on the daily paper is our own.

Use the sheet with today's paper

Uni-Sine publishes a free daily paper on the NCEA Level 3 Physics track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full NCEA exam, and it is not written by NZQA. It is Level 3 standard, not Scholarship, but the Scholarship formula set contains the Level 3 one, so it is the closest daily practice.

Common mistakes with the Scholarship Physics sheet

  • Assuming the constants are on the page. Read the question.
  • Mixing up the two hydrogen lines. The spectral line formula and the energy-level formula are separate lines with different symbols.
  • Using nanometres in the photoelectric line. Convert wavelengths to metres.
  • Leaving out the reasoning. The formula only gets you the number.

Common questions

Do you get a formula sheet in NZ Scholarship Physics?
Yes. NZQA's 2026 specification says all necessary formulae, constants and data will be provided. In 2025 the formulae were on page 3 of the exam booklet.
When is the 2026 Scholarship Physics exam?
Wednesday 18 November 2026, in the morning session, which starts at 9.30 am.
Are constants on the Scholarship Physics formula page?
Not in 2025. The charge of an electron, Planck's constant and the speed of light were printed with the question that used them.
Is the photoelectric effect formula on the sheet?
Yes: hf = φ + E_K, with E = hf, E = Δmc², the hydrogen spectral line formula and the hydrogen energy levels.

Revision cards

Say the answer first, then flip the card to check it.

Where to go next

  • Solve it

    Pendulum and SHM Simulator

    Swing a pendulum and graph its displacement, velocity and acceleration

    Open the tool
  • Learn it

    Light & Energy

    Waves, photons and the electromagnetic spectrum explained

    Start the course
  • Test it

    NCEA Level 3 Physics

    A new exam-style paper every day, with instant marking and a mark scheme

    Start today's paper
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New Zealand · NCEA Level 3NZ Scholarship Physics: exam, cut scores, examplesNZ Scholarship Physics explained: the 2026 exam date and format, NZQA cut scores for Scholarship and Outstanding 2023 to 2025, and a worked example.