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NCEA Level 2 Physics formula sheet (resource sheet)

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Formula sheet

The card below opens today's Level 2 Physics paper with the sheet in the drawer. The contents follow in our own layout, in the order of the three standards. This is the 2025 sheet, the latest NZQA has published. NZQA's 2026 specification says the formulae and the values of the physical constants will again come in a separate resource sheet with the papers, so expect the same layout.

Formula sheet

NCEA Level 2 Physics

Open formula sheet

Waves (91170)

\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}Lens equation, with object and image distances
s_is_o=f^2Lens equation, in its other form
m=\frac{d_i}{d_o}=\frac{h_i}{h_o}Magnification from distances and heights
m=\frac{f}{s_o}=\frac{s_i}{f}Magnification from the focal length
n_1\sin\theta_1=n_2\sin\theta_2Refraction (Snell's law)
\frac{n_1}{n_2}=\frac{v_2}{v_1}=\frac{\lambda_2}{\lambda_1}Refractive indices, speeds and wavelengths
v=f\lambdaWave speed
f=\frac{1}{T}Frequency and period
v=\frac{d}{t}Speed

Mechanics (91171)

v=\frac{\Delta d}{\Delta t}Average speed or velocity
a=\frac{\Delta v}{\Delta t}Acceleration
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
a_c=\frac{v^2}{r}Centripetal acceleration
F=maNewton's second law
\tau=FdTorque
F=-kxHooke's law
F_c=\frac{mv^2}{r}Centripetal force
p=mvMomentum
\Delta p=F\Delta tImpulse
E_p=\frac{1}{2}kx^2Elastic potential energy
E_k=\frac{1}{2}mv^2Kinetic energy
\Delta E_p=mg\Delta hChange in gravitational potential energy
W=FdWork done
P=\frac{W}{t}Power

Electricity and electromagnetism (91173)

E=\frac{V}{d}Electric field between plates
F=EqForce on a charge in an electric field
\Delta E_p=EqdEnergy change of a charge in a field
E_k=\frac{1}{2}mv^2Kinetic energy
I=\frac{q}{t}Current
V=\frac{\Delta E}{q}Potential difference
V=IROhm's law
P=IVPower from current and voltage
P=\frac{\Delta E}{t}Power from energy
R_T=R_1+R_2+\ldotsResistors in series
\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\ldotsResistors in parallel
F=BILMagnetic force on a current in a wire
F=BqvForce on a moving charge in a magnetic field
V=BvLInduced voltage in a moving conductor

Constants

QuantitySymbolValue
speed of light in a vacuumc3.00 × 10⁸ m s⁻¹
acceleration due to gravity, where neededg9.8 m s⁻²
charge on an electronq−1.60 × 10⁻¹⁹ C
mass of an electronm9.11 × 10⁻³¹ kg

What is not on the sheet

  • Weight, F = mg. The sheet has the gravitational potential energy line, ΔE = mgΔh, but not the weight formula. NZQA's 2026 specification says questions may use F = mg even though the standard does not mention weight force.
  • Units and symbols. The sheet does not say what each letter means. The letter f is a frequency in v = fλ and a focal length in the lens equation.
  • Metric prefixes. NZQA says prefixes such as milli and kilo will be given when needed, but you are expected to understand micro, milli, centi, kilo and mega.
  • Material data. Refractive indices, spring constants and resistances come from the question.
  • Which formula to use. Several quantities have more than one line. Choose the one with exactly the quantities you have.

How to use the sheet in the exam

  1. Write what the question gives, with units, and what it asks for.
  2. Find the standard's block, then the line that holds exactly those quantities.
  3. Convert to SI before substituting: centimetres to metres, minutes to seconds.
  4. Rearrange first, substitute second, and give the answer with a unit and a sensible number of significant figures.

Mechanics: acceleration from rest

A 1200 kg car accelerates from rest at 2.5 m s⁻² for 8.0 s. How far does it travel, and what is its final speed? The distance line that has no final speed in it is the place to start, and the initial speed is 0:

d=v_it+\frac{1}{2}at^2=0+\frac{1}{2}\times2.5\times8.0^2=80\ \text{m}
v_f=v_i+at=0+2.5\times8.0=20\ \text{m s}^{-1}

The mass is a distractor here: it matters for the force, F = ma = 1200 × 2.5 = 3000 N, but not for the motion.

Waves: refraction and a lens

Light travels from air (n = 1.00) into glass (n = 1.50) at an angle of 40° to the normal. Use the refraction line:

n_1\sin\theta_1=n_2\sin\theta_2\quad\text{so}\quad\sin\theta_2=\frac{1.00\times\sin40^\circ}{1.50}=0.4285\quad\text{so}\quad\theta_2=25.4^\circ

Now a lens of focal length 0.15 m with an object 0.40 m away. The lens line gives the image distance, and the magnification line gives the size ratio:

\frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_o}=\frac{1}{0.15}-\frac{1}{0.40}=4.1\overline{6}\quad\text{so}\quad d_i=0.24\ \text{m},\qquad m=\frac{d_i}{d_o}=\frac{0.24}{0.40}=0.60

Choosing the right line is the skill. Practise it in our Light and Energy course, then press Mark to check your answer there:

Calculate the angle of refraction for a random pair of materials and angle.

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

The Level 2 sheet and the others

The Level 3 Physics booklet gives the rotational equations but not linear motion, and uses g = 9.81 instead of 9.8. The Level 1 Physics, Earth and Space Science sheet is just eight lines. For how the three Level 2 standards work, see the NCEA Level 2 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 2 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. Open the sheet from the paper itself and practise choosing the right line under a clock.

Common mistakes with the Level 2 Physics sheet

  • Mixing up the two f's. Frequency and focal length share a letter.
  • Using the final speed formula when time is not given. Use the line with no time in it: final speed squared equals initial speed squared plus 2ad.
  • Not converting units. Work in metres, seconds and kilograms.
  • Quoting constants from memory. Take g = 9.8 m s⁻² and the electron mass, 9.11 × 10⁻³¹ kg, from the sheet.

Common questions

Do you get a formula sheet in NCEA Level 2 Physics?
Yes. NZQA supplies a Resource Sheet, L2-PHYSR, with the exam for 91170, 91171 and 91173. It carries the formulae and four constants, and you may keep it.
When is the 2026 Level 2 Physics exam?
Wednesday 18 November 2026, in the afternoon session, which starts at 2.00 pm.
What value of g does Level 2 Physics use?
The sheet says to use g = 9.8 m s⁻² where needed, and NZQA's 2026 specification agrees.
Is F = mg on the Level 2 Physics formula sheet?
No. The sheet has ΔE = mgΔh but not the weight force, though NZQA says questions may use F = mg.

Revision cards

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

Where to go next

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