How to Study for NCEA Physics Externals (Level 2 and 3)

Most students who struggle in NCEA physics can rearrange a formula. What they can't do is say which formula, and why. They open the formula sheet, scan for something with the right letters in it, substitute, and hope. Sometimes it works. In a Merit or Excellence question it almost never does, because those questions are testing whether you understand the situation, and the formula is just the last step.

Physics externals reward a specific way of working: state the principle, choose the relationship that follows from it, substitute with units, and when the question says "explain", explain in words. This guide covers what the Level 2 and 3 papers test, the habits that cost the most marks, a 4-week retrieval routine, and two worked examples.

What the physics externals actually test

Which papers you sit depends on your school's course, so confirm with your teacher and check the timetable on NZQA's NCEA site. Broadly, the externally assessed content sits in three strands at Level 2, with Level 3 extending each one.

Level 2:

• Mechanics. Motion with constant acceleration, projectiles, circular motion, forces, momentum and impulse, work, energy and power, and objects in equilibrium.
• Waves. Reflection, refraction, diffraction and interference. Lenses and mirrors, including ray diagrams. Standing waves and the relationship between wavelength, frequency and speed.
• Electricity and magnetism. Circuits (series, parallel, resistance, power), electric fields, magnetic fields and the forces they exert on moving charges and current-carrying wires, and electromagnetic induction.

Level 3:

• Mechanics. Circular motion in harder settings (banked corners, vertical circles), gravitation and satellites, rotational motion with torque and angular momentum, and simple harmonic motion.
• Waves. Doppler effect, beats, standing waves in strings and pipes, and interference and diffraction with two slits and gratings.
• Electricity. DC circuits with capacitors and inductors, and AC circuits with the phase relationships between voltage and current.

Some Level 3 courses also cover modern physics (atomic models, the photoelectric effect, nuclear processes). Which parts of your course are external and which are internal varies, so check with your teacher rather than assuming.

Within every strand, questions come in three shapes. Calculate: a number, with working and units. Explain: a paragraph of physics in words, sometimes with a diagram. Describe and calculate: the Excellence pattern, where you have to explain what's happening before you can pick the right relationship. That third shape is where most of the grade separation happens.

Where the marks are lost

The first and fifth rows are the same problem in two costumes: treating physics as formula-matching. The fix is the habit that runs through the rest of this guide: say the physics before you write the maths.

The four-line habit that fixes most of it

Every calculation, however short, gets this structure. It takes ten extra seconds and it protects you from almost every row in that table.

1. Principle. One phrase stating the physics. "Energy is conserved, ignoring air resistance." "Horizontal velocity is constant because there is no horizontal force." "Net force provides the centripetal force."
2. Relationship. The formula that follows from the principle, in symbols, before any numbers.
3. Substitution with units. Every number carries its unit. Convert first if you need to. This is where the marker sees your method even if the arithmetic goes wrong.
4. Answer with units, and direction if it's a vector. Round to match the data in the question, usually two or three significant figures. Then a one-line sanity check: is the size plausible?

The principle line is the one students skip, and the one that stops formula-hunting. If you can't write a principle, you don't yet know why the formula applies.

Explain questions: words first, formula second

When a question says "explain", the marker is looking for a chain of physical reasoning in words. A formula can be part of the chain, but it can't be the whole chain. "Because F = ma" is not an explanation. It's the name of one.

A structure that works for almost every physics explain question:

• What is happening physically. Name the quantities involved and say what's changing.
• The principle that governs it. Newton's second law, conservation of momentum, the wave model, the field.
• The consequence, in words. Link the principle to the thing the question asked about.
• The formula, if it helps. As support, showing the relationship you've just described in words.

For how markers separate Achieved, Merit and Excellence in written science answers, see what examiners look for at each grade. In physics the pattern is: Achieved names the right idea, Merit links it to the situation, Excellence links it fully, deals with every part of the question, and states any assumptions.

The 4-week routine

This assumes four to five sessions a week of about 45 minutes. If physics is one of several externals, the 8-week NCEA plan shows how it fits alongside the others. The whole routine is retrieval-based: you learn physics by producing answers from a blank page, then checking, not by reading solutions. The evidence for that is in practice beats re-reading, and it applies to physics with particular force because the exam never asks you to recognise anything.

Week 1: find out what you can't do

• Sit one practice paper for each physics external, timed, closed book. Use the formula sheet you'll have in the exam, nothing else.
• Mark it against the schedule. For every lost mark, note the topic and which of three things went wrong: wrong physics, right physics but a slip (units, conversion, direction, rounding), or no attempt.
• Sort topics into solid, shaky, missing. Notice whether your slips outnumber your physics errors.

Week 2: missing topics, from principles

• Take the biggest missing topic. Read your notes on it once. Close them. On a blank page, write down every principle you can remember for that topic, in words, and the relationship that follows from each. Compare against the notes and fill gaps in a different colour.
• Then five questions on that topic, cold, using the four-line habit on every one. Check after each. Write one line next to each mistake.
• Two days later, redo two of those questions without looking at anything first. This is spaced repetition and it's what keeps the topic from evaporating by the following week.
• Alternate two missing topics across the week.

Week 3: shaky topics, and mixing

• Same routine for the shaky pile.
• Start mixing. A projectile question, then a circuit, then a wave. The exam doesn't group by topic, and switching between topics is exactly the skill you need.
• Every session ends with one explain question written in full, in words, under a rough time limit. Mark it against the schedule and count the links in your chain.
• If slips were your main problem in Week 1, add a units-and-conversion pass to every question: circle every number, check its unit, before you substitute.

Week 4: whole papers

• Two timed papers, one at the start of the week and one at the end. Mark both properly. How to use past papers properly covers how to get the most from the marking.
• Between them, go back to whatever the first paper exposed.
• Last two days: no new content. Redo your five worst questions from the month, cold. Run the four-line habit on each one until you can do it without thinking about it.

Two worked examples

Example A: a projectile calculation

A ball rolls off a horizontal cliff top at 12 m s⁻¹. The cliff is 20 m high. Ignoring air resistance, calculate how far from the base of the cliff the ball lands. Take g = 9.8 m s⁻².

A common weak answer:

v² = u² + 2ad
v² = 12² + 2 × 9.8 × 20 = 536
v = 23.2 m

This is formula-hunting. The student saw a speed, an acceleration and a distance, found an equation containing all three, and used it. But that equation applies to motion in one direction, and the ball's horizontal speed and vertical fall are separate motions. The answer is a speed labelled as a distance, and it earns nothing.

Full-marks working:

Horizontal and vertical motion are independent.
Vertically: the ball starts with zero vertical velocity and
accelerates downward at g. Horizontally: no force acts
(air resistance ignored), so horizontal velocity is constant.

Vertical, to find the time in the air:
d = ut + ½at²          with u = 0
20 m = ½ × 9.8 m s⁻² × t²
t² = 20 ÷ 4.9 = 4.08 s²
t = 2.02 s

Horizontal, using that time:
d = vt
  = 12 m s⁻¹ × 2.02 s
  = 24.2 m

The ball lands about 24 m from the base of the cliff.

Check: 24 m is a plausible distance for something moving at 12 m s⁻¹ for about two seconds. Two significant figures matches the data given. The two lines of principle at the top are what earn the method credit, and they're also what stopped the student reaching for the wrong equation.

Example B: an explain question on circular motion

A ball on a string is swung in a horizontal circle at constant speed. Explain why the ball is accelerating even though its speed is not changing.

A weak answer:

It is accelerating because it has centripetal acceleration, a = v²/r, and the string provides the centripetal force.

Everything in that sentence is true, and it would earn very little. It names the answer without explaining it. The formula is doing the work the words are supposed to do.

What the examiner wanted:

Velocity is a vector: it has both magnitude (speed) and direction. Acceleration is the rate of change of velocity, so a change in either speed or direction is an acceleration. The ball's speed is constant, but its direction of motion is changing continuously as it moves around the circle. So its velocity is changing, and it is accelerating.

The direction of this acceleration is towards the centre of the circle, because that is the direction in which the velocity is changing (the velocity is always tangential, and the change in velocity between two nearby points on the circle points inward). By Newton's second law, an acceleration towards the centre requires a net force towards the centre. Here that force is the tension in the string. This centripetal force does not change the ball's speed, because it acts at right angles to the velocity, but it continuously changes the ball's direction, keeping it moving in a circle. The size of the acceleration is given by a = v²/r.

Count the links: velocity is a vector, acceleration is change in velocity, direction is changing, so velocity is changing, so there is acceleration; then where it points, why it points there, what force provides it, and why that force changes direction without changing speed. The formula appears once, at the end, as a supporting detail. That's the ratio the marker is looking for.

Questions students ask

Do I need to memorise formulas if there's a formula sheet? You need to know what's on it well enough to know which one applies without hunting. The sheet gives you the relationships. It doesn't tell you which principle each one belongs to, and that's what the exam tests. Practising the four-line habit builds that map.

How do I handle direction in momentum questions? Choose a positive direction before you write anything, state it ("taking right as positive"), and give every velocity a sign. A negative answer then means "moving left", not "I made a mistake". Most collision errors come from skipping this step.

How much should I write for an explain question? Enough to complete the chain: what's happening, the principle, the consequence, and any assumption. Usually four to seven sentences. If you're writing much more, you've probably repeated a point or wandered into a different question.

Is Level 3 physics much harder than Level 2? The maths steps up (vectors, radians, more rearranging) and there are more places for slips. But the way marks are earned is the same: principle, relationship, substitution with units, answer, and explanations in words. If that habit is solid at Level 2, Level 3 is mostly new content on a familiar method.

What to do today

Take one calculation and one explain question from a topic you're not sure of. Do the calculation with all four lines, including a written principle at the top. Write the explain answer in words, then count the links. Mark both honestly. Thirty minutes, and you'll know whether your problem is physics, slips or writing.