NCEA Level 3 Physics common mistakes
NCEA Level 3 Physics · Understand the traps and how to avoid them.
When calculating the magnitude of the force between two point charges or masses, the candidate substitutes the distance in centimetres (or the diameter of a sphere instead of the separation between centres) directly into Coulomb's law or Newton's law of gravitation without converting to metres first, producing answers that are wrong by factors of 10^4 or more.
The formula sheet gives the constants with SI units (N m^2 C^-2, N m^2 kg^-2) but the question stem often quotes separations in cm, mm or km, and candidates pattern-match the number straight into the equation. The inverse-square dependence massively amplifies the unit slip, so a small oversight becomes a huge error that is easy to miss on a sanity check.
What to do instead
Before substituting, write a one-line data list converting every quantity to SI base units with powers of ten shown explicitly (e.g. r = 4.0 cm = 4.0 x 10^-2 m, so r^2 = 1.6 x 10^-3 m^2). Then do an order-of-magnitude estimate first (10^-3 m squared is about a thousandth of a metre squared) and check the final answer's exponent against that estimate. For spheres, always use the centre-to-centre separation, not the surface separation.
The candidate treats a projectile or circular-motion problem as if velocity and acceleration were always parallel, resolving the initial velocity into components once and then reusing those components unchanged through the whole flight, or claiming the centripetal acceleration points along the velocity.
At Level 2 the emphasis is on resolving vectors into components; at Level 3 candidates are expected to reason about how components evolve. Many memorise 'horizontal velocity is constant, vertical velocity changes' but then fail to apply it to the vertical component's sign at the top of the trajectory, or they confuse tangential velocity with centripetal acceleration in circular motion because both are drawn from the same point on the path.
What to do instead
For projectiles, draw a small table of v_x and v_y at launch, apex and landing, and explicitly note that v_y = 0 at the apex while a_y = -g throughout (including at the apex). For circular motion, state in words that velocity is tangential and acceleration is radial, then draw both vectors at three points on the circle. Practise a question where the object is thrown at an angle and the candidate must find the velocity vector at a specified height, not just the range.
When asked to explain a phenomenon involving conservation of energy or momentum, the candidate writes 'energy is conserved so the ball bounces back' or 'momentum is conserved so the collision is elastic', using the conservation law as a conclusion rather than as a tool, and never checks whether the collision is elastic or whether energy is dissipated.
Candidates learn the slogans 'energy is conserved' and 'momentum is conserved' and deploy them as filler in explanation questions. They do not distinguish between the always-true statement (total momentum is conserved in any collision with no external impulse) and the conditional statement (kinetic energy is conserved only in elastic collisions), so they conflate the two and lose the reasoning marks.
What to do instead
For every collision, write two separate lines: 'momentum: m1u1 + m2u2 = m1v1 + m2v2 (always)' and 'kinetic energy: check by computing before and after; if different, the collision is inelastic and energy went to heat/sound/deformation'. Practise classifying a collision as elastic or inelastic from given speeds before writing any explanation. In the explanation, name the external force that is negligible and the interval over which momentum is conserved.
The candidate calculates the magnitude of a force or field correctly but gives no direction, or gives a direction that is inconsistent with the sign convention, e.g. stating that the electric field at a point due to a negative charge points towards the charge but then drawing it away, or omitting the direction entirely in a vector answer.
Level 3 questions frequently ask for 'the force on the charge' or 'the electric field at P', which are vector quantities, but candidates treat them as scalar calculations because the formula sheet supplies only magnitudes. The sign conventions for electric field (away from positive, towards negative) and for gravitational field (always towards the mass) are easily mixed up under exam pressure.
What to do instead
Adopt a fixed routine: after computing a magnitude, write 'direction:' and state it in words relative to a named reference (e.g. 'towards the -4.0 microC charge, i.e. to the left'). For fields, memorise the single rule 'field lines point in the direction a positive test charge would be pushed' and apply it to both signs. On diagrams, draw the field arrow at the point before writing the number.
In an electricity internally-assessed or exam question on DC circuits, the candidate calculates the equivalent resistance of a parallel combination as R1 + R2, or adds the internal resistance of the battery to the external resistance and then forgets to subtract the internal voltage drop when finding the terminal voltage.
The series formula is simpler and more familiar, so under time pressure candidates default to it. The internal-resistance idea is conceptually new at Level 3 and candidates treat the EMF as the terminal voltage because in Level 1 and 2 problems the battery was ideal.
What to do instead
Write the parallel formula as 1/R = 1/R1 + 1/R2 and compute the reciprocal at the end, checking that the answer is smaller than the smallest branch resistance. For terminal voltage, always draw the circuit with the internal resistance as a separate series resistor and use V_terminal = EMF - I r, then verify that V_terminal is less than the EMF. Do a quick power audit: power from EMF equals power in external resistors plus power in r.
When analysing an AC circuit or a transformer, the candidate uses peak voltage and peak current in the power formula P = VI as if they were RMS values, or uses the turns ratio on voltages but then applies the same ratio to power, claiming the transformer increases power.
The RMS concept is introduced at Level 3 and candidates see V and I in the same formula they used at Level 2, so they assume the values are interchangeable. The transformer 'steps up voltage, so it must step up power' intuition is superficially plausible and is not corrected unless the candidate has explicitly reasoned about energy conservation.
What to do instead
Write 'V_rms = V_peak / sqrt(2)' at the top of every AC question and label every given value as peak or RMS before substituting. For transformers, state the conservation line first: 'ideal transformer: P_in = P_out, so V_p I_p = V_s I_s', then derive that voltage and current ratios are inverse. Check any answer by confirming that power out is less than or equal to power in.
In a nuclear physics question, the candidate balances mass number but not atomic number (or vice versa) when writing a decay or fission equation, or writes a beta-minus decay without an antineutrino and a beta-plus decay without a neutrino.
Candidates focus on the visually obvious mass number and treat the atomic number as bookkeeping. The neutrino is a relatively recent addition to the Level 3 curriculum and is easily forgotten because it carries no charge and negligible mass, so it does not affect the numbers the candidate is used to checking.
What to do instead
For every nuclear equation, write two tally lines underneath: 'A: left = right' and 'Z: left = right', and tick both before moving on. Memorise the three decay templates explicitly, including the neutrino: alpha (A-4, Z-2), beta-minus (Z+1, plus antineutrino), beta-plus (Z-1, plus neutrino), gamma (no change in A or Z). Practise by classifying a given equation as alpha, beta-minus, beta-plus or gamma from the changes alone.
When asked about the photoelectric effect or atomic spectra, the candidate explains that brighter light gives photoelectrons more energy, or that the threshold frequency can be overcome by increasing intensity, instead of increasing frequency.
The wave model of light is intuitive and candidates carry over the classical idea that more intense light means more energy per electron. The photon model requires the counter-intuitive step that energy per photon depends only on frequency, and this is exactly the conceptual shift the standard is testing.
What to do instead
Write the photon equation E = hf at the top of the answer and state in words 'intensity controls the number of photons per second; frequency controls the energy per photon'. For the photoelectric effect, use E_k(max) = hf - phi and show that increasing intensity at fixed f cannot change E_k(max). For spectra, link each line to a specific transition and state whether a photon is absorbed or emitted and why the line energy equals the difference between levels.
The candidate writes a numerical answer with no unit, the wrong unit, or an inappropriate number of significant figures (e.g. quoting 9.80665 m s^-2 from a calculator display when the data were given to two significant figures), and does not check whether the answer is physically reasonable.
Calculator displays encourage copying all digits, and candidates have often been rewarded in earlier years for 'more precise' answers. The Level 3 schedules award marks for the correct unit and for consistency with the data's precision, and candidates do not realise that a missing unit can cost a mark even when the number is right.
What to do instead
Adopt a three-step finishing routine: (1) write the unit next to every numerical answer, including intermediate vector components; (2) round the final answer to the same number of significant figures as the least precise given value, keeping extra digits only in intermediate working; (3) run a plausibility check against a known value (e.g. a car's acceleration should be a few m s^-2, not hundreds).
In a practical investigation or data-analysis question, the candidate plots raw data without linearising, draws a line of best fit through every point including obvious outliers, and then reads a gradient without stating its units or interpreting its physical meaning.
Candidates are used to plotting y against x and reading a gradient, but Level 3 requires them to choose axes so that the relationship is linear (e.g. T^2 against L for a pendulum, or 1/v against 1/u for a lens) and to link the gradient and intercept to physical constants. The interpretation step is the one most often omitted because it requires a sentence of reasoning rather than a number.
What to do instead
Before plotting, write the theoretical relationship in the form y = mx + c and identify what to plot on each axis so that the graph is a straight line. Draw the line of best fit by eye with points balanced above and below, and note any point excluded as an outlier with a reason. After finding the gradient, write 'gradient = ... with units ... which corresponds to ...' and link it explicitly to the constant in the theoretical equation.